Folk theorem (game theory) | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Folk_theorem_(game_theory)


00:01:54 1 Preliminaries
00:03:17 2 Infinitely-repeated games without discounting
00:05:53 2.1 Subgame perfection
00:07:19 2.2 Overtaking
00:12:36 3 Infinitely-repeated games with discounting
00:14:41 3.1 Subgame perfection
00:16:32 4 Finitely-repeated games without discount
00:19:00 5 Applications
00:21:05 6 Summary of folk theorems



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SUMMARY
=======
In game theory, folk theorems are a class of theorems about possible Nash equilibrium payoff profiles in repeated games (Friedman 1971). The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept subgame-perfect Nash equilibria rather than Nash equilibrium.The Folk Theorem suggests that if the player is patient enough and far-sighted (i.e. if discount factor 
  
    
      
        δ
        →
        1
      
    
    {\displaystyle \delta \to 1}
  ) then not only can repeated interaction allow many SPE outcomes, but actually SPE can allow virtually any outcome in the sense of average payoffs. Put more simply, the theorem suggests that anything that is feasible and individually rational is possible.For example, in the one-shot Prisoner's Dilemma, if both players cooperate that is not a Nash equilibrium. The only Nash equilibrium is that both players defect, which is also a mutual minmax profile. One folk theorem says that, in the infinitely repeated version of the game, provided players are sufficiently patient, there is a Nash equilibrium such that both players cooperate on the equilibrium path. But in finitely repeated game by using backward induction it can be determined that players play Nash equilibrium in the last period of the game (which is to defect).