Myrna Wooders – Competition and Cooperation

Apr. 14, 2011

woodersNumerous applications of economics are based on models that assume individual economic actors take prices as given. Indeed, this assumption underlies many empirical studies. The question of whether such an assumption can be justified as arising in the context of individual and group optimizing behavior has been the subject of extensive investigation.

One answer to the question originates with the work of Edgeworth (1881), which argues that groups individuals cannot improve upon their part of a price-taking economic equilibrium by cooperation, that is, the set of outcomes that are stable against collective activities of groups – the core– is equivalent to the set of price-taking equilibrium outcomes.

This line of research, continued in the celebrated works of Debreu and Scarf (1963) and Aumann (1964) and in much subsequent research, treats private goods economies without externalities. Externalities, however, are common; people consume and produce in groups; individuals are affected by the presence and activities of others; individuals may enjoy being with others or they may suffer from congestion.

This presentation reviews research demonstrating that for a broad class of economies, including economies with shared goods, with indivisibilities and/or non-monotonicities, with coalition production, if there are many participants in an economy then the equivalence of the core and the set of equilibrium outcomes holds.

The presentation will conclude with some discussion of the latest results but some of the main papers reporting earlier results are listed below:

  • “Cores of many player games; nonemptiness and equal treatment,” Review of Economic Design (in press) DOI: 10.1007/s10058-009-0095-6.
  • “Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes, “(with N. Allouch), Journal of Economic Theory, Volume 140, Issue 1, May 2008, Pages 246-278.
  • “Anonymous price taking equilibrium in Tiebout Economies with a continuum of agents; Existence and characterization” (with N. Allouch and J. Conley) Journal of Mathematical Economics, Volume 45, Issues 9-10, 20 September 2009, Pages 492-510
  • « Small Group Effectiveness, Per Capita Boundedness and Nonemptiness of Approximate Cores. » Journal of Mathematical Economics (2008)
  • « An exact bound on epsilon for non-emptiness of the epsilon-cores of games, » (with A. Kovalenkov) Mathematics of Operations Research, Vol 26, No 4, Nov 2001, pp 654.678.
  • « Multijurisdictional economies, the Tiebout Hypothesis, and sorting, » Proceedings of the National Academy of Sciences Vol. 96, Issue 19, 10585-10587, September 14, 1999.
  • « Large games and economies with effective small groups, » in Game Theoretic Approaches to General Equilibrium Theory, eds. J-F. Mertens and S. Sorin, Kluwer Academic Press, Dordrecht/Boston/London (1994), 145-206.
  • « Equivalence of games and markets, » Econometrica 62 (1994), 1141-1160.

 Myrna Wooders (Vanderbilt University, Nashville TN, USA)

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