Game Theory

simultaneous move games

players make decisions at same time (blind)

SPE subgame perfect equilibrium

A complete and contingent plan of action. States what all players would do at a particular decision node whether or not they actually reach that node in equilibrium.

Nash equilibrium

A set of strategies, one for each player, where no player has an incentive to change his/her strategy. (No regrets) Not necessarily the best deal.

Backward Induction

Finds the subgame perfect equilibrium by starting at the end of the game, and uses that information to decide how players will behave at the beginning of the game.

IESDS

Iterated Elimination of Strictly Dominated Strategies Simplifies the game by removing strategies a player would never choose. (order doesn't matter when removing IESDS, and no Nash Equilibrium is removed)

IESWS

Iterated Elimination of Weakly Dominated Strategies Simplifies the game by removing strategies a player would never choose. (order matters when removing IEWDS, and you might remove a Nash Equilibrium)

Best response

Strategy(ies) that produce the greatest payoff depending on what other players choose.

Prisoner's Dilemma

Two person game that demonstrates how dominant strategies can lead to an inefficient Nash Equilibrium

Mixed strategy algorithm

derives mixed strategy Nash Equilibria by finding the particular mixed strategies that leave the other player indifferent between his/her two pure strategies

Backward induction

figure out what decisions led you to an outcome

Second price auctions

highest bidder wins but only has to pay whatever the second highest bidder put down

Payoff Matrix

shows every outcome. includes: players, strategies (choices such as up/down), and payoffs

dominant strategy

strategy preferred by player regardless of opponents move

expected utilities in MSNE

weighted averages of each of the outcomes that occur in equilibrium