602. uclapolisci - March 14, 1999 - 8:28 AM PT
Axelrod, et al.'s problem was indeed to find out how many cooperators it took to sustain cooperation (among other things), and I think his game is assisted, rather WOULD be assisted by programming in some of that Macy fellow's algortihms on critical mass. That change would move the analysis from "how many to sustain" to "how many to start". Although the system needn't be cooperative. We could then model "how many to disrupt" (i.e. revolutions). Topographical patterns matter, too, and so we can model where the players are and whether having a cluster or a group of cells matters to the invasion. The Army played that game with tanks and found out that there are real advantages to having the program figure out the proper distribution of artillery.
-JWE
PS I agree with John Searle that "mind is not a computer program", but the computer helps figure out the brute force-qualities of ideas in opposition to each other - since there DOES seem to be a regular decision calculus in place. Heck, nobody really knows (let's all be good scientists and all that), but the research has been promising to date. We've come a long way since Von Neumann and Morgenstern.
603. uzmakk - March 14, 1999 - 8:58 AM PT
Cool, polsci. Allow me to toddle along with you and Slackjaw while you work things out. You know that Pseudo has gone on vacation?
604. uclapolisci - March 14, 1999 - 9:07 AM PT
I'll miss Pseudo like I miss rattlesnakes on the road... sometimes I back up to make sure I get 'em. I said that just for shits and grins.
-JWE
605. AzureNW - March 14, 1999 - 10:54 AM PT
Oh boy, more game theory stuff. I would enjoy an organized book reading on this subject, if there is a good, accessible overview available to cover the basics.
606. AzureNW - March 14, 1999 - 11:03 AM PT
It would provide a refreshing alternative to this kind of thing, another modern application of logical elements of philosophy.
Common Information Model (CIM)
607. pellenilsson - March 14, 1999 - 1:13 PM PT
uclapolisci
Contrived posture. Contrived language. Shallowness in disguise.
Thank God for the Down Arrow!
608. Slackjaw - March 14, 1999 - 1:55 PM PT
Jonathan: "it's just a matter of finding an interaction algorithm." I presume you mean game form?
On that presumption, yes, I agree. But it seems to me that a better story than anything like the PD is an n-player generalization of either Battle of the Sexes or Stag Hunt. I cannot seem to fit ideological change into PD, but ranked coordination seems to work alright.
Your problem seems similar to one of agenda setting in national policy making, which would be very cool if done well computationally. I have recently read some stuff (John Kingdon) that looked at modeling the "behavior" of the whole policy "system," which was not very impressive. No wonder Simon & friends got so riled up in the '50s! "Is the policy process as a whole rational?" hahahaha. Why would it be? But I digress.
"my evolving problem...is how to change the value of payoffs throughout the game to signal the invasion of new normative structures - or, people changing their minds on what's valuable." Do you mean "signal" in the game-theoretic sense? If so, what are the payoff relevant actions? (This is sounding less and less like a PD.)
"Other recognition...There's some players that other players simply won't play with, and in fact prefer to kill..." Perhaps I don't understand you, but "playing" implies nothing more than mutual payoff dependence. A dictator may prefer the insurgent dead, but they still live in mutual payoff dependece--if the latter gets enough people to sign on to the revolution, that will certainly affect the former's optimal strategy. That, incidentally, sounds a lot like n-player Battle of the Sexes.
609. Slackjaw - March 14, 1999 - 1:56 PM PT
"I am not interested as much in finding out equilibria in a one game setting as I am in finding out what happens when many different players play against each other repeatedly over time." You make it sound like there's no such thing as repeated game theory. "Very large number of them" indeed! How does infinity sound?
Yes, a computer allows you to examine a huge number of iterations. Why is that valuable? Why is Axelrod more valuable than the various folk theorems?
610. Slackjaw - March 14, 1999 - 1:56 PM PT
Azure: I would gladly host a reading thread on a game theory book, but I fear it would just be you and me in it. Don't know if Irv will go for it. I can recommend some books if you like.
Uzmakk: re. "free riding"--think of a public project, like clean air or national defense. These are goods whose benefits you enjoy regardless of your contribution to the cost of providing them. Suppose we lived in a city trying to decide whether to finance such a project, and we only want to do so if the benefits to the citizens outweigh the cost of the project. Well, we can have the pointy headed bureaucrats tell us the cost--but what is the benefit?
Pretend for a minute that every citizen knew exactly what the project was worth to himself. But this is private information--nobody else really knows it. So what if we just asked people to bring their check books to city hall and announce their benefit from the project, and then write a check for that amount? Well suppose you expected everyone else's declared benefit to cover the cost. Then if you understate your benefit, you pay less but get exactly the same benefit from the project.
That's free riding. It is one of a few fundamental ideas in social science.
I know nothing of Stafford Beer & Allende.
611. Slackjaw - March 14, 1999 - 1:57 PM PT
That's AN EXAMPLE OF free riding. For pure public goods at that.
612. Slackjaw - March 14, 1999 - 2:02 PM PT
The cool part, imo, is designing taxation schemes, in ignorance of the individuals' information, so that it is in everyone's best interest to reveal their private information. That's implementation theory (part of information economics), of which auction design (mentioned above re. John Nash) is a special case. (The seller wants to know how much the buyers value the good, but that is private information.)
It's one of those things that are just fascinating--almost like magic really. Like econometric models for selection bias.
613. Slackjaw - March 14, 1999 - 2:12 PM PT
Incidentally, game theory and economic analysis more generally have been making inroads in philosophy for decades, since _A Theory of Justice_ by John Rawls leaned on analytic specifications of preference and the maximin decision criterion to arrive at a notion of justice--that which advantages the least well off. How did he get to this point? It's what the people in his world would have unanimously agreed to behind the "veil of ignorance"--before they discovered their particular alottments of society's trappings.
The general idea is to use game theory to analyze various social structures--the outcomes the structures lead to. Then decide how a group of goal seeking people likes those various structures.
A fascinating recent book on this general topic, and critical of Rawls, is _Game Theory and the Social Contract_ by Ken Binmore (I refer to vol. I--vol. II has recently come out but I haven't read it yet). Binmore examines a heap of ideas from political philosophy using a game theoretic perspective.
Requires some mathematical facility, but not much specific knowledge of game theory. Well worth the effort--one of the most enjoyable books I've read.
614. uzmakk - March 14, 1999 - 6:09 PM PT
Slackjaw, Message #610::
And me, Slackjaw, and me. What am I? Chopped liver?
615. uzmakk - March 14, 1999 - 6:18 PM PT
Pelle,Message #607:
I am not sure . It is conceivable that these game theory chaps are really saying something. An analogy would be you and I listening to two biochemists talking about their latest experiments with neuro inhibitors. It would be babble to you and me(unless you, Pelle, are a biochemist). But the fact is that the incomprehensible babble is communication between those who can speak it, and, MOST IMPORTANTLY, allows those who speak it some measure of manipulation and control of the "universe" that they are "describing".
