 Definition 3.2  A game \(\Gamma\) is an ordered triple \((N, S, \boldsymbol{u})\) consisting of the following elements:   A finite set \(N = \{1,2, \ldots ,n\}\), called the set of agents or players. For each agent \(k \in N\), there is a finite set \(S_k = \{s_{k1},s_{k2}, \ldots ,s_{kn_k}\}\), called the alternative pure strategies for agent \(k\). The Cartesian product \(S = S_1 \times \ldots \times S_n\) is called the pure strategy set for the game \(\Gamma\). A map \(\boldsymbol{u} : S \rightarrow \Re^n,\) called the utility or payoff function on the pure strategy set. At each strategy combination \(\boldsymbol{s} = (s_{1j_1}, \ldots ,s_{nj_n}) \in S\), agent \(k\)’s particular payoff or utility is given by the \(k\)th component of the value of \(\boldsymbol{u}\), that is, agent \(k\)’s utility \(u_k\) at \(\boldsymbol{s}\) is determined by   \[ u_k (\boldsymbol{s}) = I_k (\boldsymbol{u}(s_{1j_1}, \ldots ,s_{nj_n})) \]   where \(I_k (\boldsymbol{x})\) projects \(\boldsymbol{x} \in \Re^n\) onto its \(k\)th component.   