In game theory and related fields, a game form, game frame, ruleset, or outcome function is the set of rules that govern a game and determine its outcome based on each player's choices. A game form differs from a game in that it does not stipulate the utilities or payoffs for each agent.[1]
Mathematically, a game form can be defined as a mapping going from an actionspace[2][3]—which describes all the possible moves a player can make—to an outcome space. The action space is also often called a message space when the actions consist of providing information about beliefs or preferences, in which case it is called a direct mechanism.[3] For example, an electoral system is a game form mapping a message space consisting of ballots to a winning candidate (the outcome).[1] Similarly, an auction is a game form that takes each bidder's price and maps them to both a winner and a set of payments by the bidders.
The social choice function represents the desired outcome or goal of the game, such as maximizing social welfare or achieving a fair allocation of resources. The mechanism designer's task is to design the game form in such a way that when each player plays their best response (i.e. behaves strategically), the resulting equilibrium implements the desired social choice function.
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