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Game theoretical modelling of a dynamically evolving network Ⅱ: Target sequences of score 1
Market games and walrasian equilibria
1. | Universidad de Vigo, Spain |
2. | Universidad de Salamanca, Spain |
In this work, we recapitulate and compare the market game approaches provided by Shapley and Shubik [
References:
[1] |
R. M. Anderson,
An elementary core equivalence theorem, Econometrica, 46 (1978), 1483-1487.
doi: 10.2307/1913840. |
[2] |
R. M. Anderson,
Core theory with strongly convex preferences, Econometrica, 49 (1981), 1457-1468.
doi: 10.2307/1911411. |
[3] |
R. M. Anderson,
Strong core theorems with nonconvex preferences, Econometrica, 53 (1985), 1283-1294.
doi: 10.2307/1913208. |
[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. |
[5] |
K. J. Arrow and G. Debreu,
Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
doi: 10.2307/1907353. |
[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. |
[7] |
R. J. Aumann,
Markets with a continuum of traders, Econometrica, 32 (1964), 39-50.
doi: 10.2307/1913732. |
[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. |
[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. |
[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. |
[14] |
P. Dubey,
Price-quantity strategic market games, Econometrica, 50 (1982), 111-126.
doi: 10.2307/1912532. |
[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. |
[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. |
[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. |
[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. |
[19] |
J. García-Cutrín and C. Hervés-Beloso,
A discrete approach to continuum economies, Economic Theory, 3 (1993), 577-583.
doi: 10.1007/BF01209704. |
[20] |
G. Giraud,
Strategic market games: An introduction, Journal of Mathematical Economics, 39 (2003), 355-375.
doi: 10.1016/S0304-4068(03)00049-1. |
[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. |
[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. |
[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. |
[25] |
W. Hildenbrand, Cores and Equilibria of a Large Economy, Princeton Studies in Mathematical Economics, No. 5. Princeton University Press, Princeton, N.J., 1974. |
[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. |
[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. |
[28] |
E. Moreno-García,
Strategic equilibria with partially consumable withholdings, International Game Theory Review, 8 (2006), 533-553.
doi: 10.1142/S0219198906001090. |
[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. |
[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. |
[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. |
[33] |
D. Schmeidler,
Walrasian analysis via strategic outcome functions, Econometrica, 48 (1980), 1585-1593.
doi: 10.2307/1911923. |
[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. |
[38] |
M. H. Wooders,
Equivalence of games and markets, Econometrica, 62 (1994), 1141-1160.
doi: 10.2307/2951510. |
show all references
References:
[1] |
R. M. Anderson,
An elementary core equivalence theorem, Econometrica, 46 (1978), 1483-1487.
doi: 10.2307/1913840. |
[2] |
R. M. Anderson,
Core theory with strongly convex preferences, Econometrica, 49 (1981), 1457-1468.
doi: 10.2307/1911411. |
[3] |
R. M. Anderson,
Strong core theorems with nonconvex preferences, Econometrica, 53 (1985), 1283-1294.
doi: 10.2307/1913208. |
[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. |
[5] |
K. J. Arrow and G. Debreu,
Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
doi: 10.2307/1907353. |
[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. |
[7] |
R. J. Aumann,
Markets with a continuum of traders, Econometrica, 32 (1964), 39-50.
doi: 10.2307/1913732. |
[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. |
[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. |
[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. |
[14] |
P. Dubey,
Price-quantity strategic market games, Econometrica, 50 (1982), 111-126.
doi: 10.2307/1912532. |
[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. |
[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. |
[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. |
[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. |
[19] |
J. García-Cutrín and C. Hervés-Beloso,
A discrete approach to continuum economies, Economic Theory, 3 (1993), 577-583.
doi: 10.1007/BF01209704. |
[20] |
G. Giraud,
Strategic market games: An introduction, Journal of Mathematical Economics, 39 (2003), 355-375.
doi: 10.1016/S0304-4068(03)00049-1. |
[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. |
[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. |
[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. |
[25] |
W. Hildenbrand, Cores and Equilibria of a Large Economy, Princeton Studies in Mathematical Economics, No. 5. Princeton University Press, Princeton, N.J., 1974. |
[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. |
[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. |
[28] |
E. Moreno-García,
Strategic equilibria with partially consumable withholdings, International Game Theory Review, 8 (2006), 533-553.
doi: 10.1142/S0219198906001090. |
[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. |
[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. |
[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. |
[33] |
D. Schmeidler,
Walrasian analysis via strategic outcome functions, Econometrica, 48 (1980), 1585-1593.
doi: 10.2307/1911923. |
[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. |
[38] |
M. H. Wooders,
Equivalence of games and markets, Econometrica, 62 (1994), 1141-1160.
doi: 10.2307/2951510. |
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