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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 ...
However, some Cournot strategy profiles are sustained as Nash equilibria but can be eliminated as incredible threats (as described above) by applying the solution concept of subgame perfection. Indeed, it is the very thing that makes a Cournot strategy profile a Nash equilibrium in a Stackelberg game that prevents it from being subgame perfect.
There are many Nash equilibria in the Nash demand game. Any x and y such that x + y = z is a Nash equilibrium. If either player increases their demand, both players receive nothing. If either reduces their demand they will receive less than if they had demanded x or y. There is also a Nash equilibrium where both players demand the entire good.
Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium. [1] This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. In other words, there is no pair of pure strategies such that neither player ...
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:
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 game, the players ...
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.