Game form

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).

Often, a game form is a set of rules or institutions designed to implement some normative goal (called a social choice function), by motivating agents to act in a particular way through an appropriate choice of incentives.

[4] 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.