Market Games

Market Games

Jim Peck and I (1985, 1991) used the market game of Lloyd Shapley and Martin Shubik to compare the sunspot equilibrium concept to the correlated-equilibrium concept of Bob Aumann. We established that in imperfectly competitive economies sunspots are likely to matter. They showed that all correlated equilibria are SE, but that the converse is not true in general.

The work of Jim Peck and me on the existence of pure-strategy Nash equilibrium in market games was improved by Jim Peck, Steve Spear, and me (1992), which paper also analyzes in depth the structure of the market-game equilibrium set.

Jim Peck and I (1989) showed that for imperfectly competitive economies, there is a major difference between Arrow securities and Arrow-Debreu contingent claims. If any income is transferred across states of nature, then the equilibrium allocation for the securities game is not an equilibrium for the contingent-claims game. With imperfect competition, there is no useful definition of complete markets.

Jim and I (1990) showed that, even with few players but with unrestricted short sales, there is always a Nash equilibrium close to some competitive equilibrium. Hence short selling provides market liquidity.