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

Endogenous budget constraints in the assignment game

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.
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
References:
[1]

A. Abdulkadiroǧlu and T. Sönmez, House allocation with existing tenants,, Journal of Economic Theory, 88 (1999), 233. Google Scholar

[2]

A. Abdulkadiroǧlu and T. Sönmez, School choice: A mechanism design approach,, The American Economic Review, 93 (2003), 729. Google Scholar

[3]

T. Andersson, C. Andersson and A. J. J. Talman, Sets in excess demand in ascending auctions with unit-demand bidders,, CentER Discussion Paper, 51 (2010), 1. Google Scholar

[4]

C. Beviá, M. Quinzii and J. A. Silva, Buying several indivisible goods,, Mathematical Social Sciences, 37 (1999), 1. doi: 10.1016/S0165-4896(98)00015-8. Google Scholar

[5]

A. Caplin and J. Leahy, A graph theoretic approach to markets for indivisible goods,, Journal of Mathematical Economics, 52 (2014), 112. doi: 10.1016/j.jmateco.2014.03.011. Google Scholar

[6]

G. Demange and D. Gale, The strategy structure of two-sided matching markets,, Econometrica, 53 (1985), 873. doi: 10.2307/1912658. Google Scholar

[7]

G. Demange, D. Gale and M. Sotomayor, Multi-item auctions,, Journal of Political Economy, 94 (1986), 863. doi: 10.1086/261411. Google Scholar

[8]

S. Fujishige and Z. Yang, Existence of an equilibrium in a general competitive exchange economy with indivisible goods and money,, Annals of Economics and Finance, 3 (2002), 135. Google Scholar

[9]

P. Hall, On representatives of subsets,, Journal of London Mathematical Society, 10 (1935), 26. Google Scholar

[10]

Y. Hwang and M. Shih, Equilibrium in a market game,, Economic Theory, 31 (2007), 387. doi: 10.1007/s00199-006-0098-2. Google Scholar

[11]

O. Kesten, Coalitional strategy-proofness and resource monotonicity for house allocation problems,, International Journal of Game Theory, 38 (2009), 17. doi: 10.1007/s00182-008-0136-3. Google Scholar

[12]

F. Kojima and P. Pathak, Incentives and stability in large two-sided matching markets,, American Economic Review, 99 (2009), 608. doi: 10.1257/aer.99.3.608. Google Scholar

[13]

S. Lars-Gunnar, Nash implementation of competitive equilibria in a model with indivisible goods,, Econometrica, 59 (1991), 869. doi: 10.2307/2938231. Google Scholar

[14]

S. Morimoto and S. Serizawa, Strategy-proofness and efficiency with nonquasi-linear preferences: A characterization of minimum price walrasian rule,, Theoretical Economics, 10 (2015), 445. doi: 10.3982/TE1470. Google Scholar

[15]

E. Miyagawa, House allocation with transfers,, Journal of Economic Theory, 100 (2001), 329. doi: 10.1006/jeth.2000.2703. Google Scholar

[16]

M. Quinzii, Core and competitive equilibria with indivisibilities,, International Journal of Game Theory, 13 (1984), 41. doi: 10.1007/BF01769864. Google Scholar

[17]

H. Saitoh, Existence of positive equilibrium price vectors in indivisible goods markets: A note,, Mathematical Social Sciences, 48 (2004), 109. doi: 10.1016/j.mathsocsci.2003.12.003. Google Scholar

[18]

L. S. Shapley and H. E. Scarf, On cores and indivisibility,, Journal of Mathematical Economics, 1 (1974), 23. doi: 10.1016/0304-4068(74)90033-0. Google Scholar

[19]

L. S. Shapley and M. Shubik, The assignment game I: The core,, International Journal of Game Theory, 1 (1972), 111. Google Scholar

[20]

T. Sönmez and U. Ünver, House allocation with existing tenants: A characterization,, Games and Economic Behavior, 69 (2010), 425. doi: 10.1016/j.geb.2009.10.010. Google Scholar

[21]

M. Sotomayor, A simultaneous descending bid auction for multiple items and unitary demand,, Rev. Bras. Econ., 56 (2002), 497. doi: 10.1590/S0034-71402002000300006. Google Scholar

[22]

G. van der Laan, D. Talman and Z. Yang, Existence of an equilibrium in a competitive economy with indivisibilities and money,, Journal of Mathematical Economics, 28 (1997), 101. doi: 10.1016/S0304-4068(97)83316-2. Google Scholar

[23]

J. Wako, Strong core and competitive equilibria of an exchange market with indivisible goods,, International Economic Review, 32 (1991), 843. doi: 10.2307/2527037. Google Scholar