616. Slackjaw - March 15, 1999 - 12:08 AM PT
oh, sorry. And Uzmakk of the Steppe too. Well, that's three, which gives us something between a couple and a horde or throng. Again, I'd be glad to recommend books, and talk about some background, finer issues or points of confusion from time to time, but it seems better just to invade another thread occassionally with it than create a new one. It just doesn't seem like the kind of thread conducive to frayesque discussion.
I'm trying to imagine JadeGold and JJBiener arguing about the restrictions on beliefs off the path of play in perfect Bayesian vs. sequential equilibrium, and it just isn't working.
617. uzmakk - March 15, 1999 - 7:22 AM PT
Sounds like a good deal to me, Slackjaw.
618. uclapolisci - March 15, 1999 - 10:05 AM PT
I hate to keep adding terms, Slack, because it makes me feel like I'm the Wizard of Oz ("Pay no attention to that man behind the curtain!!!"), but the point about running games (and here is why I sidestepped the matter of whether Stag Hunt, or PD, or whatever is better) on a computer is because it turns out that there are some kinds of behavior that are emergent phenomena. In other words, while we think we know the possible/probable results as a function of the rules, some things happen that we wouldn't otherwise intuit from the initial conditions.
NOW I've gone full circle back to where this all started (by the way, Peon, you' still got nothin'). Since the initial conditions seem to produce (reference John Holland, Chris Langton) emergent phenomena, how do we derive the philosophical nature of cause? (Hume gave us the idea that there's a set of causes, and nothing more meaningful can be said, but I'm still trying) My question on this thread has always been this: if initial conditions are responsible for subsequent resultans (non-controversial to the extreme), then how do we define those conditions such that we're left with a meaningful description of causation? Even on a computer, the ultimate deterministic calculator (garbage in, garbage out, unless you're Peon, et alia, where it's garbage out regardless), it's hard to figure out (colloquially) "How'd THAT happen?!"
Slack writes: "Is the policy process as a whole rational?" hahahaha. Why would it be? But I digress.
You've hit the nail on the head here in passing... what seems non-rational might still be rational, if we allow rational to mean "following logically from initial conditions". I was going on about that earlier, when I said that what seems mystical or non-rational is really just a complex problem looking for a computational solution. I highly recommend "Emergence" by John Holland as a primer on this idea.
619. uclapolisci - March 15, 1999 - 10:22 AM PT
Slack: We've got a bunch of the Binmore texts here at UCLA, but I had to recall the one you mentioned, so I'll have it read by April Fool's Day (which reminds me of my least favorite two Frayers...). The abstracts on his work look really good. Thanks for the recommendation.
A professor here, Richard Rosecrans, is fond of remarking that "People of differing epistemological constitutions typically tend toward talking past and bewildering one another". Well, ain't that the truth, but at least there are some (you, Uzmakk) who stay the course (me, too).
620. uclapolisci - March 15, 1999 - 10:27 AM PT
Footnoting myself in Message #618, I think what I am saying is this: given that emergent phenomena described by Holland exist in any complex process, there seems to be a causative dysjuncture. I am trying to find a philosophical basis for describing the orderly sequence of results from conditions, EVEN WHEN THE INITIAL CONDITIONS ARE RECOGNIZED TO PRODUCE NON-LINEARITIES.
621. PSEUDOERASMUS - March 15, 1999 - 10:58 AM PT
Wow, Uclapolisci, such hostility and bitterness because I called you a flake? But the last dozen or so messages show that you're not the flake I initially took you for. I mistook your "collapse of the Soviet Union in the error term" as typical of some of the political scientism types I've met. Plus, your prose at first gave the impression of verbatim translations from Sumerian cuneiform. So I apologise for my snide tone at the beginning.
In Message #582 you chided me: "If I put the emphasis on 'causes' and then ask a question 'what causes alignment', your...intellect should look beyond its knee-jerk response to ask the insightful question - perhaps, 'what conditions produce mutual interests such that alignment is a fit response?' " But how is that an insightful question??? Any number of obvious answers come to mind: geography, economic advantages, shared norms & culture, stragetic advantage, etc. But I suspect, given your interest in computation and simulation, that you're looking for higher-order explanations than "mutual interests". But what on earth for? What problem in theory or in the real world requires it? What use is an explanation at the level of universal algorithms if I'm trying to better understand, say, why Italy switched sides in 1915?
Don't get me wrong. I don't mind explanations at the level of universal algorithms which ignore history or culture. (After all, that's partly the point of social science, as opposed to history.) For example, Jared Diamond asks in "Guns, Germs and Steel" the naive counterfactual question: why did the Europeans conquer the New World but not vice versa? (See the reading thread for the answer.) Or, as Ronald Coase once asked, "why does the firm exist?" (The answer: to minimise transaction costs.) Try out Coase's question on a historian and you tend to be greeted with total indifference, or sometimes with a violent response accompanied b
622. PSEUDOERASMUS - March 15, 1999 - 10:59 AM PT
....with a violent response accompanied by accusations of ahistorical deductivism. (I know this firsthand.)
Or to take an example from my own field: in the late 1970s and early 1980s, economists were forced to ask a question we had all thought well enough answered by David Ricardo in the early 19th century: why does international trade exist? This was not some idle speculation for the hell of it. It got asked because of the growing acknowledgment that Ricardo's answer (comparative advantage) failed to explain the direction and content of most international trade that actually takes place in the world.
The three questions, from Diamond, Coase and trade theory, are germane to addressing either real-world issues or pressing questions in scholarship. But I detect neither relevance nor insight in your higher-order question about national alignments. Don't take this comment as criticism. It's a request for information. What's the payoff in asking the question?
623. PSEUDOERASMUS - March 15, 1999 - 11:15 AM PT
Your Message #618 and Message #620 are still leaving me cold. In other words, elaborate in order to make us share your wonder.
"...while we think we know the possible/probable results as a function of the rules, some things happen that we wouldn't otherwise intuit from the initial conditions."
"Since the initial conditions seem to produce...emergent phenomena, how do we derive the philosophical nature of cause?"
Aren't you stuck in the rut of believing that determinism and causality require the ability to predict the final conditions from the initial conditions? Roger Penrose successfully disposed of that problem by illustrating a model which is both deterministic and noncomputable. (And noncomputability certainly places roadblocks to prediction.)
You've read Schelling's "Micro Motives and Macro Behaviour", yes? I've always been struck by his model of residential segregation. He uses a chessboard with #'s and O's to represent agents of different races, with simple but well-defined preferences about race, e.g., "I don't mind having neighbours of a different race, as long as I'm not totally surrounded by people of a different race". So any # surrounded by O's will move until he's not surrounded. Such preferences are consistent with a racially integrated chessboard/neighbourhood, i.e., racial integration can be an equilibrium.
Yet it turns out that slight perturbations in the initial well-integrated pattern can ignite a series of moves whose final outcome is complete segregation. This is surely an emergent phenomenon of a simple algorithm, with well defined initial conditions but surprising final conditions.
