Fast computation of the leastcore and prenucleolus of cooperative games

The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among N players. It has, however, the drawback being a linear programming problem with 2 − 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous coalitions. We also study the computation of prenucleolus, and display encouraging numerical results.