Payoff Function

A Payoff Function is a objective utility function that defines a decision reward.

• AKA: Game-Centric Utility Function.
• Example(s):
  • a Roulette Game Payoff Function.
  • a Game of Life Payoff Function.
  • a Slot Machine Payoff Function.
  • …
• Counter-Example(s):
  • an Decision-Maker Utility Function.
• See: Deontology, Expected Utility.

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References

2015

• http://en.wiktionary.org/wiki/payoff_function
  • A mathematical function describing the award given to a single player at the outcome of a game.

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Normal-form_game Retrieved:2014-9-1.
  • … In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, whereas a strategy is a complete plan of action for every stage of the game, regardless of whether that stage actually arises in play. A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility — often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a strategy profile (that is a specification of strategies for every player) and yields a representation of payoff as its output.

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