But what interesting philosophical implications are there for causality in such a phenomenon? I just don't see it. Please enlighten me.
624. uzmakk - March 15, 1999 - 11:19 AM PT
Which do you think is more "productive" pseudo. A" disinterested "search for knowledge, or one motivated by "pay-off". Which do you think is more fun? Which do you think draws from a wider perspective?
625. PSEUDOERASMUS - March 15, 1999 - 11:21 AM PT
Uzmakk: When I say "payoff" I don't mean financial or other worldly payoff, as should have been obvious from my comment.
626. PSEUDOERASMUS - March 15, 1999 - 11:23 AM PT
Well I must get offline now. Just checked in briefly. I will return on Sunday.
627. uzmakk - March 15, 1999 - 11:25 AM PT
What then? A completely theortical pay off?
628. PSEUDOERASMUS - March 15, 1999 - 11:25 AM PT
Scratch the mention of Schelling. Bad example, I just realised.
629. uclapolisci - March 15, 1999 - 12:03 PM PT
Excellently well said, Pseudoerasmus, and I shall also recant of my prior opinion of you as a mere dilettante. With my recommended daily rapprochement out of the way, I can answer your question in Seinfeld-esque manner.
As an aside, I wrote a variation of Anatol Rappaport's famous TIT FOR TAT program (again, see Axelrod/Cohen) just for fun. I called it WAY MORE TIT FOR TAT, which is probably only funny if you write programs on the side... Rest assured it's not a dirty joke - only an insight to my behavior under fire.
Now the answer: practically speaking, my (the) arguments you reference regarding cause/predicition/etc., are all worthwhile avenues of research insofar as they provide a "probable worlds" kind of analysis, but the trouble has been specifying models that don't wind up (after Sturm und Drang) producing little over the level of truism. I just read a great treatment of the truth values of possible worlds by Maria Luisa Dalla Chiara, in a text including (coincidentally enough) Ken Binmore and edited by her and Cristina Bicchieri. For instance, predicting that the USSR "could fall" isn't really helpful unless we have a decent shot at defining the conditions under which it may happen.
Which fast-forwards the argument to my remark in Message #620. As I said before, questions about alignment, etc., are (kind of) red herrings to the issue at hand. So I don't intend to dodge your question about alignments, but rather I intend to point out that I am trying to get at the same kind of question that you point out has been asked before when you write...
This was not some idle speculation for the hell of it. It got asked because of the growing acknowledgment that Ricardo's answer (comparative advantage) failed to explain the direction and content of most international trade that actually takes place in the world.
...
630. uclapolisci - March 15, 1999 - 12:07 PM PT
My personal interest is indeed in answering questions like, "Why is there international cooperation?" And on the surface that doesn't sound like much (which is why some would say "mutual interest" and leave it at that). But other questions that have the same philosophical morass beneath them offer an interesting research opportunity. Brian Arthur's work, for instance - something closer to your intellectual home - goes at the philosophical basis of cooperative behavior (sorry to assert these things... I gotta go ski this afternoon, so I'll derive the argument later if you like). Or take Robert M. Solow's essay in "Choice, Welfare, and Development: a Festschrift in Honor of Amartya K. Sen", where he calls for a theory "of the dynamics of social norms: their emergence, evolution, solidification, and/or decay". He goes on to remark that a good theory is one that can produce a lot implications from a few plausible assumptions. Now THAT's the kind of thinking that gets me interested. And I believe that my efforts answer your question as stated:
But what on earth for? What problem in theory or in the real world requires it? What use is an explanation at the level of universal algorithms if I'm trying to better understand, say, why Italy switched sides in 1915?
Unless I have perpetrated one of famous internal leaps of logic, then I hope to have made a decent address of your question (regarding why I would be trying to ask second order questions such as I have described them). If there are emergent properties (referring again to Holland from Message #620) inherent in any complex system, then we should set about trying to find out how to rationalize them, their emergence, etc.
...
631. uclapolisci - March 15, 1999 - 12:08 PM PT
It follows then (as Hume pointed out, Reason follows Passion - or rather, axioms follow from observations), that we should also exert a philosophical effort to solve what I believe is a causative dysjuncture of prior conditions leading to non-linear results. Holy shit, I actually finished on a major theme.
-JWE
PS "Seinfeld-esque" indicated my intention to use the phrase "yahda yahda yahda". It was actually Yossarian who popularized that phrase, nevertheless I found no opportunity to yahda yahda.
632. uclapolisci - March 15, 1999 - 12:11 PM PT
Rats, Pseudo and I simul-posted and I am going skiing. Until later then.
-JWE
633. pellenilsson - March 15, 1999 - 12:15 PM PT
uclapolisci
You're doing better now. But could you please cut the excessive, coqeutteishe verbiage?
634. uclapolisci - March 15, 1999 - 12:24 PM PT
Quickly and then I go... VO2-Max is calling.
Penrose constructed a Haas-ian "problematique", which had he decomposed it could have been modeled well enough.
And I have myself identified an internal leap of logic... Ricardo was about making for a better explanation, which is why questions about initial conditions and results is interesting and, I think, necessary.
For you to write as follows convinces me that we are talking past each other at the moment:
Yet it turns out that slight perturbations in the initial well-integrated pattern can ignite a series of moves whose final outcome is complete segregation. This is surely an emergent phenomenon of a simple algorithm, with well defined initial conditions but surprising final conditions. But what interesting philosophical implications are there for causality in such a phenomenon? I just don't see it. Please enlighten me.
Read the Solow essay I referenced for an (I am guessing he is an) economist's view on these things. If that one makes sense, then we'll be on common ground.
-JWE
635. uclapolisci - March 15, 1999 - 12:26 PM PT
I am excessive and coquettish. Deal. Or more prosaically, "I contain multitudes".
And the challenge still stands, Peon. Try a real academic argument ("c'mon, sweetie, I promise, it won't hurt a bit...").
-JWE
636. pellenilsson - March 15, 1999 - 12:46 PM PT
uclapolisci
What is the meaning of life?
637. uzmakk - March 15, 1999 - 1:55 PM PT
What is the meaning of meaning?
638. uzmakk - March 15, 1999 - 1:57 PM PT
Polisci:
You are a young and arrogant twerp. I like you very much.
639. Jenerator - March 15, 1999 - 3:02 PM PT
I like Bruins.
"Yet it turns out that slight perturbations in the initial
well-integrated pattern can ignite a series of moves whose final
outcome is complete segregation. This is surely an emergent
phenomenon of a simple algorithm, with well defined initial
conditions but surprising final conditions. But what interesting
philosophical implications are there for causality in such a
phenomenon? I just don't see it."
Isn't there a simpler way of saying this?
640. uclapolisci - March 15, 1999 - 5:17 PM PT
Peon. I refer you to the eminent Douglas Adams (perhaps Addams, I forget) for the answer to your question.
