Equilibrium Points in Nonzero-Sum n-Person Submodular Games

TLDR: Submodular games as mentioned in this paper are finite non-cooperative games 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.

Abstract: 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. Examples of submodular games include 1) a game version of a system with complementary products; 2) an extension of the minimum cut problem to a situation where players choose from different sets of nodes and perceive different capacities, with special cases being a game with players choosing whether or not to participate in available economic activities and a game version of the selection problem; 3) the pricing problem of competitors producing substitute products; 4) a game version of the facility location problem; and 5) a game with players determining their optimal usage of available products. 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 join...