American Institute of Mathematical Sciences

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doi: 10.3934/jdg.2020004

Market games and walrasian equilibria

Carlos Hervés-Beloso 1,, and  Emma Moreno-García 2,

1. 

Universidad de Vigo, Spain
2. 

Universidad de Salamanca, Spain

* Corresponding author: Carlos Hervés-Beloso

Received  May 2019 Published  December 2019

Fund Project: This work is partially supported by Research Grants SA049G19 (Junta de Castilla y León), ECO2016-75712-P (Ministerio de Economía y Competitividad) and ECOBAS (Xunta de Galicia)

In this work, we recapitulate and compare the market game approaches provided by Shapley and Shubik [35] and Schmeidler [33]. We provide some extensions to economies with infinitely many commodities and point out some applications and lines for future research.

Keywords: Market games, Nash equilibrium, Walrasian equilibrium.
Mathematics Subject Classification: 91B50, 91A40.
Citation: Carlos Hervés-Beloso, Emma Moreno-García. Market games and walrasian equilibria. Journal of Dynamics & Games, doi: 10.3934/jdg.2020004
References:
[1]

R. M. Anderson, An elementary core equivalence theorem, Econometrica, 46 (1978), 1483-1487.  doi: 10.2307/1913840.  Google Scholar

[2]

R. M. Anderson, Core theory with strongly convex preferences, Econometrica, 49 (1981), 1457-1468.  doi: 10.2307/1911411.  Google Scholar

[3]

R. M. Anderson, Strong core theorems with nonconvex preferences, Econometrica, 53 (1985), 1283-1294.  doi: 10.2307/1913208.  Google Scholar

[4]

A. Araujo, Lack of Pareto optimal allocations in economies with infinitely many commodities: The need for impatience, Econometrica, 53 (1985), 455-461.  doi: 10.2307/1911245.  Google Scholar

[5]

K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.  doi: 10.2307/1907353.  Google Scholar

[6]

K. J. Arrow and F. H. Hahn, General Competitive Analysis, Mathematical Economics Texts, No. 6. Holden-Day, Inc., San Francisco, Calif., Oliver & Boyd, Edinburgh, 1971.  Google Scholar

[7]

R. J. Aumann, Markets with a continuum of traders, Econometrica, 32 (1964), 39-50.  doi: 10.2307/1913732.  Google Scholar

[8]

J. Bertrand, Théorie mathématique de la richesse sociale, Journal de Savants, (1883), 499–508. Google Scholar

[9]

T. F. Bewley, Existence of equilibria in economies with infinitely many commodities, Journal of Economic Theory, 4 (1973), 514-540.  doi: 10.1016/0022-0531(72)90136-6.  Google Scholar

[10]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Researches into the Mathematical Principles of the Theory of Wealth. Macmillan, New York, 1897. Google Scholar

[11]

G. Debreu, A social equilibrium existence theorem, Proceedings of the National Academy of Sciences, 38 (1952), 886-893.  doi: 10.1073/pnas.38.10.886.  Google Scholar

[12]

G. Debreu and H. Scarf, A limit theorem on the core of an economy, International Economic Review, 4 (1963), 235-246.   Google Scholar

[13]

E. Dierker, Gains and losses at core allocations, Journal of Mathematical Economics, 2 (1975), 119-128.  doi: 10.1016/0304-4068(75)90018-X.  Google Scholar

[14]

P. Dubey, Price-quantity strategic market games, Econometrica, 50 (1982), 111-126.  doi: 10.2307/1912532.  Google Scholar

[15]

P. Dubey and J. Geanakoplos, From Nash to Walras via Shapley-Shubik. Special issue on strategic market games, Journal of Mathematical Economics, 39 (2003), 391-400.  doi: 10.1016/S0304-4068(03)00012-0.  Google Scholar

[16]

M. Faias, C. Hervés-Beloso and E. Moreno-García, Equilibrium price formation in markets with differentially informed agents, Economic Theory, 48 (2011), 205-218.  doi: 10.1007/s00199-010-0582-6.  Google Scholar

