Wooders, Myrna (2008): Market games and clubs. Published in: Springer Encyclopeida of Complexity and Systems Science (2009): pp. 53595377.

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Abstract
The equivalence of markets and games concerns the relationship between two sorts of structures that appear fundamentally different  markets and games. Shapley and Shubik (1969) demonstrates that: (1) games derived from markets with concave utility functions generate totally balanced games where the players in the game are the participants in the economy and (2) every totally balanced game generates a market with concave utility functions. A particular form of such a market is one where the commodities are the participants themselves, a labor market for example. But markets are very special structures, more so when it is required that utility functions be concave. Participants may also get utility from belonging to groups, such as marriages, or clubs, or productive coalitions. It may be that participants in an economy even derive utility (or disutility) from engaging in processes that lead to the eventual exchange of commodities. The question is when are such economic structures equivalent to markets with concave utility functions. This paper summarizes research showing that a broad class of large economies generate balanced market games. The economies include, for example, economies with clubs where individuals may have memberships in multiple clubs, with indivisibile commodities, with nonconvexities and with nonmonotonicities. The main assumption are: (1) that an option open to any group of players is to break into smaller groups and realize the sum of the worths of these groups, that is, essential superadditivity is satisfied and :(2) relatively small groups of participants can realize almost all gains to coalition formation. The equivalence of games with many players and markets with many participants indicates that relationships obtained for markets with concave utility functions and many participants will also hold for diverse social and economic situations with many players. These relationships include: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or approximate cores; (c) the equal treatment property holds  that is, both market equilibrium and the core treat similar players similarly. These results can be applied to diverse economic models to obtain the equivalence of cooperative outcomes and competitive, price taking outcomes in economies with many participants and indicate that such results hold in yet more generality.
Item Type:  MPRA Paper 

Original Title:  Market games and clubs 
Language:  English 
Keywords:  Markets; games; market games; clubs; core; marketgame equivalence; Shapley value; price taking equilibrium; small group effectiveness; inessentiality of large groups; per capita boundedness; competitive equilibrium; games with side payments; balanced games; totally balanced games; local public goods, core convergence; equal treatment property; equal treatment core; approximate core; strong epsilon core; weak epsilon core; cooperative game; asymptotic negligibility 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games H  Public Economics > H4  Publicly Provided Goods > H41  Public Goods C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C70  General 
Item ID:  33968 
Depositing User:  Myrna Wooders 
Date Deposited:  09 Oct 2011 17:51 
Last Modified:  06 Feb 2016 14:14 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/33968 