The Nash equilibria of a 3-person game

Abstract

We consider 3-person games, where each player has a finite number of pure actions: players 1, 2 and 3 have respectively m, n and q pure actions. The payoffs can be described by three 3-dimensional matrices

$$\left[ {{a_i}_{jk}} \right]_{i = 1}^m,_{j = 1}^n,_{k = 1}^q,\left[ {{b_i}_{jk}} \right]_{i = 1}^m,_{j = 1}^n,_{k = 1}^q,\left[ {{C_{ijk}}} \right]_{i = 1}^m,_{j = 1}^n,_{k = 1}^q.$$

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