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.
References
- “Market Uncertainty: Sunspot Equilibria in Imperfectly Competitive Economies” (with James Peck), Working Paper 85-21, Center for Analytic Research in Economics and the Social Sciences, University of Pennsylvania, Philadelphia, July 1985. This is more complete than the RES version.
- “Asymmetric Information and Sunspot Equilibria: A Family of Simple Examples” (with Robert J. Aumann and James Peck), Working Paper 88-34, Center for Analytic Economics, Cornell University, Ithaca, October 1988.
- “On the Nonequivalence of the Arrow-Securities Game and the Contingent-Commodities Game” (with James Peck), Part 1, Chapter 4 in Economic Complexity: Chaos, Suspots, Bubbles, and Nonlinearity (W. Barnett, J. Geweke, and K. Shell, eds.), New York: Cambridge University Press, 1989, 61-85. ISBN: 052135563X.
- “Liquid Markets and Competition” (with James Peck), Games and Economic Behavior, Vol. 2(4), December 1990, 362-377.
- “Market Uncertainty: Correlated and Sunspot Equilibria in Imperfectly Competitive Economies” (with James Peck), The Review of Economic Studies, Vol. 58(5), October 1991, 1011-1029.
- “The Market Game: Existence and Structure of Equilibrium” (with James Peck and Stephen E. Spear), Journal of Mathematical Economics, Vol. 21(3), May 1992, 271-299.