Chapter 12 The core and balancedness

Of all solution concepts of cooperative games, the core is probably the easiest to understand. It is the set of all feasible outcomes (payoffs) that no player (participant) or group of participants (coalition) can improve upon by acting for themselves. Once an agreement in the core has been reached, no individual and no group could gain by regrouping. In a free market, outcomes should be in the core; economic activities should be advantageous to all parties involved. For many games, feasible outcomes that cannot be improved upon may not exist.. In such cases one possibility is to ask that no group could gain much by recontracting. It is as if communications and coalition formations are costly. The minimum size of the set of feasible outcomes required for non-emptiness of the core is given by the so-called balancedness condition. The sets containing outcomes upon which nobody could improve by much are called -cores. The chapter discusses the theory of cores in the case of transferable utility (TU) game, the theory of cores of games with non-transferable utility (NTU), and some economic applications of the theory.