Talk:Folk theorem (game theory)

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Why is the Folk Theorem of Repeated Prisoner's Dilemma so important ?

There are many analogies between Repeated Prisoner's Dilemma (with an unknown end-round) and issues of competition, cooperation and coordination. Repeated/Iterated Prisoner's dilemma is widely used as a model in economics, business, psychology, sociology political science, and other social and information sciences. (see prisoner's dilemma / tragedy of the commons / market failure / Leviathan / public goods ). It is also widely used to describe cooperation and/or competition within and/or between species in an evolutionary setting.

Prisoner's dilemma games are characterized by each player choosing to Defect (D) or Cooperate (C). The highest payoff is for Defecting against cooperating opponents (Exploit). The lowest payoff is for cooperating against defecting opponents (Sucker). Both players defecting (mutual defection (MD)) results in lower payoffs to each player than both player cooperating (mutual cooperation (MC)). So, while going from the stable equilibrium of MD to MC would be a Pareto improvement, in single-shot Prisoner's dilemma rational economic players fail to achieve the efficiency of mutual cooperation.

Fundamentally, single-game Prisoner's dilemma demonstrates where the "invisible hand" of competition can fumble - creating an outcome that is inefficient for all players. (Note: single-game Prisoner's dilemma is fundamentally different than mixed-motive games and pure coordination games - which describe yet other situations where a pure competitive approach may produce distinctly inefficient results - see coordination games regarding the importance of focal points and/or of explicit coordination / standards).

Repeated Prisoner's dilemma (with an unknown end-round) allows for the possibility of VARYING DEGREES of cooperation and defection. The FOLK THEOREM demonstrates this key point. ANY equilibrium that pays each player an average payoff of at least the mutual defection payoff (+ epsilon) is supportable. (Cf. Folk Theorem entry regarding "Grim strategy" approach). NOTE : this does NOT imply that both players will necessarily achieve the most efficient average payoff (usually defined as the MC payoff - since typically PD games are defined so that 2*MC >= Sucker + Exploit). In fact, it states - far more broadly and far more interestingly - that ANY equilibrium in a very broad range MAY be supported. So the Folk Theorem for Repeated Prisoner's Dilemma (with unknown end round) can be used to model unequal and even ongoing expoitative relationships - preditor-prey, symbiotic or parasitic, bully-victim, noble-serf, etc. For example, if a given player (noble) is precommitted to (see entry on precommitment, and on Thomas Schelling) a grim strategy that will require the other player (serf) to allow him/herself to be exploited every k rounds, then as long as the other player (serf) gets an average payoff of AT LEAST the MD payoff + epsilon, it is in his/her interest NOT to violate the pattern of play, since triggering the GRIM outcome will result in the MD average payoff (which is dominated). This means that the disadvantaged player may have an economic interest in maintaining his/her unequal and exploited position rather than face mutual defection. (See again the advantages of precommittment in a game-theoretic or negotiation context).

Ironically, the FOLK THEOREM implies that the meta-game of Repeated Prisoner's dilemma (with an unknown end-round) is actually a mixed-motive coordination game. (See entries on coordination games and Thomas Schelling). This implies that all the tactics that may be of use in mixed motive games may apply to Repeated Prisoner's dilemma games (with an unknown end-round).

Practically, why does that matter ? Repeated Prisoner's dilemma games (with an unknown end-round) model a very broad range of situations where players - whether individuals, businesses, countries or organisms - can cooperate or fight.

(True single-game prisoner's dilemma situations are probably rare - most interactions can at least cause reputation effects, repeated games on the other hand are quite common). The FOLK THEOREM shows us - in game theory - what we observe in practical reality - that expectations and beliefs matter, that initial positions matter, that precommitment matters. It can explain the wide range of equilibria that we observe in people's interactions across and within cultures, across and within organizations, and across and within species. It provides a much richer model for economic behavior than older approaches.

                                                                (Holt, G.)

Welcome to wikipedia and thank you for your addition. If you would like this to be included in the article itself, you are welcome to add it. Although, it would be useful if it provided some sources. Not that I distrust anything said here, quite the contrary. However, wikipedia prohibits the posting of original research and so I would like to be sure this does not include any of that. Again thank you for your interest. --best, kevin [kzollman][talk] 22:40, 19 January 2007 (UTC)

[edit] A solution concept?

I'm a bit uncomfortable describing Folk Theorems as "solution concepts" within game theory. Perhaps I'm being pedantic, but my understanding is that Folk Theorems state that, under certain conditions, a wide variety of outcomes can be sustained as Nash equilibria in a repeated game. While Folk Theorems extend the possibilities for the solutions that might result for a particular game, I'd argue that Folk Theorems are not themselves solution concepts in the same sense as the Nash equilibrium, evolutionarily stable strategy, etc. Any thoughts? Mateoee 21:18, 8 May 2007 (UTC)

[edit] Intractability

The article ought to mention that the strategies alluded to in the article are, in general, intractable to compute.^[1] Gdr 20:53, 8 March 2008 (UTC)