[17]

M. Faias, E. Moreno-García and M. Wooders, A strategic market game approach for the private provision of public goods, Journal of Dynamics and Games, 1 (2014), 283-298.  doi: 10.3934/jdg.2014.1.283.  Google Scholar

[18]

G. Fugarolas-Alvarez-Ude, C. Hervés-Beloso, E. Moreno-García and J. P. Torres-Martínez, A market game approach to differential information economies, Economic Theory, 38 (2009), 321-330.  doi: 10.1007/s00199-006-0170-y.  Google Scholar

[19]

J. García-Cutrín and C. Hervés-Beloso, A discrete approach to continuum economies, Economic Theory, 3 (1993), 577-583.  doi: 10.1007/BF01209704.  Google Scholar

[20]

G. Giraud, Strategic market games: An introduction, Journal of Mathematical Economics, 39 (2003), 355-375.  doi: 10.1016/S0304-4068(03)00049-1.  Google Scholar

[21]

M. Greinecker and K. Podczeck, Core equivalence with differentiated commodities, Journal of Mathematical Economics, 73 (2017), 54-67.  doi: 10.1016/j.jmateco.2017.08.005.  Google Scholar

[22]

C. Hervés-Beloso and H. del Valle-Inclán Cruces, Continuous preference orderings representable by utility functions, Journal of Economic Surveys, 33 (2019), 179-194.   Google Scholar

[23]

C. Hervés-Beloso, E. Moreno-García and M. R. Páscoa, Manipulation-proof equilibrium in atomless economies with commodity differentiation, Economic Theory, 14 (1999), 545-563.  doi: 10.1007/s001990050339.  Google Scholar

[24]

C. Hervés-Beloso and E. Moreno-García, Walrasian analysis via two-player games, Games and Economic Behaviour, 65 (2009), 220-233.  doi: 10.1016/j.geb.2007.12.001.  Google Scholar

[25]

W. Hildenbrand, Cores and Equilibria of a Large Economy, Princeton Studies in Mathematical Economics, No. 5. Princeton University Press, Princeton, N.J., 1974.  Google Scholar

[26]

L. Hurwicz, Outcome functions yielding Walrasian and Lindhal allocations at Nash equilibrium points, Review of Economic Studies, 46 (1979), 217-227.  doi: 10.2307/2297046.  Google Scholar

[27]

M. A. Khan, Oligopoly in markets with a continuum of traders: An asymptotic interpretation, Journal of Economic Theory, 12 (1976), 273-97.  doi: 10.1016/0022-0531(76)90078-8.  Google Scholar

[28]

E. Moreno-García, Strategic equilibria with partially consumable withholdings, International Game Theory Review, 8 (2006), 533-553.  doi: 10.1142/S0219198906001090.  Google Scholar

[29]

J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1950), 48-49.  doi: 10.1073/pnas.36.1.48.  Google Scholar

[30]

J. Ostroy and W. Zame, Nonatomic economies and the boundaries of perfect competition, Econometrica, 62 (1994)), 593-633.   Google Scholar

[31]

K. Podczeck, On core-Walras equivalence in Banach lattices, Journal of Mathematical Economics, 41 (2005), 764-792.  doi: 10.1016/j.jmateco.2004.04.001.  Google Scholar

[32]

D. J. Roberts and A. Postlewaite, : The incentives for price-taking behavior in large exchange economies, Econometrica, 44 (1976), 115–127. doi: 10.2307/1911385.  Google Scholar

[33]

D. Schmeidler, Walrasian analysis via strategic outcome functions, Econometrica, 48 (1980), 1585-1593.  doi: 10.2307/1911923.  Google Scholar

[34]

L. S. Shapley, Non-cooperative general exchange, Theory of Measure of Economic Externalities, (1976). Google Scholar

[35]

L. Shapley and M. Shubik, Trade using one commodity as a means of payment, Journal of Political Economy, 85 (1977), 937-968.   Google Scholar

[36]

