Game Theory

game theory

study of strategic interactions and payoffs

elements of game

players, strategies and payoffs

payoff matrix

represents payoffs for each player for each strategy

simultaneous move game

pick strategies at the same time

dominant strategy

one player's best response, regardless of what the other person does

dominant strategy equilibrium

when each strategy used is a dominant strategy

no dominant strategy

more than one equilibrium
the best choice for each is not the same

nash equilibrium

each player chooses a strategy that is best, given the strategies of others

requirements for nash equilibrium

all players understand the frame and the payoffs of each strategy
all players recognize that the other players understand the game and payoffs

tragedy of commons revisited

dominant strategy equilibrium leads to an outcome that is quite bad for both players together

zero-sum game

when one player wins, the other loses

pure strategy

always choosing one particular strategy for a situation

mized strategy

randomly choosing different strategies

extensive-form games

there is an order to play instead of simultaneous play

game tree

representation of an extensive-form game

backward induction

considering the last decision and deducing what the previous decisions have been

first-mover advantage

when the first player in a sequential game benefits from being first