Representation of transferable utility games by coalition production economies

Abstract

a b s t r a c tWe prove that, by the method of construction of a coalition production economy due to Sun et al. [Sun, N., Trockel, W., Yang, Z., 2008. Competitive outcomes and endogenous coalition formation in an n-person game. Journal of Mathematical Economics 44, 853-860], every transferable utility (TU) game can be generated by a coalition production economy. Namely, for every TU game, we can construct a coalition production economy that generates the given game. We briefly discuss the relationship between the core of a given TU game and the set of Walrasian payoff vectors for the induced coalition production economy.

Competitive outcomes and the inner core of NTU market games

“…Another interesting related line of research is to continue to look at the class of games that are linked to coalition production economies as analyzed by Inoue (2010b). Given a balanced NTU game Inoue (2010b) defines a coalition production economy such that this economy represents the game and has moreover the whole inner core as the set of competitive equilibrium payoff vectors.…”

“…Similarly to the approach of Billera and Bixby (1974), Inoue (2010b) uses coalition production economies as in Sun et al (2008) instead of markets. Inoue (2010b) shows that every compactly generated NTU game can be represented by a coalition production economy.…”

“…Inoue (2010b) shows that every compactly generated NTU game can be represented by a coalition production economy. Moreover, he proves that there exists a coalition production economy whose set of competitive payoff vectors coincides with the inner core of the balanced cover of the original NTU game.…”