American Institute of Mathematical Sciences

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March & April  2015, 2(3&4): 207-225. doi: 10.3934/jdg.2015002

Endogenous budget constraints in the assignment game

David Cantala 1, and  Juan Sebastián Pereyra 2,

1. 

Centro de Estudios Económicos, El Colegio de México, Camino al Ajusco 20, Fuentes del Pedregal, 10740 Mexico City, Mexico
2. 

ECARES - Solvay Brussels School of Economics and Management, Université libre de Bruxelles and F.R.S.-FNRS, Ave. F.D. Roosevelt 42, B1050 - Brussels, Belgium

Received  October 2014 Revised  April 2015 Published  November 2015

This paper studies economies with indivisible goods and budget-constrained agents with unit-demand who act as both sellers and buyers. In prior literature on the existence of competitive equilibrium, it is assumed the indispensability of money, which in turn implies that budgets constraints are irrelevant. We introduce a new condition, Money Scarcity (MS), that considers agents' budget constraints and ensures the existence of equilibrium. Moreover, an extended version of Gale's top trading cycles algorithm is presented, and it is shown that under MS this mechanism is strategy-proof. Finally, we prove that this mechanism is the unique mechanism that minimizes money transactions at equilibrium.
Keywords: auction mechanism., indivisibility, endogenous budget constraint, top trading cycles, Assignment game, competitive equilibrium.
Mathematics Subject Classification: Primary: 91B68, 91A80; Secondary: 91B2.
Citation: David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002
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show all references

References:
[1]

Journal of Economic Theory, 88 (1999), 233-260. Google Scholar

[2]

The American Economic Review, 93 (2003), 729-747. Google Scholar

[3]

CentER Discussion Paper, 51 (2010), 1-17. Google Scholar

[4]

Mathematical Social Sciences, 37 (1999), 1-23. doi: 10.1016/S0165-4896(98)00015-8.  Google Scholar

[5]

Journal of Mathematical Economics, 52 (2014), 112-122. doi: 10.1016/j.jmateco.2014.03.011.  Google Scholar

[6]

Econometrica, 53 (1985), 873-883. doi: 10.2307/1912658.  Google Scholar

[7]

Journal of Political Economy, 94 (1986), 863-872. doi: 10.1086/261411.  Google Scholar

[8]

Annals of Economics and Finance, 3 (2002), 135-147. Google Scholar

[9]

Journal of London Mathematical Society, 10 (1935), 26-30. Google Scholar

[10]

Economic Theory, 31 (2007), 387-392. doi: 10.1007/s00199-006-0098-2.  Google Scholar

[11]

International Journal of Game Theory, 38 (2009), 17-21. doi: 10.1007/s00182-008-0136-3.  Google Scholar

[12]

American Economic Review, 99 (2009), 608-627. doi: 10.1257/aer.99.3.608.  Google Scholar

[13]

Econometrica, 59 (1991), 869-877. doi: 10.2307/2938231.  Google Scholar

[14]

Theoretical Economics, 10 (2015), 445-487. doi: 10.3982/TE1470.  Google Scholar

[15]

Journal of Economic Theory, 100 (2001), 329-355. doi: 10.1006/jeth.2000.2703.  Google Scholar

[16]

International Journal of Game Theory, 13 (1984), 41-60. doi: 10.1007/BF01769864.  Google Scholar

[17]

Mathematical Social Sciences, 48 (2004), 109-112. doi: 10.1016/j.mathsocsci.2003.12.003.  Google Scholar

[18]

Journal of Mathematical Economics, 1 (1974), 23-37. doi: 10.1016/0304-4068(74)90033-0.  Google Scholar

[19]

International Journal of Game Theory, 1 (1972), 111-130.  Google Scholar

[20]

Games and Economic Behavior, 69 (2010), 425-445. doi: 10.1016/j.geb.2009.10.010.  Google Scholar

[21]

Rev. Bras. Econ., 56 (2002), 497-510. doi: 10.1590/S0034-71402002000300006.  Google Scholar

[22]

Journal of Mathematical Economics, 28 (1997), 101-109. doi: 10.1016/S0304-4068(97)83316-2.  Google Scholar

[23]

International Economic Review, 32 (1991), 843-852. doi: 10.2307/2527037.  Google Scholar

[24]

Economics Letters, 78 (2003), 41-47. doi: 10.1016/S0165-1765(02)00206-9.  Google Scholar

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