... our example, these equations produce y1 (a21 a11 ) + y2 (a 22 a 12 ) = x (b 12 b11 ) + x (b 22 b21 ) = Since x = x and y2 = y1 , we get y1 (3 (2) ) + (1 y1 )(1 0) = y1 + (1 y1 ) = ... we get a two-person zero-sum game, A Note 2. 7 These are non-cooperative games with no side payments Denition 2. 2 The (pure) strategy (i , j ) is a Nash equilibrium solution to the game (A, B) ... players 2. 2 .2 Properties of Nash strategies Thanks to Esra E Aleisa for this question 2- 1 7 Denition 2. 3 The pure strategy pair (i1 , j1 ) weakly dominates (i2 , j2 ) if and only if ai1 ,j1 ai2 ,j2...