[24]

Z. Yang, A competitive market model for indivisible commodities,, Economics Letters, 78 (2003), 41. doi: 10.1016/S0165-1765(02)00206-9. Google Scholar

show all references

References:
[1]

A. Abdulkadiroǧlu and T. Sönmez, House allocation with existing tenants,, Journal of Economic Theory, 88 (1999), 233. Google Scholar

[2]

A. Abdulkadiroǧlu and T. Sönmez, School choice: A mechanism design approach,, The American Economic Review, 93 (2003), 729. Google Scholar

[3]

T. Andersson, C. Andersson and A. J. J. Talman, Sets in excess demand in ascending auctions with unit-demand bidders,, CentER Discussion Paper, 51 (2010), 1. Google Scholar

[4]

C. Beviá, M. Quinzii and J. A. Silva, Buying several indivisible goods,, Mathematical Social Sciences, 37 (1999), 1. doi: 10.1016/S0165-4896(98)00015-8. Google Scholar

[5]

A. Caplin and J. Leahy, A graph theoretic approach to markets for indivisible goods,, Journal of Mathematical Economics, 52 (2014), 112. doi: 10.1016/j.jmateco.2014.03.011. Google Scholar

[6]

G. Demange and D. Gale, The strategy structure of two-sided matching markets,, Econometrica, 53 (1985), 873. doi: 10.2307/1912658. Google Scholar

[7]

G. Demange, D. Gale and M. Sotomayor, Multi-item auctions,, Journal of Political Economy, 94 (1986), 863. doi: 10.1086/261411. Google Scholar

[8]

S. Fujishige and Z. Yang, Existence of an equilibrium in a general competitive exchange economy with indivisible goods and money,, Annals of Economics and Finance, 3 (2002), 135. Google Scholar

[9]

P. Hall, On representatives of subsets,, Journal of London Mathematical Society, 10 (1935), 26. Google Scholar

[10]

Y. Hwang and M. Shih, Equilibrium in a market game,, Economic Theory, 31 (2007), 387. doi: 10.1007/s00199-006-0098-2. Google Scholar

[11]

O. Kesten, Coalitional strategy-proofness and resource monotonicity for house allocation problems,, International Journal of Game Theory, 38 (2009), 17. doi: 10.1007/s00182-008-0136-3. Google Scholar

[12]

F. Kojima and P. Pathak, Incentives and stability in large two-sided matching markets,, American Economic Review, 99 (2009), 608. doi: 10.1257/aer.99.3.608. Google Scholar

[13]

S. Lars-Gunnar, Nash implementation of competitive equilibria in a model with indivisible goods,, Econometrica, 59 (1991), 869. doi: 10.2307/2938231. Google Scholar

[14]

S. Morimoto and S. Serizawa, Strategy-proofness and efficiency with nonquasi-linear preferences: A characterization of minimum price walrasian rule,, Theoretical Economics, 10 (2015), 445. doi: 10.3982/TE1470. Google Scholar

[15]

E. Miyagawa, House allocation with transfers,, Journal of Economic Theory, 100 (2001), 329. doi: 10.1006/jeth.2000.2703. Google Scholar

[16]

M. Quinzii, Core and competitive equilibria with indivisibilities,, International Journal of Game Theory, 13 (1984), 41. doi: 10.1007/BF01769864. Google Scholar

[17]

H. Saitoh, Existence of positive equilibrium price vectors in indivisible goods markets: A note,, Mathematical Social Sciences, 48 (2004), 109. doi: 10.1016/j.mathsocsci.2003.12.003. Google Scholar

[18]

L. S. Shapley and H. E. Scarf, On cores and indivisibility,, Journal of Mathematical Economics, 1 (1974), 23. doi: 10.1016/0304-4068(74)90033-0. Google Scholar

[19]

L. S. Shapley and M. Shubik, The assignment game I: The core,, International Journal of Game Theory, 1 (1972), 111. Google Scholar

[20]

T. Sönmez and U. Ünver, House allocation with existing tenants: A characterization,, Games and Economic Behavior, 69 (2010), 425. doi: 10.1016/j.geb.2009.10.010. Google Scholar

[21]

M. Sotomayor, A simultaneous descending bid auction for multiple items and unitary demand,, Rev. Bras. Econ., 56 (2002), 497. doi: 10.1590/S0034-71402002000300006. Google Scholar

[22]

G. van der Laan, D. Talman and Z. Yang, Existence of an equilibrium in a competitive economy with indivisibilities and money,, Journal of Mathematical Economics, 28 (1997), 101. doi: 10.1016/S0304-4068(97)83316-2. Google Scholar

[23]

