7.3.2. Payoff

In game theory, a payoff represents the numerical outcome or value that a player receives based on the combination of strategies chosen by all players in a given game. Payoffs are used to quantify the benefits or costs associated with different combinations of actions taken by the players.

There are two common ways to represent payoffs in game theory, which is also provided in MLPro-GT-Native:

(1) Payoff Matrix: A payoff matrix is a table that shows the payoffs for each player corresponding to all possible combinations of strategies. In a two-player game, the matrix typically has rows representing the strategies of one player and columns representing the strategies of the other player. The intersection of a row and a column provides the payoffs to each player based on their chosen strategies. Payoffs can be expressed as numerical values, utility units, or any other relevant measure.

(2) Transfer Function: In some cases, especially in cooperative game theory, payoffs may be expressed using a transfer function. A transfer function describes how the total value or utility generated by a coalition of players is distributed among its members. It specifies how the payoff gained by the coalition is divided among individual players. Transfer functions are often used in cooperative games to model scenarios where players form alliances and share the benefits of their joint actions.

In summary, payoffs in game theory are the numerical outcomes associated with different combinations of strategies chosen by players. Whether represented in a payoff matrix or through transfer functions, payoffs provide a quantitative measure of the success or utility that each player obtains in a given strategic interaction.

• 7.3.2.1. Payoff Matrix
• 7.3.2.2. Transfer Function