Abstract
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 (Shapley and Shubik in J Econ Theory 1:9–25, 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aubin J.P. (1979). Mathematical methods of games and economic theory. North-Holland, Amsterdam
Aubin J.P. (1981). Cooperative fuzzy games. Math Operat Res 6:1–13
Bondareva O. (1962). The theory of the core in an n-person game (in Russian). Vestn Leningr Univ 13:141–142
Branzei R., Dimitrov D., Tijs S. (2003). Convex fuzzy games and participation monotonic allocation schemes. Fuzzy Sets Syst 139:267–281
Butnariu D. (1980). Stability and Shapley value for an n-persons fuzzy game. Fuzzy Sets Syst 4:63–72
Laraki R. (2004). On the regularity of the convexification operator on a compact set. J Convex Anal 11:209–234
Moulin H. (1988). Axioms of cooperative decision making, pp 98–102. Cambridge university press, Cambridge
Shapley L.S. (1967). On balanced sets and cores. Naval Res Logist Q 14:453–460
Shapley L.S., Shubik M. (1969). On market games. J Econ Theory 1:9–25
Sharkey W.W., Telser L.G. (1978). Supportable cost functions for the multiproduct firm. J Econ Theory 18:23–37
Telser L.G. (1978). Economic theory and the core. The university of Chicago press, Chicago
Author information
Authors and Affiliations
Corresponding author
Additional information
Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”.
An anonymous referee of Economic Theory is acknowledged for his/her comments
Rights and permissions
About this article
Cite this article
Azrieli, Y., Lehrer, E. Market Games in Large Economies with a Finite Number of Types. Economic Theory 31, 327–342 (2007). https://doi.org/10.1007/s00199-006-0094-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-006-0094-6