Axiomatic Theory of Bargaining with a Variable Number of by William Thomson

By William Thomson

This publication extrapolates at the Nash (1950) therapy of the bargaining challenge to think about the placement the place the variety of bargainers could fluctuate. The authors formulate axioms to specify how ideas may still reply to such adjustments, and supply new characterizations of the entire significant strategies in addition to the generalizations of those options.

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1) would not be affected of course by this domain restriction. But the necessity would. INV, and MON, then for all P e (9 such that 3 | P | - 2 ^ f l , F^K on Lp. But in that proof no attempt was made to minimize the number of additional agents, and tighter bounds could perhaps be found. 2 that in order to be able to conclude that F^K on Lp for |P| = 2, it suffices to have the option to introduce only one additional agent; a different construction, not reproduced here, shows similarly that in order to be able to conclude that F ^ K on Lp for |p| = 3, two additional agents suffice.

The axiom has been the object of a large amount of attention, and it has been adapted to a number of other contexts. In the social choice literature, it is now known under a variety of names, such as Property a, contraction consistency, and the Chernoff condition. ] Here we will keep the phrase independence of irrelevant alternatives, which seems to have remained standard in bargaining theory (see Roth, 1979b), with a warning that the axiom should not be confused with the condition of the same name used by Arrow (1951).

Note that T is a symmetric element of L<2 and that eQePO(T). PO and SY, F(T) = eQ. By the choice of n9 TPDS. Let now T'eXQ be denned by Tf = cch{SyeQ}. Clearly, TDT' and F(T) e T. A, F(T')=F(T). Also, Tj> = S, and by MON, F(S)=F(T£)^FP(T') = eP = E(S). D. 2 Removing the axioms one at a time In order to better understand the role played by each axiom in the main characterization proof, we investigate here what additional solutions would be made possible by its removal. ) be a list of nonnegative and possibly infinite real numbers such that ap ^ aQ for all P, Qe (P with PCQ.

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