M. Shubik, Commodity money, oligopoly, credit and bankruptcy in a general equilibrium model, Western Economic Journal, 11 (1973), 24-38.   Google Scholar

[37]

R. Tourky and N. C. Yannelis, Markets with many more agents than commodities: Aumann's "hidden" assumption, Journal of Economic Theory, 101 (2001), 189-221.  doi: 10.1006/jeth.2000.2705.  Google Scholar

[38]

M. H. Wooders, Equivalence of games and markets, Econometrica, 62 (1994), 1141-1160.  doi: 10.2307/2951510.  Google Scholar

show all references

References:
[1]

R. M. Anderson, An elementary core equivalence theorem, Econometrica, 46 (1978), 1483-1487.  doi: 10.2307/1913840.  Google Scholar

[2]

R. M. Anderson, Core theory with strongly convex preferences, Econometrica, 49 (1981), 1457-1468.  doi: 10.2307/1911411.  Google Scholar

[3]

R. M. Anderson, Strong core theorems with nonconvex preferences, Econometrica, 53 (1985), 1283-1294.  doi: 10.2307/1913208.  Google Scholar

[4]

A. Araujo, Lack of Pareto optimal allocations in economies with infinitely many commodities: The need for impatience, Econometrica, 53 (1985), 455-461.  doi: 10.2307/1911245.  Google Scholar

[5]

K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.  doi: 10.2307/1907353.  Google Scholar

[6]

K. J. Arrow and F. H. Hahn, General Competitive Analysis, Mathematical Economics Texts, No. 6. Holden-Day, Inc., San Francisco, Calif., Oliver & Boyd, Edinburgh, 1971.  Google Scholar

[7]

R. J. Aumann, Markets with a continuum of traders, Econometrica, 32 (1964), 39-50.  doi: 10.2307/1913732.  Google Scholar

[8]

J. Bertrand, Théorie mathématique de la richesse sociale, Journal de Savants, (1883), 499–508. Google Scholar

[9]

T. F. Bewley, Existence of equilibria in economies with infinitely many commodities, Journal of Economic Theory, 4 (1973), 514-540.  doi: 10.1016/0022-0531(72)90136-6.  Google Scholar

[10]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Researches into the Mathematical Principles of the Theory of Wealth. Macmillan, New York, 1897. Google Scholar

[11]

G. Debreu, A social equilibrium existence theorem, Proceedings of the National Academy of Sciences, 38 (1952), 886-893.  doi: 10.1073/pnas.38.10.886.  Google Scholar

[12]

G. Debreu and H. Scarf, A limit theorem on the core of an economy, International Economic Review, 4 (1963), 235-246.   Google Scholar

[13]

E. Dierker, Gains and losses at core allocations, Journal of Mathematical Economics, 2 (1975), 119-128.  doi: 10.1016/0304-4068(75)90018-X.  Google Scholar

[14]

P. Dubey, Price-quantity strategic market games, Econometrica, 50 (1982), 111-126.  doi: 10.2307/1912532.  Google Scholar

[15]

P. Dubey and J. Geanakoplos, From Nash to Walras via Shapley-Shubik. Special issue on strategic market games, Journal of Mathematical Economics, 39 (2003), 391-400.  doi: 10.1016/S0304-4068(03)00012-0.  Google Scholar

[16]

M. Faias, C. Hervés-Beloso and E. Moreno-García, Equilibrium price formation in markets with differentially informed agents, Economic Theory, 48 (2011), 205-218.  doi: 10.1007/s00199-010-0582-6.  Google Scholar

[17]

M. Faias, E. Moreno-García and M. Wooders, A strategic market game approach for the private provision of public goods, Journal of Dynamics and Games, 1 (2014), 283-298.  doi: 10.3934/jdg.2014.1.283.  Google Scholar

[18]

G. Fugarolas-Alvarez-Ude, C. Hervés-Beloso, E. Moreno-García and J. P. Torres-Martínez, A market game approach to differential information economies, Economic Theory, 38 (2009), 321-330.  doi: 10.1007/s00199-006-0170-y.  Google Scholar

