EQUILIBRIUM POINTS IN NON-ZERO-SUM N-PERSON SUBMODULAR GAMES

A submodular game is a finite noncooperative game in which the set of feasible joint decisions is a sublattice and the cost function of each player has properties of submodularity and antitone differences. A fixed point approach establishes the existence of a pure equilibrium point for certain submodular games. Two algorithms which correspond to fictitious play in dynamic games generate sequences of feasible joint decisions converging monotonically to a pure equilibrium point. Bounds show these algorithms to be very efficient when the set of feasible decisions is finite. An optimal decision for each player is an isotone function of the decisions of other players.