Cores,aggressiveness and the breakdown of cooperation in economic games

The paper develops the use of the core as a solution concept in game theory in two interrelated directions. In the first place, an indicator of aggressiveness of claims is introduced in a modified definition of the core. The modified core may be smaller than the usual core, and may fail to exist if aggressiveness increases beyond some critical level. In the second place the article gives a formulation of a mixed cooperative/non-cooperative game, in which the game will be played cooperatively within coalitions, but non-cooperatively as between coalitions. A mixed cooperative/non-cooperative solution obtains if the grand coalition of all players fail to materialize because the various claims are incompatible. The two directions referred to are interrelated because the level of aggressiveness may be decisive for whether or not the grand coalition, and possibly other coalitions, will break down. The final section of the paper draws some general conclusions and relates the approach to other ideas in the literature.