Representation of TU games by coalition production economies
AbstractWe prove that every transferable utility (TU) game can be generated by a coalition production economy. Given a TU game, the set of Walrasian payoff vectors of the induced coalition production economy coincides with the core of the balanced cover of the given game. Therefore, a Walrasian equilibrium for the induced coalition production economy always exists. The induced coalition production economy has one output and the same number of inputs as agents. Every input is personalized and it can be interpreted as agent's labor. In a Walrasian equilibrium, every agent is permitted to work at several firms. In a Walrasian equilibrium without double-jobbing, in contrast, every agent has to work at exactly one firm. This restricted concept of a Walrasian equilibrium enables us to discuss which coalitions are formed in an equilibrium. If the cohesive cover or the completion of a given TU game is balanced, then the no-double-jobbing restriction does not matter, i.e., there exists no difference between Walrasian payoff vectors and Walrasian payoff vectors without double-jobbing.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 430.
Length: 36 pages
Date of creation: Apr 2010
Date of revision:
Coalition production economy; transferable utility game; core; Walrasian equilibrium; Walrasian equilibrium without double-jobbing; coalition structure;
Find related papers by JEL classification:
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
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