Local stability and optimality in continuous games

We study games with continuous payoff functions $J_i (\sigma _1 , \cdots ,\sigma _N )$, $i = 1, \cdots ,N$, where a strategy for player $i$ is to choose a real number $\sigma _i $ and is pure. Small adjustments by coalitions and responses by other coalitions are analyzed on the basis that one coalition may discipline another if the latter makes an adjustment which is favorable to itself. This concept provides a natural definition for defensive coalitions and for optimality based on a pair of coalitions which are both defensible. More general optimal states for the whole game, under limited information conditions, contain all the well-known optima and are closely related to the limiting states of an explicit time-dependent adjustment process. The optima are supported by the data of Fouraker and Siegel and the sequences of adjustments in their experiments are clarified.