Game theory is a set of tools for analyzing strategic decision-making involving two or more opponents. A game involves players with different strategies and payoffs that depend on the strategies chosen. Games can be zero-sum, where one player's gains equal another's losses, or non-zero-sum. Pure strategies prescribe a single strategy, while mixed strategies randomly select among multiple strategies. Zero-sum games with a finite number of pure strategies may have a pure strategy equilibrium or require mixed strategies if no pure strategy saddle point exists. Linear programming can be used to solve for mixed strategy equilibria in such games.