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Profile Documents Logout
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The Monopolistic Competitor:
The Monopolistic Competitor:

... do not choose the same thing because if they choose the same thing, you do the game again. e. There is no pure strategy in Rock, Paper, Scissors that’s a Nash Equilibrium GT-5) In game theory, a “mixed strategy” means the player should a. choose a different strategy than your opponent b. choose the ...
An Introduction to Game Theory
An Introduction to Game Theory

... isolation, for convenience if not for anything else. In other words, they assume that to understand ...
How much would you pay to change a game before
How much would you pay to change a game before

... is unobserved by all other players, DM’s willingness to pay to change the parameter values is given by the sum of two factors. The first factor is how the change directly affects DM’s payoffs, holding the strategies of all players constant (including DM’s). The second factor is how DM optimally adju ...
Symmetric Nash equilibria
Symmetric Nash equilibria

Lecture Notes on Adverse Selection and Signaling
Lecture Notes on Adverse Selection and Signaling

... decision depends on her unobservable characteristics in a manner that adversely affects the uninformed agents in the market. In the labor market context, adverse selection arises only relatively less capable workers accept a firm’s employment offer at any given wage. From our illustration in last se ...
Subsidization to induce tipping
Subsidization to induce tipping

... primary result of this paper is that asymmetric subsidy programs will eliminate the inferior equilibrium at less expense to the government agency than a uniform subsidy program, whether or not all agents are identical and even if private values are anonymous. The asymmetric subsidy scheme which we d ...
Chapter 9: Reflective Reason and Equilibrium Refinements
Chapter 9: Reflective Reason and Equilibrium Refinements

... this the local best response (LBR) criterion. The LBR criterion appears to render the traditional refinement criteria superfluous. The traditional refinement criteria are all variants of subgame perfection, and hence suffer from the fact that there is generally no good reason for rational agents to ...
Walrasian Analysis via Two-Player Games
Walrasian Analysis via Two-Player Games

... The extension of the Cournot tradition to general equilibrium was pioneered by the already cited works by Shubik (1973), Shapley (1976) and Shapley and Shubik (1977). In order to overcome the difficulty that an agent might want to sell in one market and buy in another, Shapley and Shubik explicitly ...
Stochastically stable states in an oligopoly with differentiated goods
Stochastically stable states in an oligopoly with differentiated goods

... assumptions about the behavior of firms, the quantity setting or Cournot approach and the price setting or Bertrand approach. It is well understood that in an oligopoly with substitutes, the Bertrand equilibrium is more efficient than the Cournot equilibrium ŽSee Singh and Vives, 1984; Cheng, 1985; ...
Continuous Time Contests with Private Information
Continuous Time Contests with Private Information

Context$Dependent Forward Induction Reasoning
Context$Dependent Forward Induction Reasoning

... cannot play.) In particular, the convention corresponds to a type structure, where each type of Bob assigns probability one to Ann’s playing Up. (In Section 3, we formally describe the type structure corresponding to the lady’s choice convention.) Under this convention, a rational Bob plays Out, thi ...
Coalition-Proof Equilibrium
Coalition-Proof Equilibrium

... strategy equilibrium consists of players 1 and 2 each choosing heads Žtails. and player 3 choosing tails Žheads.. In the mixed strategy equilibrium each player chooses heads with probability 12 . The game does not have a CPNE, as each of the Nash equilibria is upset by a deviation of the coalition o ...
Closed
Closed

On extensive form implementation of contracts in differential
On extensive form implementation of contracts in differential

... A PBE consists of a set of players’ optimal behavioral strategies, and consistent with these, a set of beliefs which attach a probability distribution to the nodes of each information set. Consistency requires that the decision from an information set is optimal given the particular player’s beliefs ...
Non-Additive Beliefs in Solvable Games
Non-Additive Beliefs in Solvable Games

Chapter 16
Chapter 16

Negotiation joint plans/schedules for agents Worth
Negotiation joint plans/schedules for agents Worth

Stochastic Learning Dynamics and Speed of Convergence in
Stochastic Learning Dynamics and Speed of Convergence in

... Nash equilibrium is the central solution concept for noncooperative games, but many natural learning dynamics do not converge to Nash equilibrium without imposing strong conditions on the structure of the game and/or the players’ level of rationality. Even in those situations where the learning dyna ...
Hard-core measures
Hard-core measures

b strategic interaction in static industries: oligopolistic competition
b strategic interaction in static industries: oligopolistic competition

... maximization. Moreover, players' rationality is common knowledge. An event E is defined to be common knowledge if all players know E, all players know that all other players know E, all players all players know that all other players know that all other players know E, ad infinitum. The second basic ...
e-Consistent equilibrium in repeated games - IMJ-PRG
e-Consistent equilibrium in repeated games - IMJ-PRG

Perfect Correlated Equilibria
Perfect Correlated Equilibria

The Complexity of Partial-observation Stochastic Parity Games With
The Complexity of Partial-observation Stochastic Parity Games With

... and an action in A1 gives the next state in S2 (which belongs to player 2); and δ : SP → D(S1 ) given a probabilistic state gives the probability distribution over the set of player-1 states. The set of edges is as follows: E = {(s, t) | s ∈ SP , t ∈ S1 , δ(s)(t) > 0} ∪ E ′ , where E ′ ⊆ S2 × SP . T ...
On the Formal Semantics of IF-like Logics
On the Formal Semantics of IF-like Logics

Long run equilibria in an asymmetric oligopoly
Long run equilibria in an asymmetric oligopoly

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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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