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Equilibrium payoffs in a Bertrand-Edgeworth model
Equilibrium payoffs in a Bertrand-Edgeworth model

... in the presence of capacity constraints and product differentiation. This is precisely the aim of the present note. We consider a Hotelling duopoly model pricing game with fixed locations. We assume that one firm is possibly capacity constrained while the other holds an abritrarily large capacity. F ...
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Agent-Based Modeling of Coporate Takeover

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... other player uses.  We will explain these concepts with the classic example of Prisoner’s Dilemma. Example: Prisoner’s Dilemma The story: Ann and Bob have been caught stealing a car. The police suspect that they have also robbed the bank, a more serious crime. The police has no evidence for the rob ...
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... If a given entry in a payoff matrix corresponds to a Nash equilibrium, then we know that any other value in that column must be less than or equal to the entry value, so that any other pure strategy choices for Player A would be worse or tied compared to A’s equilibrium strategy, given that Player B ...
Class Project (Project 2) - University of Arizona Math
Class Project (Project 2) - University of Arizona Math

... Is Strategy 4 optimal ? • No • This is the real world of business, where we expect our competitors to be well-managed companies • other 18 companies are sitting in their offices and boardrooms making the same calculations that we have just performed. Given the results, other companies will also ele ...
Nash equilibrium, rational expectations, and heterogeneous beliefs
Nash equilibrium, rational expectations, and heterogeneous beliefs

... has two types, and each type of each player has two actions. Essential to the example is a particular kind of pooling: each type of a player cannot perfectly identify the conditional distribution over the other’s types, conditional on the action that she is taking, but she could identify this condi ...
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Existence and computation of equilibria of first

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Stochastic stability in a learning dynamic with best

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Game Theory MA 4264 Lecturer: Zhao Gongyun Office: S17 # 08

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Toward the fair sharing of profit in a supply network formation

... acceptable to all of them and guarantees coalitional stability. In cooperative game theory, several concepts have been introduced for approaching the stability issue. A necessary condition for the stability of a coalition is that no set of players is able to increase its members’ profits by forming ...
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The Hex game and its mathematical side

oligop99
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Evolution leads to Kantian morality

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NOTES ON NASH EQUILIBRIUM 1. 2 × 2 games, pure

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Noncooperative Convex Games: Computing

... http://pure.iiasa.ac.at/4167/ Working Papers on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting t ...
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... Prisoners’ dilemma is a game based on two premises: (1) Each player has an incentive to choose an action that benefits him or herself at the other player’s expense. (2) When both players act in this way, both are worse off than if they had chosen different actions. ...
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XX On the Complexity of Approximating a Nash Equilibrium

Nash equilibrium, rational expectations, and heterogeneous beliefs
Nash equilibrium, rational expectations, and heterogeneous beliefs

... particular kind of pooling: each type of a player cannot perfectly identify the conditional distribution over the other’s types, conditional on the action that she is taking, but she could identify this conditional distribution had she taken the other action. This is true for each type of each play ...
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TIME AVERAGE REPLICATOR AND BEST REPLY

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Strategic Behavior in Non-Atomic Games

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Repeated Games with Differential Time Preferences

... the players’ overall utility outside the feasible set of the stage-game. Therefore, the set of all feasible payoffs of the repeated game is typically larger than that of the stage-game. The second fact, that not every feasible payoff can be sustained by an equilibrium, is due to individual rationali ...
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a game-theoretic approach - Security and Cooperation in Wireless

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What Is Oligopoly?

... If both players are rational and choose their actions in this way, the outcome is an equilibrium called Nash equilibrium—first proposed by John Nash. Finding the Nash Equilibrium The following slides show how to find the Nash equilibrium. ...
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Prisoner's dilemma

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely ""rational"" individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it, ""prisoner's dilemma"" (Poundstone, 1992), presenting it as follows:Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is: If A and B each betray the other, each of them serves 2 years in prison If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with him, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other. The interesting part of this result is that pursuing individual reward logically leads both of the prisoners to betray, when they would get a better reward if they both kept silent. In reality, humans display a systematic bias towards cooperative behavior in this and similar games, much more so than predicted by simple models of ""rational"" self-interested action. A model based on a different kind of rationality, where people forecast how the game would be played if they formed coalitions and then they maximize their forecasts, has been shown to make better predictions of the rate of cooperation in this and similar games given only the payoffs of the game.An extended ""iterated"" version of the game also exists, where the classic game is played repeatedly between the same prisoners, and consequently, both prisoners continuously have an opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and Prisoner's Dilemma tournaments have been held to compete and test algorithms.The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behaviour. In casual usage, the label ""prisoner's dilemma"" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation.
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