Cores of Many-Player Games; Nonemptiness and Equal Treatment
AbstractThis paper provides sufficient conditions to ensure nonemptiness of approximate cores of many-player games and symmetry of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity -- an option open to a group of players is to partition into smaller groups and realize the worths of these groups and (b) small group effectiveness (SGE) -- almost all gains to collective activities can be realized by cooperation only within members of some partition of players into relatively small groups. Another condition, small group negligibility (SGN), is introduced and shown to be equivalent to SGE. SGN dictates that small groups of players cannot have significant effects on average (i.e., per capita) payoffs of large populations; thus, SGN is a analogue, for games with a finite player set, of the condition built into models with a continuum of player that sets of measure zero can be ignored. SGE implies per capita boundedness (PCB), that the supremum of average or per capita payoffs is uniformly bounded above. Further characterization of SGE in terms of its relationship to PCB is provided. It is known that if SGE does not hold, then approximate cores of many-player games may be empty. Examples are developed to show that if SGE does not hold and if there are players of "scarce types" (in other works, players with scarce attributes) then even if there is only a finite number of types of players and approximate cores are non-empty, symmetry may be lost; moreover, even players of abundant types may be treated asymmetrically by the core.
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Bibliographic InfoPaper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0918.
Date of creation: Oct 2009
Date of revision:
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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html
Core; approximate cores; equal treatment; core convergence; small group effectiveness; symmetry; per capita boundedness; small group negligibility; games with a continuum of players partitioning games; kernel;
Other versions of this item:
- Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer, vol. 14(1), pages 131-162, March.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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