The Cournot Duopoly Model. 3 . Exercise 1. Consider the "asymmetric Cournot duopoly game" where the If c1 P0 + c1, what is the Nash equilibrium? .. Investors can withdraw on date 1 (before the project matures) or. 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. Lecture 6 - Nash Equilibrium; Dating and Cournot. Game Theory · Yale Then we analyze the classic Cournot model of imperfect competition between firms.
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.
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There is common knowledge that all players meet these conditions, including this one. 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. For example, a computer capable of flawless logical play facing a second flawless computer will result in equilibrium. Introduction of imperfection will lead to its disruption either through loss to the player who makes the mistake, or through negation of the common knowledge criterion leading to possible victory for the player.
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An example would be a player suddenly putting the car into reverse in the game of chickenensuring a no-loss no-win scenario.
In many cases, the third condition is not met because, even though the equilibrium must exist, it is unknown due to the complexity of the game, for instance in Chinese chess. The criterion of common knowledge may not be met even if all players do, in fact, meet all the other criteria.
This is a major consideration in " chicken " or an arms racefor example. Where the conditions are met[ edit ] In his Ph. One interpretation is rationalistic: This idea was formalized by Aumann, R.
Nash equilibrium dating and cournot duopoly
Brandenburger,Epistemic Conditions for Nash Equilibrium, Econometrica, 63, who interpreted each player's mixed strategy as a conjecture about the behaviour of other players and have shown that if the game and the rationality of players is mutually known and these conjectures are commonly know, then the conjectures must be a Nash equilibrium a common prior assumption is needed for this result in general, but not in the case of two players.
In this case, the conjectures need only be mutually known. A second interpretation, that Nash referred to by the mass action interpretation, is less demanding on players: What is assumed is that there is a population of participants for each position in the game, which will be played throughout time by participants drawn at random from the different populations.
If there is a stable average frequency with which each pure strategy is employed by the average member of the appropriate population, then this stable average frequency constitutes a mixed strategy Nash equilibrium. For a formal result along these lines, see Kuhn, H. Due to the limited conditions in which NE can actually be observed, they are rarely treated as a guide to day-to-day behaviour, or observed in practice in human negotiations.
However, as a theoretical concept in economics and evolutionary biologythe NE has explanatory power.
The payoff in economics is utility or sometimes moneyand in evolutionary biology is gene transmission; both are the fundamental bottom line of survival.
Researchers who apply games theory in these fields claim that strategies failing to maximize these for whatever reason will be competed out of the market or environment, which are ascribed the ability to test all strategies. This conclusion is drawn from the " stability " theory above. In these situations the assumption that the strategy observed is actually a NE has often been borne out by research.
The blue equilibrium is not subgame perfect because player two makes a non-credible threat at 2 2 to be unkind U. The Nash equilibrium is a superset of the subgame perfect Nash equilibrium. WomenHeart encourages women of all ages to know their risk for heart disease and get an annual check up to keep an eye on important numbers like their cholesterol, it isn't true, I can't ever take back.
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