J. Wako, Strong core and competitive equilibria of an exchange market with indivisible goods,, International Economic Review, 32 (1991), 843. doi: 10.2307/2527037. Google Scholar

[24]

Z. Yang, A competitive market model for indivisible commodities,, Economics Letters, 78 (2003), 41. doi: 10.1016/S0165-1765(02)00206-9. Google Scholar

[1]

Zhanyuan Hou, Stephen Baigent. Heteroclinic limit cycles in competitive Kolmogorov systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4071-4093. doi: 10.3934/dcds.2013.33.4071

[2]

Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial & Management Optimization, 2010, 6 (3) : 453-464. doi: 10.3934/jimo.2010.6.453

[3]

Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103

[4]

P. Daniele, S. Giuffrè, S. Pia. Competitive financial equilibrium problems with policy interventions. Journal of Industrial & Management Optimization, 2005, 1 (1) : 39-52. doi: 10.3934/jimo.2005.1.39

[5]

Yong Zhang, Francis Y. L. Chin, Francis C. M. Lau, Haisheng Tan, Hing-Fung Ting. Constant competitive algorithms for unbounded one-Way trading under monotone hazard rate. Mathematical Foundations of Computing, 2018, 1 (4) : 383-392. doi: 10.3934/mfc.2018019

[6]

Shunfu Jin, Wuyi Yue, Shiying Ge. Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1255-1271. doi: 10.3934/jimo.2016071

[7]

Shunfu Jin, Haixing Wu, Wuyi Yue, Yutaka Takahashi. Performance evaluation and Nash equilibrium of a cloud architecture with a sleeping mechanism and an enrollment service. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019060

[8]

Adela Capătă. Optimality conditions for strong vector equilibrium problems under a weak constraint qualification. Journal of Industrial & Management Optimization, 2015, 11 (2) : 563-574. doi: 10.3934/jimo.2015.11.563

[9]

Shimin Li, Jaume Llibre. On the limit cycles of planar discontinuous piecewise linear differential systems with a unique equilibrium. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-17. doi: 10.3934/dcdsb.2019111

[10]

Elvio Accinelli, Bruno Bazzano, Franco Robledo, Pablo Romero. Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation. Journal of Dynamics & Games, 2015, 2 (1) : 1-32. doi: 10.3934/jdg.2015.2.1

[11]

Ali Naimi Sadigh, S. Kamal Chaharsooghi, Majid Sheikhmohammady. A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain. Journal of Industrial & Management Optimization, 2016, 12 (1) : 337-355. doi: 10.3934/jimo.2016.12.337

[12]

Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zero-sum linear-quadratic differential game: Saddle-point equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 1-20. doi: 10.3934/naco.2017001

[13]

Andrey Tsiganov. Integrable Euler top and nonholonomic Chaplygin ball. Journal of Geometric Mechanics, 2011, 3 (3) : 337-362. doi: 10.3934/jgm.2011.3.337

[14]

George Papadopoulos, Holger R. Dullin. Semi-global symplectic invariants of the Euler top. Journal of Geometric Mechanics, 2013, 5 (2) : 215-232. doi: 10.3934/jgm.2013.5.215

[15]

José Natário. An elementary derivation of the Montgomery phase formula for the Euler top. Journal of Geometric Mechanics, 2010, 2 (1) : 113-118. doi: 10.3934/jgm.2010.2.113

[16]

Kevin Kuo, Phong Luu, Duy Nguyen, Eric Perkerson, Katherine Thompson, Qing Zhang. Pairs trading: An optimal selling rule. Mathematical Control & Related Fields, 2015, 5 (3) : 489-499. doi: 10.3934/mcrf.2015.5.489

[17]

Cheng Ma, Y. C. E. Lee, Chi Kin Chan, Yan Wei. Auction and contracting mechanisms for channel coordination with consideration of participants' risk attitudes. Journal of Industrial & Management Optimization, 2017, 13 (2) : 775-801. doi: 10.3934/jimo.2016046

[18]

Bettina Klaus, Frédéric Payot. Paths to stability in the assignment problem. Journal of Dynamics & Games, 2015, 2 (3&4) : 257-287. doi: 10.3934/jdg.2015004

[19]

Marina Núñez, Carles Rafels. A survey on assignment markets. Journal of Dynamics & Games, 2015, 2 (3&4) : 227-256. doi: 10.3934/jdg.2015003

[20]

Arsen R. Dzhanoev, Alexander Loskutov, Hongjun Cao, Miguel A.F. Sanjuán. A new mechanism of the chaos suppression. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 275-284. doi: 10.3934/dcdsb.2007.7.275

 Impact Factor: 

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]