-JWE
641. JJBiener - March 15, 1999 - 8:24 PM PT
Slacker - "I'm trying to imagine JadeGold and JJBiener arguing about the restrictions on beliefs off the path of play in perfect Bayesian vs. sequential equilibrium, and it just isn't working."
They say the only thing worse than being talked about is not being talked about. Don't worry, I take no offense at your comments. Actually, you are quite accurate. I would never engage in a discussion about game theory or anything similar. It bores me to tears. Jade, however, has some unusual interests, so she might be up for it. Whatever you do, don't restrict your discussions to those things I would participate in. I don't get involved in most discussions even in subjects that interest me. I wouldn't even be in this thread except I was told that I was mentioned.
So go ahead and do your thread. I think you will have enough interest for a decent discussion.
642. Raskolnikov - March 15, 1999 - 9:11 PM PT
Slack: You have shown a lot of ability in making game theory fun and informative before, and have gotten a lot of involvement when you present and describe the usefulness of specific games. I think that if you described game theory solely on the abstract mathematical level, all but a few Fraygrants' eyes would glaze over. But if you stuck to the broad concepts, the often counter-intuitive solutions, and their wide application in areas ranging from telecommunications policy to evolutionary biology, you could get a lively discussion going.
643. Slackjaw - March 16, 1999 - 3:14 AM PT
Jonathan,
"but the point about running games (and here is why I sidestepped the matter of whether Stag Hunt, or PD, or whatever is better) on a computer is because it turns out that there are some kinds of behavior that are emergent phenomena." So? You still need some structure to put into the thing. Axelrod gets nothing without starting with the PD (and you might say he didn't get much even with that structure!). What are these critters doing, as they go around and flip each others' color bits? It can't all be emergent. Ultimately, you still need a story.
My question shouldn't have been, why computational?, but instead, why Axelrodian? I have not yet read his "new" book, but why was Evolution of Coop. best done by computer? I agree, some things are--when you have local interactions, global regularities, etc. That is an area where the computational method is uniquely well suited, and that's how it will make inroads in social science. (You heard it here first.) EoC doesn't seem special in that way. Is Axelrod's more recent stuff? Again, why is *Axelrod* more valuable than folk theorems, not why is *computational* valuable in addition.
(Incidentally, I don't exactly know why, but I am not that impressed with EoC, perhaps because of all the confusion is engendered.
Quiz: tit for tat
___ is evolutionarily stable in the infinitely repeated PD
___ is subgame perfect in the infinitely repeated PD
___ "Won out" in Robert Axelrod's evolutionary simulation
_X_ None of the above)
'what seems non-rational might still be rational, if we allow rational to mean "following logically from initial conditions".' But of course that isn't what I meant, nor what Simon & co. meant, nor what most social scientists mean by the term rational. Best pick another term.
Haven't gotten around to the Holland book yet, but I intend to.
644. Slackjaw - March 16, 1999 - 3:14 AM PT
hahahaha Rask, that was very diplomatic of you. Perhaps elliot will come by and give a translation. I'm afraid it wouldn't be a very useful thread unless participants actually went through a book on the subject, a prospect that would be unattractive to most and not really useful in the fray. Instead, I shall continue my usual practice of hijacking threads from time to time.
JJ: I'm glad you weren't offended, because I certainly didn't mean that offensively. "It bores me to tears." Oh, see, you need the thread most of all. I promise it would fascinate you! But alas, it is a nonthread.
645. wexxford1 - March 16, 1999 - 4:52 AM PT
Reason the philosophy folks are missing ? They're involved in people's capitalism .All hands are to the scriptwriting pumps for Madison Avenue nonsense.Heck, remember the Amurrican Nobel prizewinners who gave their all for Long Term Capital--the outfit that lost $1 trillion one morning trading Russian bonds and other ephemera ? They disappeared from the radar screen , too, when the orders came down from on high . When Madison Avenue says :" Bring on dem philosophers" on they will charge with their comedic lines for your personal enjoyment . Don't thank me folks . Jest trying to help you Amurricans get through the people's capitalism thingy .
646. uclapolisci - March 16, 1999 - 8:46 AM PT
Slack... first an internal dialogue... some things I hear and they don't stick. Others, they stick, but for superficial reasons. Some stick, and I won't know why for a while - until my conscious mind lets it out of my pre-conscious. This is all psycho-babble, I know, but it's how I explain the creative process to myself. What you said falls into that last category. My pre-conscious is screaming at me to pay attention, but I don't yet have the reason in the forefront of my mind.
Tell me where I can get up to speed on folk theorems, because I admit to not knowing what you're talking about when you use that term.
-JWE
647. uclapolisci - March 16, 1999 - 8:52 AM PT
Wexx... I love it! To quote a fictional character I know, "It's just life... We all get through it."
-JWE
PS I was a (gasp) stockbroker when LTC did its Houdini. What a riot!
648. uclapolisci - March 16, 1999 - 9:18 AM PT
Slack: Folk Theorem... I think the crux of our coversation turns on the definition of the folk theroem as regards the conditional "if players discount the future sufficiently little, there exists a Nash Equilibrium of the infinitely repeated game where, for all i, player i's average payoff is v-sub-i".
My point on this is that the folk theorem does not sufficiently account for the perpetual novelty that Holland argues will obtain in complex systems. Discounting doesn't work so well when the players can't tell what the future payoffs will be for their present behavior, and I'm trying to build empirical cases where I think this can be shown. Any situation where social, national, or institutional boundaries are in flux - for instance Central Africa and Central Europe and Central America (it's bad to be Central??? That's just a joke...) - offer some insight into what it means to have a complex system with perpetual novelty as a dominant feature.
649. ChristinO - March 16, 1999 - 9:26 AM PT
Jen,
Hmmm.....sounds like a description of "stirring" to me. Think I'll go make a G&T and put the swizzle stick to use.
650. uclapolisci - March 16, 1999 - 10:55 AM PT
ChristinO: My sweetie's and my favorite summer drink is ginger ale (Vernor's, for those cognoscenti among us) and gin, which we call Djinn-djinns.
651. uclapolisci - March 16, 1999 - 11:00 AM PT
Slack - Follow up to Message #648: It's not so much uncertainty of what the payoffs will be, although I guess that's as precise as I am going to get "off the cuff". Rather, I think the changing nature of the payoff-producing structures is more at fault for turbulence. I am thinking of something along the lines of Ernst Haas and institutional learning as I write this, but I'm still flying in pre-conscious IFR conditions.
652. ChristinO - March 16, 1999 - 11:00 AM PT
Sounds yummy!
BTW, looking at your moniker I wondered if you are still here in LA. If so I'm hosting a SoCal Fraygrant gathering in May and would love for you and your sweetie to attend if you're available. Feel free to drop me a line at
Cocuddehy@hotmail.com
for further info.
653. uclapolisci - March 16, 1999 - 11:08 AM PT
Follow-up to Message #634: The reason even the segregation result is interesting is because the conditions did not a priori establish complete segregation as the only possible outcome. Therefore there could have been many different outcomes, only one of which was complete segregation. If anything could have happened, how does one meaningfully ascribe cause in the instance of the one thing that did?
