18.5 : Payoffs

In game theory, a payoff refers to the result a player receives based on their own actions and the actions of others. Payoffs are typically measured in terms of business profits or consumer satisfaction. They are central to decision-making, as players aim to choose strategies that maximize their payoff, given the potential responses of others.

A payoff matrix visually represents the possible outcomes for each combination of players' strategies. The matrix structure helps clarify the potential profits or losses the players might face.

For example, imagine two restaurants on the same street, Restaurant X and Restaurant Y. If each has a binary choice of either maintaining prices or offering discounts, there are four possible outcome scenarios with different payouts to each restaurant. The respective payoffs to their decisions are revealed in each cell of the payoff matrix. The first number in each pair represents the profit of Restaurant X, and the second number represents Restaurant Y's profit.

If both restaurants decide to keep regular prices, each might earn $500. However, if Restaurant X offers a discount while Restaurant Y keeps its prices high, Restaurant X could attract more customers, earning $700, while Restaurant Y earns only $300. The reverse would be true if Restaurant Y offers a discount and Restaurant X does not. Lastly, if both restaurants offer discounts, they each make only $400, as the competition reduces overall profits for both restaurants.

Analyzing the payoff matrix, each restaurant might aim to identify an equilibrium strategy—where neither restaurant has an incentive to deviate from their choice, given the competitor's best course of action.

The payoff matrix helps players visualize how different strategies interact and what results they can expect. By analyzing the matrix, each restaurant can predict how the competitor might act and adjust its pricing strategy accordingly to avoid losing profit or missing opportunities. This structured approach makes it easier for businesses to make informed decisions that maximize their payoffs while also considering potential competitive moves and their impacts.