noncooperative (Nash) equilibrium solution

Definition

A pair of strategies {row i*,column j*}\{\text{row } i^*, \text{column } j^*\} is said to constitute a noncooperative (Nash) equilibrium solution to a bimatrix game if the following pair of inequalities is satisfied for all i=1,...,mi=1,...,m and all j=1,...,nj=1,...,n: ai*j*≤aij*bi*j*≤bi*j\begin{align} a_{i^* j^*} \leq a_{ij^*} \\ b_{i^* j^*} \leq b_{i^* j} \end{align} The pair (ai*j*,bi*j*)(a_{i^* j^*}, b_{i^* j^*}) is known as a noncooperative (Nash) equilibrium outcome of the bimatrix game.

References

  1. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999, pp. 78-79.