-JWE
654. Slackjaw - March 16, 1999 - 12:25 PM PT
Jonathan,
"Discounting doesn't work so well when the players can't tell what the future payoffs will be for their present behavior, and I'm trying to build empirical cases where I think this can be shown."
I presume you mean "constant discount rates" rather than "discounting" itself, for the latter is simply an indication that people prefer payoff today to payoff tomorrow, or if you prefer is a reflection of the knowledge that they may cease to exist. Now your objection could well be leveled against constant discount rates, but doesn't necessarily spell trouble for the folk theorem. Let the discount rates bounce around all you want--just take their infimum and you have a folk theorem.
Incidentally, the "sufficiently patient" may not be very patient at all, depending on the payoffs. That just means there exists a delta* in (0,1) such that for all delta > delta*, any payoff stream better than the minimax security level can be attained. delta* need not be very big. (For a discussion of folk theorems, see Myerson, _Game Theory_, ch. 7.)
So that's what goes into a folk theorem, and we get that cooperation is a possible but by no means guaranteed outcome. It seems like rather more went into Axelrod's story, that makes it harder to make a direct connection to real world interaction, either evolutionary or purposive (but especially the latter). So the punch line is, cooperation is a possible but by no means guaranteed outcome. What helps its cause? Oh, the shadow of the future, etc. We knew that already. Axelrod's models (the "old" ones, anyway) don't rely on turbulence, emergence, etc.--the stuff that's cool about computational.
655. Slackjaw - March 16, 1999 - 12:26 PM PT
"I think the changing nature of the payoff-producing structures is more at fault for turbulence." But you make it sound as if everything can be endogenous. The distinction between individuals and institutions (one representation of which is a game form) is useful--while the latter change the former, they also take it as given day to day. It would be cool if you had a good model of game form change (or maybe dispense with the notion of game forms altogether if it's too hard to put a metric over them to describe their change), but you need a starting point.
But is that what you're trying to explain? I thought it was turbulence in ideology, or something closer to that at least.
"The reason even the segregation result is interesting is because the conditions did not a priori establish complete segregation as the only possible outcome." In your opinion, is it a necessary condition for a model to be interesting that its outcome depends on the realization of some random variable?
656. Slackjaw - March 16, 1999 - 12:33 PM PT
"Let the discount rates bounce around all you want--just take their infimum and you have a folk theorem." Things could be more complicated if players were uncertain about their or others' discount rates, but I believe you could still get something.
Incidentally, for my money, the coolest model of cooperation in a prisoners' dilemma setting was the Gang of Four (Kreps, Milgrom, Roberts & Wilson) "types" model. They used a *finitely* repeated PD (as did Axelrod, but shhhh...), where in the standard setting perpetual defection is the only subgame perfect equilibrium strategy, but included some tiny probability that a player was an "irrational" cooperator--an altruist or something who always cooperates. The (quite surprising) result is that cooperation can be sustained for a number of rounds that is independent of the horizon of the game! So you can get almost 100% cooperation in the finite PD, by making this seemingly tiny change.
657. uzmakk - March 16, 1999 - 1:16 PM PT
Goodness!!!! What DOES it mean????
658. pellenilsson - March 16, 1999 - 1:19 PM PT
Why are some postings from the ucla collective signed -JWE and some not?
659. uzmakk - March 16, 1999 - 1:19 PM PT
Forget Game Theory, forget modelling, forget the lot of it. Keep your eyes open for the up coming Folk Theorm Thread.
660. uzmakk - March 16, 1999 - 1:20 PM PT
Pelle:
You are supposed to be in bed.
661. Slackjaw - March 16, 1999 - 3:24 PM PT
hahaha uzmakk. Hate to tell you like this, but these folk theorems are part of game theory.
Message #657 you tell me what you don't follow and I'll explain it.
If you are interested, I will recommend a book on the subject approapriate for your level of intestinal fortitude and fear (or lack thereof) of mathematics
662. uzmakk - March 16, 1999 - 3:30 PM PT
Ahhhhhhh, Slackjaw. But the upcoming Folk Theorems are not. I may reread and take you up on your offer, but I am actually having too much fun right now. I thank you very sincerely for your offer.
663. uzmakk - March 17, 1999 - 3:49 AM PT
Slackjaw:
If I had the time I would take you up on your offer immediately. I would sit for three or four days and study, but those days are over. There is work, so much work. But I can't pass up your offer entirely. I am going to print out this last volley of "game theory" and see what I can make of it in my leisure over the next month. My mathematical training goes only to HS calculus, but my sister swims very strongly in the mathematical universe. She is even more busy than I am, however, but I will enlist her help if the "fascination" should sieze me.
But, to begin---- How did "folk theorems" come by the "name" "folk theorems"? The whim of some "egghead" mathemetician modelling us flesh and bone folk?
664. Slackjaw - March 17, 1999 - 4:54 AM PT
"The whim of some "egghead" mathemetician modelling us flesh and bone folk?" hahahaha, that's a great explanation. No, it's because the origins of the statement and proof (of the first theorem in the class anyway) are murky, but somehow it wound up in the "folk wisdom" of the field. Probably several people did it at conferences (though there were but a few dozen game theorists on earth at the time so they must've collectively forgotten--they had a habit of sharing each other's work and giving away publications to colleagues). Jim Friedman (no relation to Milton) actually took the trouble to publish the "original" folk theorem in the early '70s for posterity, so this is sometimes known as Friedman's folk theorem--kind of defeats the "folk" part though.
There is actually a whole class of these theorems for various types of games. They all have the same general flavor--they deal with what can be achieved in the equilibrium of an infinitely repeated game, depending on discount rates. (Folk theorems are actually not at all specific to game theory either.)
665. Slackjaw - March 17, 1999 - 4:55 AM PT
'I am going to print out this last volley of "game theory" and see what I can make of it in my leisure over the next month.'
This is such a bad way to learn anything about the subject that it's saddening to see someone's interest wasted on it, though I certainly understand the time constraint.
At least get yourself a copy of _Thinking Strategically_ by Avinash Dixit and Barry Nalebuff--it's a pop-intro to the basics in the field, written with a strong business slant. There might be 2 equations in it, tops. It's a quick read. A more complete introduction, less whimsical (but not more technical), is _Game Theory and the Law_ by Baird, Gertner and Picker. Also has 2 equations, and all intution is framed in the context of analyzing legal rules. A decent elementary treatment.
And how do you lug your printer around with you on the steppe?
666. Slackjaw - March 17, 1999 - 5:02 AM PT
At the very, very least, check out this brief discussion by David Levine--coincidentally enough, an econ professor at UCLA who also, coincidentally enough, counts proofs of several more recent folk theorems to his credit.
