Lattice games

Lattice games are real-valued functions de...ned on a ...nite lattice L. The basic players are the nonzero join-irreducible elements of the lattice and the coalitions are its elements. If L is the Boolean algebra 2 then we obtain a n-person game. Gilboa and Lehrer introduced the global games, which are lattice games where L = ¦n, the lattice of all partitions of N ordered by re...nement. Faigle and Kern investigated a special type of cooperative game with precedence constraints. In this model L is the distributive lattice of the order ideals of a partially ordered set. We study two special classes of lattice games: topological games and convex geometry games. Finally, we de...ne the join and the union Shapley values for decomposition of coalitions with the join and the set-union operations. AMS subject classi...cations (1991). 90D12, 06B05, 52B40