XI. Game theory
XI. a. Introduction & definitions
- Game theory modelling strategic behaviour by agents/players understanding
actions of some agents impacting actions of other agents interdependence
between actions of agents
- Applications of game theory: study of oligopolies (pricing based on other firms’
pricing), study of joint monopolies (i.e., cartels ≠ conducive to cooperation &
likely of deviation from price), study of military strategies & auctions
- Game consisting in:
o Set of players
o Set of strategies for each player
o Payoffs to each player for every possible combination of strategies by
players
- Table showing payoffs to players for each of possible action combinations =
game’s payoff matrix
- Example of two-player game
Players 1 & 2
Player 1 – two actions: Up & Down
Player 2 – two actions: Left & Right
Game’s payoff matrix: player 1’s (row player) payoff shown first ; player 2’s (column
player) payoff
XI. b. Predicting outcomes
- Predictions using dominance criterion for comparing strategies predicting
outcome
- Strictly dominant strategy = strategy producing higher payoff than any other
strategy for every possible combination of rivals’ strategies
o Strategy = strictly dominant when beating every other strategy
regardless of other players’ play
- Strictly dominated strategy (by at least one other strategy) = strategy
producing lower payoff than one alternative strategy for every possible
combination of other players’ strategies
o Strategy = strictly dominated when at least one other strategy beating
strategy regardless of players’ play
XI. a. Introduction & definitions
- Game theory modelling strategic behaviour by agents/players understanding
actions of some agents impacting actions of other agents interdependence
between actions of agents
- Applications of game theory: study of oligopolies (pricing based on other firms’
pricing), study of joint monopolies (i.e., cartels ≠ conducive to cooperation &
likely of deviation from price), study of military strategies & auctions
- Game consisting in:
o Set of players
o Set of strategies for each player
o Payoffs to each player for every possible combination of strategies by
players
- Table showing payoffs to players for each of possible action combinations =
game’s payoff matrix
- Example of two-player game
Players 1 & 2
Player 1 – two actions: Up & Down
Player 2 – two actions: Left & Right
Game’s payoff matrix: player 1’s (row player) payoff shown first ; player 2’s (column
player) payoff
XI. b. Predicting outcomes
- Predictions using dominance criterion for comparing strategies predicting
outcome
- Strictly dominant strategy = strategy producing higher payoff than any other
strategy for every possible combination of rivals’ strategies
o Strategy = strictly dominant when beating every other strategy
regardless of other players’ play
- Strictly dominated strategy (by at least one other strategy) = strategy
producing lower payoff than one alternative strategy for every possible
combination of other players’ strategies
o Strategy = strictly dominated when at least one other strategy beating
strategy regardless of players’ play
