Question

According to Folk theorem, explain what sort of insight it provides to firms seeking to escape the Nash Equilibrium of the static Prisoners’ Dilemma game played in highly competitive (Cournot or Bertrand) markets

Answer 1

Flok theorem (game theory)

definition : Flok theorem (game theory) are a class of theorem about possible nash equilibrium payoff profiles in repeated games.The original Folk theorem concerned the payoffs profiles in repeated games.

Nash equilory

definition : the nash equilibrium named after American mathematician John Forbes Nash Jr.It is a solution concept of a non cooperative game involving two or more players is assumed to know the equilibrium strateries of the other players.

prisoner's dilemma :

definition: The prisoners dilemma is a standard example of a game analysed in game theory that shows why two completely rational individuals might not cooperate,even if it appears that it is their nest intrests to do so.

the literature focuses on two equilibria that arise from assuming that the government knows the correct model. Called the Nash equilibrium and the Ramsey plan, they come from different timing protocols. The outcome with a Ramsey plan is better than that for a Nash equilibrium. This is the time inconsistency problem. To define a Nash equilibrium, we need Definition 3.1 A government best response map xt = B(^xt) solves the problem me xt E(U2 t + y 2 t ) (3.5) subject to (2.1), (2.2), taking x^t as given. The best response map is xt = 2 + 1U + 2 2 + 1 x^t: (3.6) A Nash equilibrium incorporates a government best response and rational expectations for the public.

Nash equilibrium is a pair (x; x^) satisfying (a) x = B(^x), and (b) x^ = x. A Nash outcome is the associated (Ut ; yt). Definition 3.3 The Ramsey plan xt solves the problem of minimizing (3.5) subject to (2.1), (2.2), and (2.3). The Ramsey outcome is the associated (Ut ; yt). A Ramsey outcome dominates a Nash outcome. The Ramsey plan is x^t = xt = 0 and the Ramsey outcome is Out = U