Two-level cooperation in a class of non-zero-sum differential games

Abstract

A two-level game is considered. At the first level, the set of players N is partitioned into coalitions Si ⊂ N, i = 1, . . ., m, such that Si ∩ Sj = ∅ for i 6= j and each coalition plays against other coalitions a non-zero-sum cooperative differential game with prescribed duration and nontransferable payoffs. At the second level, within each coalition, the players are engaged in a cooperative differential game with prescribed duration and transferrable payoffs. The concept of solution is proposed for this type of two-level games. The properties of a solution, namely, its time consistency or dynamic stability, are studied. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.