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Repeated games allow for the study of the interaction between immediate gains and long-term incentives. A finitely repeated game is a game in which the same one-shot stage game is played repeatedly over a number of discrete time periods, or rounds. Each time period is indexed by 0 < t ≤ T where T is the total number of periods.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games ( Friedman 1971 ). [1] 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 ...
A game can have more than one Nash equilibrium. Even if the equilibrium is unique, it might be weak: a player might be indifferent among several strategies given the other players' choices. It is unique and called a strict Nash equilibrium if the inequality is strict so one strategy is the unique best response:
Subgame perfect equilibrium. In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in ...
The Nash equilibrium was the most common agreement (mode), but the average (mean) agreement was closer to a point based on expected utility. [11] In real-world negotiations, participants often first search for a general bargaining formula, and then only work out the details of such an arrangement, thus precluding the disagreement point and ...
The group's total payoff is maximized when everyone contributes all of their tokens to the public pool. However, the Nash equilibrium in this game is simply zero contributions by all; if the experiment were a purely analytical exercise in game theory it would resolve to zero contributions because any rational agent does best contributing zero, regardless of whatever anyone else does.
The Nash Equilibrium in the Bertrand model is the mutual best response; an equilibrium where neither firm has an incentive to deviate from it. As illustrated in the Diagram 2, the Bertrand-Nash equilibrium occurs when the best response function for both firm's intersects at the point, where P 1 N = P 2 N = M C {\displaystyle P_{1}^{N}=P_{2}^{N ...
That is, if at any time period all the players play a Nash equilibrium, then they will do so for all subsequent rounds. (Fudenberg and Levine 1998, Proposition 2.1) In addition, if fictitious play converges to any distribution, those probabilities correspond to a Nash equilibrium of the underlying game. (Proposition 2.2)