667. uzmakk - March 17, 1999 - 5:32 AM PT
Thank you so much, Slackjaw. Game theory sounds right up my alley. I read Levine and will purchase the books that you mentioned. I don't think the mathematics will give me much trouble, a couple of equations. Besides, its all the rage isn't it?. I shall purchase the books in lew of food for my family, a new suit and a haircut. So much for standard economic behavior.
668. uzmakk - March 17, 1999 - 5:36 AM PT
Slackjaw:
You ask how I lug my printer around on the steppe. I lug my entire livelyhood around on the steppe in a giant chariot made from a discarded tractor trailer and pulled by a team of 40 horses.
669. Slackjaw - March 17, 1999 - 5:47 AM PT
"So much for standard economic behavior." Hey, who said anything about the content of utility functions?
670. uzmakk - March 17, 1999 - 10:04 AM PT
Ya, who said anything about the content of utility functions?
671. uclapolisci - March 17, 1999 - 10:22 AM PT
What KIND of horses?
- Pelle's Evil Twin, "Skippy"
672. uzmakk - March 17, 1999 - 1:15 PM PT
My own breed, polsci, a cross between great great great uncle Genghis's own steed, and Percheron draft horses. Magnificent!
673. Slackjaw - March 17, 1999 - 1:20 PM PT
Uzmakk of the Steppe:
you implied that purchasing books instead of haircuts, sustenance et al. was contrary to standard economic behavior. But it need not be, depending on your preferences, ie., utility function (assuming you have one).
674. uclapolisci - March 17, 1999 - 1:28 PM PT
My god, they sound like worthy battle steeds! Outstanding!
-JWE
675. uzmakk - March 17, 1999 - 2:50 PM PT
My God, Slackjaw, I may not have a utility function. Is that the same as not having a soul, or does it mean that I am an unmotivated slug.
676. uzmakk - March 17, 1999 - 3:57 PM PT
Its a funny thing, Slack jaw, I just had half a raft of questions ready to go for you and I said to myself. Woa, buddy, why don't you just read the book first. That's what I will do.
677. uzmakk - March 17, 1999 - 4:11 PM PT
Is the basic stuff of the Universe information rather than matter or energy? Is it atleast useful to think and act as if this is so? If so, what is the nature and implications of the "cybernetic, information theoretical, game theoretical , communication" revolution? Can we develop , must we develop new "models" and ideas of "control"? We certainly seem to have problems to which the ideas can be applied. I guess that's sort of what you guys do?
678. uzmakk - March 17, 1999 - 4:12 PM PT
Is the basic stuff of the Universe information rather than matter or energy? Is it atleast useful to think and act as if this is so? If so, what is the nature and implications of the "cybernetic, information theoretical, game theoretical , communication" revolution? Can we develop , must we develop new "models" and ideas of "control"? We certainly seem to have problems to which the ideas can be applied. I guess that's sort of what you guys do?
679. Slackjaw - March 18, 1999 - 8:36 PM PT
not sure what you mean by 'control,' but I think that these kinds of issues--information transmission between conflicting parties, for example--has become a topic in (analytical) social science because people figured a way to use our modeling technology (game theory, for example) to say something about them. In fact, that is what the area of information economics is all about. Some party in a relationship has information another party doesn't but would like to have--what are the implications of this? Sometimes, for example our notions of the 'efficiency' or welfare properties of institutions of exchange, the implications are quite striking.
I know next to nothing about cybernetics...I don't know what a canonical cybernetic problem is or the point of view of that field. So I can't say whether it would be useful for us to use its insights; I can only say that at present we don't. Why don't you tell me a little more about it?
680. uzmakk - March 19, 1999 - 9:39 AM PT
I will make an effort, Slackjaw. I know that there are journals available in the field. All my knowledge comes from books 50 year old. Same with my understanding of game theory. Can't do it now. Got a call from the main man yesterday, business is expanding, turn around too slow," Do something Uzmakk!!." Game theory, cybernetics and fun, or feed the family and get down to business? Got to be a way to do both. I really should lay off the Fray for about 2 months. I will, however, continue to work in my usual distracted state and try to come up with something. What I come up with will certainly be a folk understanding composed of folk theorems(my meaning not yours) and many many questions for your consideration..
681. uclapolisci - March 19, 1999 - 11:42 AM PT
Slack: I thought the extension of the Folk Theorem was to formalize the idea "Oh, we already know all about YOU TYPES...". That's what I thought the small discounting was about, and also the Nash Equilibrium in an infinitely played game... In other words, if we have an entrenched idea about that group of people OVER THERE (i.e they suck, and that's not going to change), then it over-rides the conventional wisdom (that a payment today is better than one tomorrow), since if those people are going to always suck then any payment is fine forever... Or am I going all wrong about this?
-JWE
682. ChristinO - March 19, 1999 - 12:55 PM PT
Slack,
Does Game Theory help you with Trivial Pursuit?
683. FreeToChoose - March 19, 1999 - 1:36 PM PT
Slackjaw, It appears I should have posted this here:
Here's an article in Slate you will enjoy:
auction
684. Slackjaw - March 19, 1999 - 6:04 PM PT
Uzmakk,
ah, oh well. Life on the steppe must be challenging. I respect the need to feed the family. Look forward to your contributions when you can make them.
Jonathan,
I must confess, I don't know what to make of your last post. What group of people over where? I can't tell if you are objecting to the extension I suggested or what.
Chris,
Theoretically, it probably could if one team's early success had an effect on another team's performance, but the uncertainty involved in that is probably too deep for much beyond trivial insights to emerge (eg, if you can get to a brown pie square or roll again and you need a brown pie to win, don't go to roll again).
FTC,
Thanks for the link--I saw that before. A pretty good article, really. I recently ran some experients designed to get a handle on the particular type of irrationality used in bidding in auctions. The guys I work for have been marketing a novel equilibrium concept in which players make errors in a particular way and account for the fact that others do to (so the existence of this equilibrium is shown as a fixed point in this error accounting process), and I am carrying out my duties as their faithful lackey.
Sadly, the results don't look as strong for the auction data as for some other experiments we have looked at, but they are still a lot better than Nash equilibrium.
Incidentally, I am reading right now a book on Bayesian statistics. Really fascinating stuff. I'm on vacation at the moment so I have less time to post than usual, but I will be better prepared to talk about it than a year ago or whatever it was. I'm not really reading it for any particular reason so it's a low priority, but I am sincerely trying to get through it. It's a lot of game theory by a different name and in a different context, so it should go fairly quickly.
685. Slackjaw - March 19, 1999 - 6:18 PM PT
Diva, in case you come in here, see Message #666, the Message of the Beast, for a link to a site with a brief discussion of game theory. I will say more later but I gotta go now and drink some beer on the beach.
686. uzmakk - March 20, 1999 - 7:50 AM PT
Quickly!!!!! Resignify message 666 before the peasants march upon the Philosophy and Mathematics thread and word of this divine coincidence spreads.
