Game theory Flashcards
What is a dominant strategy?
A player has a (strictly) dominant strategy if, for each possible action that his opponent can take, that strategy leads to a payoff that is strictly greater than the payoff associated with any of his other strategies
• A player can have no more than one dominant strategy and in many games will have none
If a rational player has a dominant strategy, he must play it
What is the prisoner dilema?
What is a dominated stategy?
A player has a (strictly) dominated strategy if, for each possible action that his opponent can take, he has another strategy that leads to a payoff that is strictly greater than the payoff associated with the original strategy
A rational player will never play a dominated stategy
This works if players are rational
common knowledge of player’s rationality and payoffs
common knowledge of the rules of the game
What is best response?
A strategy, x, is a best response for a player to an opposition strategy if, given that opposition strategy, the strategy x achieves at least as high a payoff as any other strategy that is available
What is Nash equllibrium?
A NE is a set of strategies, one for each player, such that each player’s strategy is a best response to the other players’ strategies
In order for the NE of a game to be a compelling solution assumes:
– Players are rational
– The rules of the game are common knowledge
– Common knowledge of players’ rationality
– A source of ‘Common Beliefs’ (essentially, shared understanding of how the game will be played)
• Focal Points • Pre-game communication • Learning • Convention
what are the advantages to moving first or second in an extensive game?
In some games (typically those with multiple NE) there is an advantage to moving first.
In others there is an advantage to moving second (typically those with no NE).
Finally, in some games the order of play makes no difference (typically those with one NE)
