Editing Strategy (game theory) (section)

==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, a game of [[rock paper scissors]] comprises a single move by each player&mdash;and each player's move is made without knowledge of the other's, not as a response&mdash;so each player has the finite strategy set {rock paper scissors}.

A strategy set is infinite otherwise. For instance the [[Fair division|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]], games that are played over a series of time, the strategy set consists of the possible rules a player could give to a [[robot]] or [[Software agent|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]], or games in which players have incomplete information about one another, 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.

===Choosing a strategy set===
In applied game theory, the definition of the strategy sets is an important part of the art of making a game simultaneously solvable and meaningful. The game theorist can use knowledge of the overall problem, that is the friction between two or more players, to limit the strategy spaces, and ease the solution.

For instance, strictly speaking in the Ultimatum game a player can have strategies such as: ''Reject offers of ($1, $3, $5, ..., $19), accept offers of ($0, $2, $4, ..., $20)''. Including all such strategies makes for a very large strategy space and a somewhat difficult problem. A game theorist might instead believe they can limit the strategy set to: {Reject any offer ≤ ''x'', accept any offer > ''x''; for ''x'' in ($0, $1, $2, ..., $20)}.