Payoffs and Outcomes

Game Theory · Axiom Academy

Unit 1 - Introduction to Game Theory A payoff is a numerical value representing a player's satisfaction or utility from a particular outcome of the game. Payoffs can represent various real-world quantities: Monetary profit - dollars earned or lost in a business decision Utility - subjective satisfaction or happiness Years added/subtracted - in Prisoner's Dilemma (prison sentences) Points or scores - in competitive games The key insight: higher payoffs are always better for the player. A payoff of 5 is preferred to a payoff of 3, regardless of what those numbers represent. 2. Outcomes as Strategy Combinations An outcome is a complete description of what happens in the game - it's the result of all players choosing their strategies simultaneously. Player 1 chooses from strategies A, B Player 2 chooses from strategies X, Y There are 4 possible outcomes : (A,X), (A,Y), (B,X), (B,Y) In strategic form games, payoffs are typically displayed in a payoff matrix (also called a normal form or bimatrix game). Each cell contains the payoffs for all players at that outcome. Two friends trying to meet up can choose between Coffee Shop or Library. They each prefer meeting up to missing each other, but have different preferences about the location. 4. Ordinal vs. Cardinal Payoffs Understanding the difference between ordinal and cardinal payoffs is crucial for correctly analyzing games:

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