Bargaining-equilibrium equivalence

Bhowmik, Anuj and Saha, Sandipan (2023): Bargaining-equilibrium equivalence.

Abstract

The paper tries to answer one of the more nascent questions in the literature on general equilibrium theory by investigating the equivalence between the set of club equilibrium states and the bargaining set for a club economy. Clubs in this framework are treated in a parallel fashion to private goods as articles of choice. Each club membership is composed of three components: (i) the individual's characteristics; (ii) the profile of the club. and (iii) the club project. Thus clubs are identified through their profile and the particular project they undertake. We introduce the bargaining set for such an economy in lieu of Mas-Colell \cite{Mas : 89} and define a two-step veto mechanism. In this paper we establish that non-equilibrium states are those against which there exist a set of agents who agree upon a mutually beneficial trade agreement amongst themselves or in other words there exists a Walrasian objection to such states. In what follows from the literature is that Walrasian objections are justified as well which thereby helps us establish our equivalence.

• Item Type: MPRA Paper
• Language: English
• Keywords: Club goods, Bargaining set, Walrasian objection, Justified objection, Bargaining-Equilibrium equivalence.
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium; D - Microeconomics > D6 - Welfare Economics; D - Microeconomics > D6 - Welfare Economics > D62 - Externalities; H - Public Economics > H4 - Publicly Provided Goods

References

1) Anderson, Robert M., Walter Trockel, and Lin Zhou. ``Nonconvergence of the Mas-Colell and Zhou bargaining sets." Econometrica 65 (1997), 1227--1239.

2) R.J. Aumann, ``Markets with a continuum of traders." Econometrica

3) Aumann, Robert J. ``Disadvantageous monopolies." Journal of Economic Theory 6 (1973), 1--11.

4) Aumann, Robert J., and Michael Maschler. ``The bargaining set for cooperative games". Princeton Univ NJ, 1961.

5) Aubin, Jean-Pierre. ``Mathematical methods of game and economic theory." Courier Corporation, 2007.

6) Bhowmik, Anuj, and Japneet Kaur. ``Competitive equilibria and robust efficiency with club goods ." IGIDR Working Paper, Working Paper Number, WP-2022-14.

7) Bhowmik, Anuj, and Sandipan Saha. ``On blocking mechanisms in economies with club goods." MPRA Working Paper, (2022).

8) Buchanan, James M. ``An Economic Theory of Clubs." Economica 32 (1965), 1--14.

9) Debreu, Gerard, and Herbert Scarf. ``A limit theorem on the core of an economy." International Economic Review 4 (1963), 235--246.

10) Ellickson, Bryan, Birgit Grodal, Suzanne Scotchmer, and William R. Zame. ``Clubs and the Market." Econometrica 67 (1999), 1185-1217.

11) Ellickson, Bryan, Birgit Grodal, Suzanne Scotchmer, and William R. Zame. ``Clubs and the market: Large finite economies." Journal of Economic Theory 101 (2001), 40--77.

12) Engl, Greg, and Suzanne Scotchmer. ``The core and the hedonic core: Equivalence and comparative statics." Journal of Mathematical Economics 26 (1996), 209--248.

13) Gilles, Robert P., and Suzanne Scotchmer. ``Decentralization in replicated club economies with multiple private goods." Journal of Economic Theory 72 (1997), 363--387

14) Herv\'{e}s-Beloso, Carlos, and Emma Moreno-Garc\'{i}a. ``Competitive equilibria and the grand coalition." Journal of Mathematical Economics 44 (2008): 697-706.

15) Herv\'{e}s-Beloso, Carlos, Javier Herv\'{e}s-Est\'{e}vez, and Emma Moreno-Garc\'{i}a. ``Bargaining sets in finite economies." Journal of Mathematical Economics 74 (2018), 93--98.

16) Herv\'{e}s-Est\'{e}vez, Javier, and Emma Moreno-Garc\'{i}a. ``A limit result on bargaining sets." Economic Theory 66 (2018), 327--341.

17) Hervés‐Estévez, Javier, and Emma Moreno‐García. ``Some equivalence results for a bargaining set in finite economies." International Journal of Economic Theory 14 (2018): 129--138.

18) Liu, Jiuqiang. ``Equivalence of the Aubin bargaining set and the set of competitive equilibria in a finite coalition production economy." Journal of Mathematical Economics 68 (2017), 55--61.

19) Liu, Jiuqiang, and Huihui Zhang. ``Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy." International Journal of Game Theory 45 (2016), 1095-1109.

20) Maschler, Michael. ``An advantage of the bargaining set over the core." Journal of Economic Theory 13 (1976), 184--192.

21) Mas-Colell, Andreu. ``Efficiency and decentralization in the pure theory of public goods." The Quarterly Journal of Economics 94 4 1980, 625--641.

22) Mas-Colell, Andreu. ``An equivalence theorem for a bargaining set." Journal of Mathematical Economics 18 (1989), 129--139.

23) Saha, Sandipan. ``An Essay on Bargaining Sets." M.Phil. thesis submitted at Indira Gandhi Institute of Development Research. (2023).

24) Schmeidler, David. ``A remark on the core of an atomless economy." Econometrica 40 (1972), 579.

25) Scotchmer, Suzanne. ``Externality Pricing in Club Economics." Ricerche Economiche (1996), 347--366.

26) Scotchmer, Suzanne. ``On price-taking equilibria in club economies with nonanonymous crowding. ``Journal of Public Economics 65 (1997), 75--88.

27) Scotchmer, Suzanne, and Myrna Holtz Wooders. ``Competitive equilibrium and the core in club economies with anonymous crowding." Journal of Public Economics 34 (1987): 159--173.

28) Vind, Karl. ``A third remark on the core of an atomless economy." Econometrica 40 (1972), 585.