[19]

J. García-Cutrín and C. Hervés-Beloso, A discrete approach to continuum economies, Economic Theory, 3 (1993), 577-583.  doi: 10.1007/BF01209704.  Google Scholar

[20]

G. Giraud, Strategic market games: An introduction, Journal of Mathematical Economics, 39 (2003), 355-375.  doi: 10.1016/S0304-4068(03)00049-1.  Google Scholar

[21]

M. Greinecker and K. Podczeck, Core equivalence with differentiated commodities, Journal of Mathematical Economics, 73 (2017), 54-67.  doi: 10.1016/j.jmateco.2017.08.005.  Google Scholar

[22]

C. Hervés-Beloso and H. del Valle-Inclán Cruces, Continuous preference orderings representable by utility functions, Journal of Economic Surveys, 33 (2019), 179-194.   Google Scholar

[23]

C. Hervés-Beloso, E. Moreno-García and M. R. Páscoa, Manipulation-proof equilibrium in atomless economies with commodity differentiation, Economic Theory, 14 (1999), 545-563.  doi: 10.1007/s001990050339.  Google Scholar

[24]

C. Hervés-Beloso and E. Moreno-García, Walrasian analysis via two-player games, Games and Economic Behaviour, 65 (2009), 220-233.  doi: 10.1016/j.geb.2007.12.001.  Google Scholar

[25]

W. Hildenbrand, Cores and Equilibria of a Large Economy, Princeton Studies in Mathematical Economics, No. 5. Princeton University Press, Princeton, N.J., 1974.  Google Scholar

[26]

L. Hurwicz, Outcome functions yielding Walrasian and Lindhal allocations at Nash equilibrium points, Review of Economic Studies, 46 (1979), 217-227.  doi: 10.2307/2297046.  Google Scholar

[27]

M. A. Khan, Oligopoly in markets with a continuum of traders: An asymptotic interpretation, Journal of Economic Theory, 12 (1976), 273-97.  doi: 10.1016/0022-0531(76)90078-8.  Google Scholar

[28]

E. Moreno-García, Strategic equilibria with partially consumable withholdings, International Game Theory Review, 8 (2006), 533-553.  doi: 10.1142/S0219198906001090.  Google Scholar

[29]

J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1950), 48-49.  doi: 10.1073/pnas.36.1.48.  Google Scholar

[30]

J. Ostroy and W. Zame, Nonatomic economies and the boundaries of perfect competition, Econometrica, 62 (1994)), 593-633.   Google Scholar

[31]

K. Podczeck, On core-Walras equivalence in Banach lattices, Journal of Mathematical Economics, 41 (2005), 764-792.  doi: 10.1016/j.jmateco.2004.04.001.  Google Scholar

[32]

D. J. Roberts and A. Postlewaite, : The incentives for price-taking behavior in large exchange economies, Econometrica, 44 (1976), 115–127. doi: 10.2307/1911385.  Google Scholar

[33]

D. Schmeidler, Walrasian analysis via strategic outcome functions, Econometrica, 48 (1980), 1585-1593.  doi: 10.2307/1911923.  Google Scholar

[34]

L. S. Shapley, Non-cooperative general exchange, Theory of Measure of Economic Externalities, (1976). Google Scholar

[35]

L. Shapley and M. Shubik, Trade using one commodity as a means of payment, Journal of Political Economy, 85 (1977), 937-968.   Google Scholar

[36]

M. Shubik, Commodity money, oligopoly, credit and bankruptcy in a general equilibrium model, Western Economic Journal, 11 (1973), 24-38.   Google Scholar

[37]

R. Tourky and N. C. Yannelis, Markets with many more agents than commodities: Aumann's "hidden" assumption, Journal of Economic Theory, 101 (2001), 189-221.  doi: 10.1006/jeth.2000.2705.  Google Scholar

[38]

M. H. Wooders, Equivalence of games and markets, Econometrica, 62 (1994), 1141-1160.  doi: 10.2307/2951510.  Google Scholar

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