game theory
3 parts of a game theory
1. A game has players 2. A game has actions the players can take 3. A game has outcomes that result from those actions
when is the normal form best used?
The Normal Form is best used when representing a 2-player game where the players are moving simultaneous or each player makes his or her decision without knowing the action of the other player
dynamic game
a game in which players move sequentially • These types of games can be represented by the Extensive Form
extensive form
a game tree showing which player moves at each stage of the game and the actions available to that player
normal form
a matrix with the rows representing the actions of one player, the columns representing the actions of the other player, and the cells representing the outcomes from those actions
mixed strategy
a strategy that assigns probabilities to each action at each possible stage of the game
dominant strategy
a strategy that is the best response no matter what the strategies of the other players
nash equilibrium
each player's strategy is a best response to the strategies of the other players
best response
the strategy that results in the most favorable outcome for a player given the strategies of the other players
nash equilibrium
• A game with finitely many players and finitely many actions for each player always has at least one Nash Equilibrium • Note that the Nash Equilibrium may require the players use mixed strategies
strategy
• A strategy specifies the actions a player will take at each possible stage of the game
game theory
• Game Theory studies strategic behavior in situations where each person's outcome depends on everyone's actions • In deciding which action to take, you have to consider how other people will respond to it, and they have to consider how you will respond to their actions • A classic example in Game Theory is the Prisoners' Dilemma
dynamic games
• In Dynamic Games, you find the Nash Equilibrium by working backwards • Find the best response in the last turn first, and then find the best response in the nextto-last turn given the best response in the last turn • Continue backwards to find the strategies for each player and the Nash Equilibrium
prisoner's dilemma
• In the Prisoners' Dilemma, there are 2 players • These players are criminals who have been arrested • While being interrogated by the police, each player has 2 actions: confess to the crime or don't confess to the crime • The outcome for each player is the jail time that results from both players' actions
repeated games
• Repeated Game - the same game is played over and over by the same players • Players may cooperate in a repeated game even if they don't when the game is only played once • Potentially cooperating in the future provides incentives to cooperate now