Core and Stable Sets of Large Games Arising in Economics

It is shown that the core of a non-atomic glove-market game which is defined as the minimum of finitely many non-atomic probability measures is a von-Neumann Morgenstern stable set. This result is used to characterize some stable set of large games which have a decreasing returns to scale property. We also study exact non-atomic glove-market games. In particular we show that in a glove-market game which consists of the minimum of finitely many mutually singular non-atomic measures, the core is a von-Neumann Morgenstern stable set if the game is exact. We also discuss the intuitive appeal of the equivalence of the core and stable set. We do this by employing the theory of social situations [5] and highlighting the negotiation processes that underlie these two notions.