Lecture 6 - Nash Equilibrium; Dating and Cournot. Game Theory · Yale. We apply the 4 - Cournot Duopoly: Real World Examples. SUGGESTIONS FOR YOU. In game theory, the Nash equilibrium, named after the late mathematician John Forbes Nash Jr. Forbes Nash, Jr. A version of the Nash equilibrium concept was first known to be used in by Antoine Augustin Cournot in his theory of oligopoly. However, Nash's definition of equilibrium is broader than Cournot's. To know more about her nash equilibrium dating and cournot oligopoly can be followed in different social net working sites like Facebook, twitter and Instagram.
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If these conditions are met, the cell represents a Nash equilibrium. Check all columns this way to find all NE cells. Stability[ edit ] The concept of stabilityuseful in the analysis of many kinds of equilibria, can also be applied to Nash equilibria. A Nash equilibrium for a mixed-strategy game is stable if a small change specifically, an infinitesimal change in probabilities for one player leads to a situation where two conditions hold: If these cases are both met, then a player with the small change in their mixed strategy will return immediately to the Nash equilibrium.
The equilibrium is said to be stable. If condition one does not hold then the equilibrium is unstable. If only condition one holds then there are likely to be an infinite number of optimal strategies for the player who changed. In the "driving game" example above there are both stable and unstable equilibria. If either player changes their probabilities slightly, they will be both at a disadvantage, and their opponent will have no reason to change their strategy in turn.
Stability is crucial in practical applications of Nash equilibria, since the mixed strategy of each player is not perfectly known, but has to be inferred from statistical distribution of their actions in the game. In this case unstable equilibria are very unlikely to arise in practice, since any minute change in the proportions of each strategy seen will lead to a change in strategy and the breakdown of the equilibrium.
The Nash equilibrium defines stability only in terms of unilateral deviations. In cooperative games such a concept is not convincing enough.
Strong Nash equilibrium allows for deviations by every conceivable coalition. In fact, strong Nash equilibrium has to be Pareto efficient. As a result of these requirements, strong Nash is too rare to be useful in many branches of game theory.
However, in games such as elections with many more players than possible outcomes, it can be more common than a stable equilibrium. A refined Nash equilibrium known as coalition-proof Nash equilibrium CPNE  occurs when players cannot do better even if they are allowed to communicate and make "self-enforcing" agreement to deviate.
Nash equilibrium - Wikipedia
Every correlated strategy supported by iterated strict dominance and on the Pareto frontier is a CPNE. CPNE is related to the theory of the core. Finally in the eighties, building with great depth on such ideas Mertens-stable equilibria were introduced as a solution concept. Mertens stable equilibria satisfy both forward induction and backward induction.
In a game theory context stable equilibria now usually refer to Mertens stable equilibria. Occurrence[ edit ] If a game has a unique Nash equilibrium and is played among players under certain conditions, then the NE strategy set will be adopted.
Sufficient conditions to guarantee that the Nash equilibrium is played are: The players all will do their utmost to maximize their expected payoff as described by the game. The players are flawless in execution. The players have sufficient intelligence to deduce the solution. The players know the planned equilibrium strategy of all of the other players. The players believe that a deviation in their own strategy will not cause deviations by any other players. There is common knowledge that all players meet these conditions, including this one.
nash equilibrium dating and cournot oligopoly
So, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on. Where the conditions are not met[ edit ] Examples of game theory problems in which these conditions are not met: The first condition is not met if the game does not correctly describe the quantities a player wishes to maximize.
In this case there is no particular reason for that player to adopt an equilibrium strategy.
Intentional or accidental imperfection in execution.