The Epsilon Core of a Large Replica Game

Cooperative behavior lies at the very heart of economics and the fundamental concept of a cooperative social equilibrium is the core. However, the power of the core concept is limited by the fact that the nonemptiness of the core can be assured only in certain ideal environments. In this paper, it is shown. that all members of a class of games with many players and relatively few types of players have non-empty approximate cores and the approximation can be made better as the number of players increases. Since Shapley and Shubik (1966) first introduced concepts of approximate cores, a number of authors have demonstrated sufficient conditions for nonemptiness of approximate cores of large economies, cf. Kannai (1969, 1970), Hildenbrand, Schmeidler and Zamir (1973), and Khan and Rashid (1975). With the exception of Khan and Rashid’s work, all these results deal only with the exchange of private goods; Khan and Rashid consider production with the firms exogenously given. Recently, this author obtained sufficient conditions for non-emptiness of approximate cores of large replica economies with a local public good and endogenous jurisdiction formation [Wooders