687. uzmakk - March 20, 1999 - 10:48 AM PT
Slackjaw,:
Now mathematics is a fabrication of the human mind. I believe you said something like this somewhere on the Fray. Sometimes it impinges on "reality" and when it does this is very exciting. I used the word "control" and you said you were not quite sure of my meaning. If this is not too much trouble I would like you to do this for me. I just got my monthly copy of Harper's yesterday. Inside there is an "annotation" entitled The Green Machine: Is Monsanto sowing the seeds of change, or destruction? This article seems to bring all the right questions together in one spot, and we are speaking of "concrete" behavior, reality. Genetic engineering, the law, corporate motivation, strange new boundaries, with what player in a game do we side?, seeds as intellectual property,i.e. the physical entity grown in the farmer's field, and an obvious need by the corporation to "control". The word "bioserfdom" is used. I am curious to know how a game theoretician would analyse the situation described in the article..At your pleasure, Slackjaw, if at all. How about you, uclapolsci? I certainly won't be offended if you tell me you are too busy, or that I am off topic. But it seems on to me..
688. Slackjaw - March 20, 1999 - 2:50 PM PT
no, not off topic...sounds cool. This thread should be a sort of philosophical bazaar (and/or bizarre) and we should make the most of it while we have it. I won't be able to get that article probably until I return toward the end of next week. Oh, maybe I will run across it before then.
let me just post this briefly--so, people have seen that web site, and gotten a short general description of game theory. Generally, a game is any social situation, a situation in which two or more decision makers (people, firms, etc.) interact. I mean interact in this sense: the best decision any decision maker ("player") can make depends on the decisions made by everyone else. This is the idea of mutual payoff dependence.
Game theory in that sense is a generalization of single-person decision theory, which is generally interesting when there is some uncertainty. E.g., a person must make a choice about which lottery to buy. Well, in a game, the uncertainty can come from the outside like this, thanks to 'nature', but the heart of game theory is generating this uncertainty--uncertainty over what you get from choosing a particular action--within the game itself.
In decision theory, we talk about people who have well defined goals and pursue them effectively. This is what an economist means by 'rational behavior.' What is useful about this is that it allows you to represent the preferences of a decision maker by a function. It specifies the 'payoff' or 'utility' a decision maker gets by making a particular decision, depending on the realization of some uncertainty. For example, depending on your choice of portfolio in financial markets and depending on some uncertainty at the time you invest, you earn different returns. This sort of thing is sometimes studied in decision theory. The idea is to maximize the utility function subject to some constraints, like a budget.
689. Slackjaw - March 20, 1999 - 2:50 PM PT
Instead of just solving an optimization problem (which is not always trivial, say if there's a lot of randomness and the decisions must be made over time), game theory is about the optimization problem of all the players, being solved simultaneously, where some of the constraints are the choices of others. For example, think of the simple game called matching pennies. You and a friend must each announce "H" or "T". If you both say H or both say T, you get $1 from your friend. If you say different things, you must give $1 to your friend.
This is a game, in that we have specified the players, the actions they can take, and the payoffs they each get from any combination of actions.
It also illustrates a particular type of game: a zero sum game. If you add up the payoffs the players get from any combination of actions, the sum is 0.
It illustrates too a very important concept: the importance of randomization. A strategy a player can choose is say H for sure, say T for sure, or say each with some probability. We assume that this sort of randomization over your own strategies is allowed. And in this game, it's sensible--if your choice was predictable, you'd lose $1 for sure. This is called a "mixed strategy"--obfuscation is an option.
That's about it for now, I will say some more later.
690. CalGal - March 20, 1999 - 3:22 PM PT
Slack,
You know, I just went through my bookshelves a couple months ago and was ruthless. I am pretty sure that one of the books I gave away was the textbook I got--which is very irritating if you're actually going to start explaining it. I could actually have used it!
I remember *that* name--A Course in Game Theory, by Martin Osborne. What I am not sure of is the name of the book I ordered--which was on the order slip I had folded up in the book, because *of course* I would be returning it some day, right?
I just did a search on Game Theory on Amazon, to see if any of the names rang a bell. It may have been Game Theory: A Non-Technical Introduction, by Morton Davis.
Anyway, about a year ago, you recommended several books on the subject and one of them was definitely less technical than the others. That was the one I ordered but it wasn't the one I received.
691. stostosto - March 20, 1999 - 4:45 PM PT
"Is philosophy dead?",
the mighty thread
is now for all appearances dead.
But, lo, it lives beyond its death
transcending to, at loss of breath,
philosophy and math.
692. Slackjaw - March 20, 1999 - 11:55 PM PT
By the way, anyone actually reading these words should feel free to delurk at any time. This is not going to be a whole lot of fun if I just write a bunch of posts. If something isn't clear, or you don't believe something, or you think something is a dumb way to study human interaction, then by all means speak up. Speak I say!
I should also note, obviously your portfolio's performance depends on uncertainty at the time of your decision and down the road too. What I meant was, these things are uncertain at the time of your decision.
Now then. Historically, games like matching pennies, zero sum games, were analyzed first. They have a particularly simple structure mathematically, in that maximizing one person's utility, accounting for randomness and given the other (possibly random) choice of the other player, is the same as minimizing another person's, subject to the similar appropriate constraints.
The thing about them is that they are not always so interesting economically or socially. We in social science rarely find interest in situations of such unadulterated conflict. There is no common ground in these games, and there is always a winner and a loser. But early attempts by game theorists to study non-zero sum games proved very unsuccessful, despite the concerted effort of some of the most brilliant mathemeticians of this century, like von Neumann, Kuhn, Tucker, etc. The seminal tract on game theory, _Theory of Games and Economic Behavior_ by John von Neumann and Oskar Morgestern, is a testament to this. The book is thoroughly abstruse, even to most game theorists, and essentially no progress was made on non-zero sum games. (Incidentally, a 'constant sum game', one where the sum of the payoffs to all the various players under every possible combination of actions sum to the same constant, are mathematically equivalent to zero sum games.)
693. Slackjaw - March 20, 1999 - 11:56 PM PT
For zero sum games, of 2 or any number n of players, the solution, specification of what rational players will do, is to be found from something called 'minimax' analysis. The idea is, you lay out what you get from each action, depending on what the other players do. So, for matching pennies, if you say H, you get $1 if the other player says H, and -$1 if the other player says T. If you say T, you get -$1 if the other player says H and $1 if the other player says T. Then the minimax solution is to find the maximum payoff you can possibly get from each of your strategies, and then play the strategy with the smallest maximum. If several strategies satisfy this criterion, randomize over them.
The reason why this is 'the' solution is because it maximizes the player's expected payoff in the game (a fact whose proof is simply the duality theorem of linear programming). If you are rational, and want to get the highest possible expected payoff you can, this is the strategy you choose. It turns out that in matching pennies, in accordance with intution, the optimal randomization is to play each choice with probability .5.
The reason vN-M, for all their collective brilliance (most of which resided in von Neumann, pronounced "von NOY-man"), had trouble beyond zero sum games was that they had trouble thinking outside their own analytical box, to use that rather faddish expression. A young mathemetician named John Nash entered the picture at that point, and changed the course of game theory.
