Continuous Static Games

Abstract

Let N denote the number of players . It is usually assumed that the set of all feasible strategies of each player has at least two elements. If \(S_k\) is the strategy set of player k, then its payoff function \(\phi _k\) is defined on the set of all simultaneous strategies , which is denoted by \(S=S_1 \times S_2 \times \dots \times S_N\), and \(\phi _k(\underline{s})\), for all \(\underline{s} \in S\) is a real number. The normal form of the game is given as \(G=\{ N; S_1, S_2, \dots , S_N; \phi _1, \dots , \phi _N \}\). The game is continuous, if all sets \(S_k\) are connected and all payoff functions \(\phi _k\) are piecewise continuous.