Bargaining Sets with Small Coalitions

Ulla Schjødt and Birgitte Sloth ()
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Ulla Schjødt: Institute of Mathematics, University of Copenhagen

No 90-18, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: The paper considers various cooperative equilibrium/solution concepts for atomless exchange economies. A famous result states that in such economies the core is equal to the set of Walrasian equilibria. We consider two arguments against using the core as solution concept in large economies: (1) A coalition will not block an allocation, if the agents fear that this will imply counterobjections from other coalitions, and there by result in an allocation which is worse than the original allocation. (2) A coalition will not block an allocation, if the coalition is too large to form. Each argument leads to definition of new solution concepts. (1) leads to the 'bargaining set' (two different definitions are considered in the paper) and (2) leads to 'the e-core'. We discuss these solution concepts and their relation to the core and the Walrasian equilibria. Then we try to define solution concepts taking both arguments into consideration. The results show that the bargaining set is not an equilibrium concept, but a concept demanding either equilibrium or 'no equilibria one step away', and that the bargaining set, in contrast to the core, is very sensible to the exact definition.

Keywords: bargaining; coalition; game theory and bargaining theory (search for similar items in EconPapers)
JEL-codes: C78 (search for similar items in EconPapers)
Pages: 14 pages
Date: 1990-11
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Published in: International Journal of Game Theory, 1994, 23(1) pp 49-55

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