Read the summary and the most important questions on Games and Information An Introduction to Game Theory | 9781405136662 | Eric Rasmusen

• 1 The rules of the game

• 1.1 Definitions

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• What are the essential elements of a game?

   players, actions, payoffs, andinformation— PAPI

• 1.2 Dominated and dominated strategies: the prisoners dilemma

• Describe a dominated strategy

  The strategy sd i is a dominated strategy if it is strictly inferior to some other strategy no matter what strategies the other players choose, in the sense that whatever strategies they pick, his payoff is lower with s

• Describe a dominant strategy

  The strategy s∗ i is a dominant strategy if it is a player’s strictly best response to any strategies the other players might pick, in the sense that whatever strategies they pick, his payoff is highest with s∗

• Describe the prisoners dilemma

  Whenever you observe individuals in a conflict that hurts them all, your first thought should be of the Prisoner’s Dilemma.

• Describe a cooperative game

  A cooperative game is a game in which the players can make binding commitments, as opposed to anoncooperative game, in which they cannot.

• 1.3 Iterated dominance: the battle of the bismarck see

• Describe a weakly dominated strategy

  Strategy s0 i is weakly dominated if there exists some other strategy s00 i for player i which is possibly better and never worse, yielding a higher payoff in some strategy profile and never yielding a lower payoff.

• Describe an iterated dominance equilibrium

  An iterated dominance equilibrium is a strategy pro file found by deleting a weakly dominated strategy from the strategy set of one of the players, recalculating to find which remaining strategies are weakly dominated, deleting one of them, and continuing the process until only one strategy remains for each player.

• Describe a zero-sum game

  A zero-sum game is a game in which the sum of the payoffs of all the players is zero whatever strategies they choose. A game which is not zero-sum is nonzero-sum game or variable- sum.

• 1.4 Nash equilibrium

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• When is there a nash equilibrium

  The strategy pro file s∗ is a Nash equilibrium if no player has incentive to deviate from his strategy given that the other players do not deviate.

• Describe a battle of the sexes game

  The third game we will use to illustrate Nash equilibrium is the Battle of the Sexes, a conflict between a man who wants to go to a prizefight and a woman who wants to go to a ballet. While selfish, they are deeply in love, and would, if necessary, sacrifice their preferences to be with each other.