I shall say more about that later, but I want to back up a bit first. You may be wondering, what the hell is all this about, after all? The purpose of game theory--and the 'theory' of game theory--is the study of predicting how rational players actually play the game. (I will say more about the rational part later.) And you will notice from matching pennies that the games are sometimes very simple 'toy' games. Social scientists use games as simplified descripti
694. Slackjaw - March 20, 1999 - 11:57 PM PT
Social scientists use games as simplified description of a situation in which they are interested, and use game theoretic analysis on this simplified world. The hope is that we can cross back over to the real world after the toy one has been figured out, and use the insights about the toy world on the real one.
Also note about matching pennies that decisions are made simultaneously, and only once. Game theory is not limited to this. A game in 'extensive form' takes place over some period of time, and specifies the order in which players move, what they can do on each move, and what they can know when they take each move (e.g., are the strategies chosen on each previous move by other players observable?). This is in addition to the specification of who the players are, and what they get from each possible combination of strategies.
A dizzying array of prediction models, or 'solution' or 'equilibrium concepts', has been advanced in the subject's history. I want to start with the most basic one of all. It is the concept of domination.
From the perspective of any given player, this concept requires no assumptions about the other players' utility function. Informationally, then, it is the weakest of all the solution concepts in game theory. The only assumption required to accept for it to be applicable is rational behavior (ie, the desire maximize your own payoffs, whatever may be their source), and certainty about what the other players in the game can possibly do on their moves. A player doesn't need to know other players' payoffs from a given combination of strategies in order to engage in this reasoning.
695. Slackjaw - March 20, 1999 - 11:59 PM PT
The concept is simply this: suppose that you consider all the possible (non-randomized, or 'pure'--like H or T in matching pennies) strategies available to you. Suppose that, for any given choice of the other player, one of these pure strategies gives you a higher payoff than all other strategies. This is called a dominant strategy. The others are dominated.
For example, suppose that in matching pennies, your payoffs were like so: if you said H and the other player H, you get $1; if you say H and the other player T you get $1.01; if you say T and the other H, you get -$1; and if you say T and the other T you get $1 (so your payoffs from T don't change). Then H is a dominant strategy. For suppose the other player says H. Then H gives you a higher payoff than T: 1 > -1. But suppose the other player says T. Then again, H gives you a higher payoff than T: 1.01 > 1.00. So no matter what the other player does, you get your highest payoff by playing H. This is a strong reason to pick H. If a consultant recommended something different to you, at the very least you would require a damn good explanation.
But now suppose you were the other player (player 2), and player 1 had the payoff structure specified immediately above. If we make the additional assumption that you know player 1 is rational, what should you do? Well, you know that player 1 has a dominant strategy, *and that player 1 knows this.* Nothing you could ever do could lead a rational player 1 to play T. But then you might as well eliminate his choice of T from consideration--he would NEVER want to use it. So, assume that he deletes his dominated strategy.
696. Slackjaw - March 20, 1999 - 11:59 PM PT
(last one)
But then you have a sort of derived game. You have 2 choices but player 1 has only 1 choice, H. In this derived game, you get -$1 from your choice of H, but $1 from your choice of T. In this new game, pl. 2 has a dominant strategy too: T. Then, by iterated deletion of dominated strategies, we arrive at a deried game in which each player has only 1 choice! This is the 'solution' of the game, modified matching pennies.
This logic is very compelling, and in this game it leads to a solution in which the sum of the payoffs earned by each player are as high as can possibly be--no combination of actions leads to a sum of payoffs higher than $2.01. This solution is called 'efficient' for this reason. But this compelling logic turns out to be very subvsersive in a game known as the Prisoners' Dilemma, also solvable in dominant strategies.
This is a very familiar example from game theory; if someone wants to describe it, please do. I have to go for a while and don't know when I'll get back here.
697. Slackjaw - March 21, 1999 - 12:12 AM PT
I should also note, actually, that if you want a book on the subject, it really depends on your facility with math. If you want light reading, with very little actual math, a good book is _Thinking Strategically_ by Dixit and Nalebuff. (I have not read the book CalGal mentioned but would be interested in hearing reactions.)
A more structured book, but not having any more equations in it (I think it has 2 equations) is _Game Theory and the Law_ by Baird, Gertner and Picker. The book, obviously, deals with the application of game theory to the analysis of various types of legal rules. Its discussion of game theory really is pretty good intuitively, and the examples are a neat illustration (if only a scratch of the surface) of what a wide range of game theoretic concepts can do in a subject.
A more mathematical treatment, but not one that I would call mathematical, is _Game Theory for Applied Economists_ by Robert Gibbons. This requires good algebra skills and actually has a formal proof or two in it. The main advantages of the book are that it covers the standard topics of an introductory graduate course on game theory for social scientists, but is less mathematical, more intuitive, and teaches primarily by example. This book serves the niche better than, say, _Games and Information_ by Eric Rasmussen, even though I prefer the orientation of the latter, because it is shorter and goes through more examples, and manages to be simultaneously less mathematical but more rigorous.
698. Slackjaw - March 21, 1999 - 12:12 AM PT
At the advanced introductory level, at least 3 books are available: _A Course in Game Theory_ by Martin Osborne and Ariel Rubinstein, _Game Theory_ by Drew Fudenberg and Jean Tirole, and _Game Theory_ by Roger Myerson. I haven't read the first, hate the second and love the third. I find the intution in Fudenberg and Tirole to be somewhat opaque at a first pass, and the treatment is more nonchalant or flippant about some important results and/or delicate constructs. Myerson's book is a tour de force, requiring a substantial investment, but worth it. You really have to wrap your mind around it, and it's not good for 'random access' such as one wants in a reference, but to learn the subject in all its glory, the book is simply unparalelled.
699. Slackjaw - March 21, 1999 - 12:16 AM PT
okay, one more, really
"even though I prefer the orientation of the latter, because it [THE FORMER, NOT THE LATTER] is shorter and goes through more examples, and manages to be simultaneously less mathematical but more rigorous."
700. stostosto - March 21, 1999 - 2:30 PM PT
Slackjaw
I hope this in your Message #692 "If something isn't clear, or you don't believe something, or you think something is a dumb way to study human interaction, then by all means speak up. Speak I say!"
isn't a response to my Message #691.
I assure you that was not a hint of dissatisfaction, not with this thread in general, nor with your contributions in particular - which I enjoy and admire.
I wasn't even lurking in this thread. I just jumped to it when I saw it had changed name. I thought I'd follow up on an observation I made way back at the beginning of the thread
"The "Is philosophy dead?" thread is apparently not dead yet.
Which is really nothing but a childish game I play with myself. Perhaps I shouldn't have bothered people here with it...
I can also assure you that *if* the unlikely event occurred that I would be unhappy with anything you or others said in these threads, I would either say so directly, or keep it to myself and go on to other threads and doings.