Functional Dependence in Strategic Games (extended abstract)

Table 1: Coordination Game Note that in the case of the coordination game, we also have bBa. However, for the game described by Table 2 statement aBb is true, but bBa is false. The main focus of this paper is functional dependence in multiplayer games. For example, consider a “parity” game with three players a, b, c. Each of the players picks 0 or 1, and all players are rewarded if the sum of all three numbers is even. This game has four different Nash equilibria: (0,0,0), (0,1,1), (1,0,1), and (1,1,0). It is easy to see that knowledge of any two players’ strategies in a Nash equilibrium reveals the third. Thus, using our notation, for example a,bBc. At the same time, ¬(aB c). b1 b2 a1 1,1 0,0 a2 0,0 1,1 a3 1,1 0,0