# Game Theory

version from 2016-01-08 15:45

## Section

Strict DominanceOccurs when the utility gained from playing a strategy si is strictly less than the utility gained from playing strategy si* regardless of the strategy of the other player
RationalisabilityPlayers use all information available to them in order to maximise utility (allows us to iteratively eliminate strictly dominated strategies in order to narrow down the potential strategies of each player)
Nash EquilibriumA pair of strategies whereby each strategy is a best reply to the other, and there are no profitable deviations to be made
Profitable DeviationOccurs when a player can increase their utility by moving away from a proposed pair of strategies
Reaction FunctionThe set of all combinations of output that are profit maximising (given the other firm). Found by differentiating a firm's profit function and setting the result equal to zero
Mixed Nash EquilibriumA pair of mixed strategies whereby each mixed strategy is a best reply to the other, and there are no profitable deviations to be made
Subgame Perfect EquilibriumA strategy profile whereby the action specified at each subgame is a Nash equilibrium
Backward InductionA method of solving extensive form games by working backwards from the terminal nodes, calculating the Nash Equilibrium of each subgame in-turn
Extensive Form GameA game which is expressed in the tree form. Occurs whenever there is a time concept in a game
Normal Form GameA game expressed using a payoff matrix. Occurs whenever each player is assumed to be playing simultaneously
Infinitely-Repeated GameIf a game is infinitely-repeated, as long as the future is valuable enough, there is an incentive for cooperation to occur
Trigger StrategyA strategy for a game which changes whenever certain criteria are met. Can be a Nash Equilibrium as long as the future is valuable enough
Folk TheoremThe observation that in repeated games, people will cooperate in order to maximise each others' utility. When one person deviates, they are punished. This occurs as long as society as a whole is patient
Perfect Bayesian EquilibriumAn equilibrium whereby, for any player and their information sets, the actions that their strategy specifies at that information set must maximise their expected payoff given their beliefs (specified using Bayes' Rule whenever possible) and given the subsequent play of the game
Bayesian UpdatingWhenever a play in an extensive format game receives additional information, they are able to update their beliefs regarding the likelihood of receiving a certain payoff (given by Bayes' Rule)