Payoff Matrix Examples

Game Theory · Axiom Academy

EXAMPLE Payoff Matrix Examples Learn to construct and analyze strategic form games step-by-step Game Scenario: The Advertising Battle Two competing coffee shops must decide whether to advertise heavily or not advertise at all. If both advertise, they split the market (each gets 3 units of profit) If neither advertises, they also split the market peacefully (each gets 5 units) If one advertises and the other doesn't, the advertiser captures the market (gets 8 units) while the other loses customers (gets 1 unit) Outcome: ( 3 , 3 ) - both split the market after advertising costs If Player 2 Advertises: P1 gets 3 (Advertise) vs 1 (Don't) → Advertise is better If Player 2 Doesn't Advertise: P1 gets 8 (Advertise) vs 5 (Don't) → Advertise is better Player 1's dominant strategy: Advertise (always yields higher payoff) By symmetry, Player 2 also has dominant strategy: Advertise Equilibrium: (Advertise, Advertise) with payoffs ( 3 , 3 ) Note: This is a Prisoner's Dilemma - both would be better off at (5,5) if neither advertised, but individual incentives lead to a worse outcome! Excellent work! You've mastered payoff matrix construction and analysis. Here's what we learned: Matrix Structure: Rows represent one player's strategies, columns represent the other player's strategies. Each cell contains both players' payoffs in the format (Player 1 payoff, Player 2 payoff).

This is the written version of the interactive lesson above. See the full Game Theory course.