Game Theory ECON

Simultaneous Move Game

A game where players choose strategies at the same time using a payoff matrix

Sequential Move Game

A game where players move at different times using a game tree

Dominant Strategy

A strategy that gives a player the highest payoff regardless of the other player's choice

Dominant Strategy Equilibrium

An outcome where all players choose their dominant strategy

Nash Equilibrium

A strategy profile where each player's choice is the best response to the other's choice

Relationship Between Dominant Strategy and Nash Equilibrium

Every dominant strategy equilibrium is a Nash equilibrium, but not every Nash equilibrium involves dominant strategies

Payoff Matrix

A table showing outcomes for each strategy combination in a simultaneous game

Best Response

The strategy that maximizes a player's payoff given the other player's action

Prisoner's Dilemma

A Nash equilibrium where players end up worse off than a cooperative outcome

Conditions for a Prisoner's Dilemma

Mutual cooperation is better, but mutual defection is the Nash equilibrium

Oligopoly Quantity Game Example Outcome

Both firms choose high quantity in Nash equilibrium

Split-or-Steal Game Insight

"Steal" is a dominant strategy for both players, leading to a low-payoff equilibrium

Games With No Nash Equilibrium

Games like rock-paper-scissors and penalty kicks

Games With Multiple Nash Equilibria

Coordination games such as choosing left or right in driving

Repeated Game

A simultaneous game played many times, allowing cooperation and punishment strategies

Entry Game

A sequential game where a potential entrant chooses to enter and the incumbent chooses to fight or accommodate

Backward Induction

Solving a sequential game by analyzing decisions from the last move backward

Subgame Perfect Nash Equilibrium

A Nash equilibrium that is credible in every subgame, found through backward induction

First-Mover Advantage

When the player who moves first can secure a better outcome by committing early

Second-Mover Advantage

When reacting to the other player's move creates an advantage

Tariff Trade War Game Insight

Backward induction predicts both countries escalate tariffs due to incentives in each stage

Price-Matching Policy Effect

Removes incentives for competitors to undercut prices and shifts the game equilibrium

Price-Matching Sequential Result

Alpha chooses high, Beta chooses high, because low prices cannot gain an advantage under matching

Driving Coordination Game Insight

Two Nash equilibria exist: both choosing left or both choosing right

High Effort vs Low Effort Game Insight

Can form a prisoner's dilemma when mutual high effort is better but not stable

Repeated Oligopoly Game Insight

Repetition can sustain low-quantity collusion even though one-shot Nash is high quantity

Game Tree

A branching diagram showing sequential decisions and payoffs

Simultaneous Game Assumption

Players know the strategies and payoffs available to everyone

Sequential Game Assumption

Players know the full structure of the tree and all payoffs