Outcome (game theory)

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In game theory, the outcome of a game is the ultimate result of a strategic interaction with one or more people, dependant on the choices made by all participants in a certain exchange. It represents the final payoff resulting from a set of actions that individuals can take within the context of the game. Outcomes are pivotal in determining the payoffs and expected utility for parties involved.^[1] Game theorists commonly study how the outcome of a game is determined and what factors affect it.

In game theory, a strategy is a set of actions that a player can take in response to the actions of others. Each player’s strategy is based on their expectation of what the other players are likely to do, often explained in terms of probability.^[2] Outcomes are dependent on the combination of strategies chosen by involved players and can be represented in a number of ways; one common way is a payoff matrix showing the individual payoffs for each players with a combination of strategies, as seen in the payoff matrix example below. Outcomes can be expressed in terms of monetary value or utility to a specific person. Additionally, a game tree can be used to deduce the actions leading to an outcome by displaying possible sequences of actions and the outcomes associated.^[3]

A commonly used theorem in relation to outcomes is the Nash equilibrium. This theorem is a combination of strategies in which no player can improve their payoff or outcome by changing their strategy, given the strategies of the other players. In other words, a Nash equilibrium is a set of strategies in which each player is doing the best possible, assuming what the others are doing to receive the most optimal outcome for themselves.^[4] It is important to note that not all games have a unique nash equilibrium and if they do, it may not be the most desirable outcome.^[5] Additionally, the desired outcomes is greatly affected by individuals chosen strategies, and their beliefs on what they believe other players will do under the assumption that players will make the most rational decision for themselves.^[6] A common example of the nash equilibrium and undesirable outcomes is the Prisoner’s Dilemma game.^[7]