# Game Theory

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therobbdj's
version from
2016-01-08 15:45

## Section

Question | Answer |
---|---|

Strict Dominance | Occurs 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 |

Rationalisability | Players 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 Equilibrium | A pair of strategies whereby each strategy is a best reply to the other, and there are no profitable deviations to be made |

Profitable Deviation | Occurs when a player can increase their utility by moving away from a proposed pair of strategies |

Reaction Function | The 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 Equilibrium | A 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 Equilibrium | A strategy profile whereby the action specified at each subgame is a Nash equilibrium |

Backward Induction | A method of solving extensive form games by working backwards from the terminal nodes, calculating the Nash Equilibrium of each subgame in-turn |

Extensive Form Game | A game which is expressed in the tree form. Occurs whenever there is a time concept in a game |

Normal Form Game | A game expressed using a payoff matrix. Occurs whenever each player is assumed to be playing simultaneously |

Infinitely-Repeated Game | If a game is infinitely-repeated, as long as the future is valuable enough, there is an incentive for cooperation to occur |

Trigger Strategy | A 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 Theorem | The 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 Equilibrium | An 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 Updating | Whenever 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) |

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