game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

and related fields, a game form, game frame, ruleset, or outcome function is the set of

rules Rule or ruling may refer to: Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule tha ...

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 A public utility company (usually just utility) is an organization that maintains the infrastructure for a public service (often also providing a service using that infrastructure). Public utilities are subject to forms of public control and r ...

or payoffs for each agent. Mathematically, a game form can be defined as a mapping going from an ''action'' ''space''—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. For example, an

electoral system An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

is a game form mapping a message space consisting of

ballot A ballot is a device used to cast votes in an election and may be found as a piece of paper or a small ball used in voting. It was originally a small ball (see blackballing) used to record decisions made by voters in Italy around the 16th cent ...

s to a winning candidate (the outcome). Similarly, an

auction An auction is usually a process of Trade, buying and selling Good (economics), goods or Service (economics), services by offering them up for Bidding, bids, taking bids, and then selling the item to the highest bidder or buying the item from th ...

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. Often, a game form is a set of rules or

institution An institution is a humanly devised structure of rules and norms that shape and constrain social behavior. All definitions of institutions generally entail that there is a level of persistence and continuity. Laws, rules, social conventions and ...

s designed to implement some

normative Normativity is the phenomenon in human societies of designating some actions or outcomes as good, desirable, or permissible, and others as bad, undesirable, or impermissible. A Norm (philosophy), norm in this sense means a standard for evaluatin ...

goal (called a social choice function), by motivating agents to act in a particular way through an appropriate choice of

incentive In general, incentives are anything that persuade a person or organization to alter their behavior to produce the desired outcome. The laws of economists and of behavior state that higher incentives amount to greater levels of effort and therefo ...

s. Then, the game form is called an implementation or mechanism. This approach is widely used in the study of

auctions An auction is usually a process of Trade, buying and selling Good (economics), goods or Service (economics), services by offering them up for Bidding, bids, taking bids, and then selling the item to the highest bidder or buying the item from th ...

and

s. 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 design Mechanism design (sometimes implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called Game form, mechanisms or institutions—that produce good outcomes according to Social ...

er'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.

References

Game theory Mechanism design Social choice theory {{econ-stub