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In game theory, rationalizability or rationalizable equilibria is a solution concept which generalizes Nash equilibrium. The general idea is to provide the weakest constraints on players while still requiring rational players. It was first discovered independently by Bernheim (1984) and Pearce (1984). In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
Matching Pennies is the name for a simple example game used in game theory. ...
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
In economics and game theory, the participants are sometimes considered to have perfect rationality: that is, they always act in a rational way, and are capable of arbitrarily complex deductions towards that end. ...
Constraints on beliefs
Consider a simple coordination game (the payoff matrix is to the right). The row player can play a if she can reasonably believe that the column player could play A, since a is a best response to A. She can reasonably believe that the column player can play A if it is reasonable for column to believe that the row player could play a. He can believe that she will play a if it is reasonable for him to believe that she could play a, etc. In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
It has been suggested that this article or section be merged with normal form game. ...
In game theory, the best response is the strategy in a single period that creates the most favorable immediate outcome for the current player, taking other players strategies as given. ...
This provides a infinite chain of consistent beliefs that result in the players playing (a, A). This makes (a, A) a rationalizable equilibrium. A similar process can be repeated for (b, B). Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In Game Theory, the prisoners dilemma is a type of non-zero-sum game. ...
Not every strategy in every game is rationalizable. Consider a prisoner's dilemma pictured to the left. Row player would never play c, since c is not a best response to any strategy by the column player. This is an example of a more general fact, that a strategy which is strictly dominated cannot be part of a rationalizable equilibrium. Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In Game Theory, the prisoners dilemma is a type of non-zero-sum game. ...
In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ...
Conversely, for two-player games, the set of all rationalizable strategies can be found by iterated elimination of strictly dominated strategies. In games with more than two players, however, there may be strategies that are not strictly dominated, but which can never be the best response. By the iterated elimination of all such strategies one can find the rationalizable strategies for a multiplayer game.
Rationalizability and Nash equilibria It can be easily proved that every Nash equilibria is a rationalizable equilibria, however the converse is not true. Some rationalizable equilibria are not Nash equilibria. This makes the rationalizability concept a generalization of Nash equilibrium concept. Matching pennies | H | T | | h | 1, -1 | -1, 1 | | t | -1, 1 | 1, -1 | As an example, consider the game matching pennies pictured to the right. In this game the only Nash equilibrium is row playing h and t with equal probability and column playing H and T with equal probability. However, all the pure strategies in this game are rationalizable. Matching Pennies is the name for a simple example game used in game theory. ...
A pure strategy is a term used to refer to strategies in Game theory. ...
Consider the following reasoning: row can play h if it is reasonable for her to believe that column will play H. Column can play H if its reasonable for him to believe that row will play t. Row can play t if its reasonable for her to believe that column will play T. Column can play T if it reasonable for him to believe that row will play h (beginning the cycle again). This provides a infinite set of consistent beliefs that results in row playing h. A similar argument can be given for row playing t, and for column playing either H or T.
References - Bernheim, D. (1984) Rationalizable Strategy Behavior. Econometrica 52: 1007-1028.
- Fudenberg, Drew and Jean Tirole (1993) Game Theory. Cambridge: MIT Press.
- Pearce, D. (1984) Rationalizable Strategy Behavior and the Problem of Perfection. Econometrica 52: 1029-1050.
- Ratcliff, J. (1992–1997) lecture notes on game theory, §2.2: "Iterated Dominance and Rationalizability"
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