Market games in large economies with a finite number of types ∗

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley-Shubik theorem on market games (1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players.