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Game Theory
Definitions of Terms From Games of Strategy by Dixit
62
Economics
12/29/2010

Term
 Non-Cooperative Game
Definition
 Games in which join action agreements are not enforceable
Term
 Screening
Definition
 strategy of a less-informed player to elicit information credibly from a more informed player
Term
 Signaling
Definition
 strategy of a more informed player to convey his “good” information credibly to a less informed player
Term
 Strategic Uncertainty
Definition
 a player uncertainty about an opponent’s moves made in the past or made at the same time as her own.
Term
 Rollback
Definition
 analyzing the choices that rational players will make at all nodes of a game, starting at the terminal nodes and working backward to the initial node.
Term
 Assurance Game
Definition
 a game where each player has two strategies, say cooperate and not, such that the best response of each is to cooperate if the other cooperates, not if not, and the outcome from (cooperate, cooperate) is better for both than the outcome of (not, not)
Term
 Best Response
Definition
 the strategy that is optimal for one player, given the strategies actually played by the other players, or the belief of this player about the other players’ strategy choices.
Term
 Dominance Solveable
Definition
 a game where iterated elimination of dominated strategies leaves a unique outcome, or just one strategy for each player.
Term
 Constant Sum Game
Definition
 a game in which the sum of all players’ payoffs is a constant, the same for all their strategy combinations.
Term
 Coordination Game
Definition
 - a game with multiple nash equilibria, where he player are unanimous about the relative merits of the equilibria
Term
 Focal Point
Definition
 a configuration of strategies for the players in a game, which emerges as the outcome because of the convergence of the players’ expectations on it.
Term
 Minimax
Definition
 in a zero-sum game, for the player whose strategies are arrayed along the columns, this is the minimum of the columns over the maximum attained for the same row-column pair.
Term
 Nash Equilibrium
Definition
 - a configuration of strategies one for each player) such that each player’s strategy is best for him, given those of the other players (can be in pure or mixed strategies)
Term
 Continuous Strategy
Definition
 a choice over a continuous range of real numbers available to a player.
Term
 Opponent's Indifference Property
Definition
 A probability such that the equilibrium mixture of strategies yields equal expected payoffs
Term
Definition
 Information asymmetry where a player's type is private information
Term
 Babbling Equilibrium
Definition
 Equilibrium that is chosen disregarding communication
Term
 Bayesian-Nash Equilibrium
Definition
 Players use their best actions and infer informations from the actions of others
Term
 Cheap Talk Equilibrium
Definition
 Strategies are chosen using players' interpretation of communication, and the communication is chose by calculating the actions that will ensue
Term
 Incentive-Compatability Conditions (Contstraints)
Definition
 Constraints on an incentive scheme that makes it optimal for the agent of each type to reveal his true type through his actions
Term
 Moral Hazard
Definition
 A situation of asymmetry where one player's actions are not directly observable by others
Term
 Partially Revealing Equilibrium
Definition
 A perfect Bayesian equilibrium in a game of incomplete information where actions reveal some information of the players' types
Term
 Participation Condition (Constraint)
Definition
 A constraint on an incentive scheme or screening device that gives the more informed player an expected payoff at least as high as without it
Term
 Perfect Bayesian Equilibrium
Definition
 An equilibrium where each player's strategy is optimal at all nodes given his beliefs and beliefs at each node are updatet using information available
Term
 Pooling Equilibrium
Definition
 A perfect Bayesian Equilibrium in a game of assymmetric information where actions in the equilibrium cannot be used to distinguish type
Term
 Type
Definition
 Players who posses different private information in a game of asymmetric information
Term
 Semiseparating Equilibrium
Definition
 A perfect Bayesian equilibrium in a game of incomplete information where actions reveal some information of the players' types
Term
 Contingent Strategy
Definition
 plan of action that depends on other players' actions in previous plays
Term
 Discount Factor
Definition
 In a repeated game, the fraction by which the next period's payoffs are multiplied to make them comparable with this period's payoffs
Term
 Effective Rate of Return
Definition
 Rate of return corrected for the probability of noncontiuation of an investment
Term
 Grim Strategy
Definition
 A strategy of noncooperation forever in the future. Used as a threat of punishment in an attempt to sustain cooperation
Term
 Infinite Horizon
Definition
 A repeated game that has no definite end
Term
Definition
 In a prisoner's dilemma with asymmetric players a situation where a large player chooses to cooperate even though he knows that the smaller player will cheat
Term
 Penalty
Definition
 One time costs that induces plays to take actions that are in their joint interests
Term
 Present Value
Definition
 Total payoff over time multiplied by the appropriate discount factor to make them comparable to the initial period's payoffs
Term
 Punishment
Definition
 Costs that can be inflicted on an individual to induce him to take actions that are in the joint interests of all players
Term
 Repeated Play
Definition
 One time game is played repeatedly in successive periods
Term
 Tit-for-Tat
Definition
 In a repeated prisoners dilemma, cooperating on the first play and doing each period what the other player did the previous
Term
 Trigger Strategy
Definition
 Cooperate until a rival chooses to defect, then switches to noncooperation for a specified period.
Term
 Coercion
Definition
 Same as opression, forcing a player to accept a lower payoff in asymmetric equilibrium while favored players get higher payoffs
Term
 Collective Action Problem
Definition
 A problem of achieving an outcome that is best for society as a whole even if the payoffs for individuals leads to a different equilibrium
Term
 Convention
Definition
 A mode of behavior that is automatically a focal point because it is in each individual's interest to follow it when others are expected to follow too.
Term
 Custom
Definition
 A mode of behavior that is automatically a focal point because it is in each individual's interest to follow it when others are expected to follow too.
Term
 Externality
Definition
 When one person's action affects the payoff of another person
Term
 Internalize the Externality
Definition
 Offer a reward or penalty for the external benefits of harm of an individual's actions by bringing his private incentives in line with social optimality
Term
 Locked In
Definition
 A situation where players continue in one Nash equilibrium that is worse for everyone than another Nash equilibrium
Term
 Marginal Private Gain
Definition
 The change in an individuals payoff as the result of a small change in his continuous strategy
Term
 Marginal Social Gain
Definition
 The change in aggregate as the result of a small change in his continuous strategy
Term
 Nonexcludable Benefits
Definition
 Benefits that are available to each individual regardless if he has paid the costs
Term
 Nonrival Benefits
Definition
 Benefits that when enjoyed by one person does not detract from another person's enjoyment of the same benefits
Term
 Norm
Definition
 A pattern of behavior that is established in society by a process of education or culture. Someone who behaves differently experiences a negative payoff
Term
 Opression
Definition
 Same as coercion, forcing a player to accept a lower payoff in asymmetric equilibrium while favored players get higher payoffs
Term
 Pluralistic Ignorance
Definition
 A situation of collective action where no individual knows the right action, so everyone takes cues from each other possibly resulting in the persistence of wrong choices
Term
 Pure Public Good
Definition
 A good or facility that benefits all members of a group, nobody can be excluded and one person's enjoyment does not detract from others
Term
 Sanction
Definition
 Punishment approved by society for someone who violates an accepted pattern of behavior
Term
 Social Optimum
Definition
 In a collective game when the payoffs of individuals can be summed, the sum of the total players' payoffs is maximized
Term
 Spillover Effect
Definition
 Externality, When one person's action affects the payoff of another person
Term
 Mechanism Design
Definition
 The process that the more informed player uses to devise the correct set of incentives for the less informed player
Term
 Price Discrimination
Definition
 A firm charging an individualized prices based on willingness to pay
Term
 Principal
Definition