Strategy (game Theory) - Strategy Set

A player's strategy set defines what strategies are available for them to play.

A player has a finite strategy set if they have a number of discrete strategies available to them. For instance, in a single game of Rock-paper-scissors, each player has the finite strategy set {rock, paper, scissors}.

A strategy set is infinite otherwise. For instance, an auction with mandated bid increments may have an infinite number of discrete strategies in the strategy set {$10, $20, $30, ...}. Alternatively, the Cake cutting game has a bounded continuum of strategies in the strategy set {Cut anywhere between zero percent and 100 percent of the cake}.

In a dynamic game, the strategy set consists of the possible rules a player could give to a robot or agent on how to play the game. For instance, in the Ultimatum game, the strategy set for the second player would consist of every possible rule for which offers to accept and which to reject.

In a Bayesian game, the strategy set is similar to that in a dynamic game. It consists of rules for what action to take for any possible private information.