2014, 1(2): 283-298. doi: 10.3934/jdg.2014.1.283

A strategic market game approach for the private provision of public goods

1. 

Departamento de Matemática, FCT, Universidade Nova de Lisboa, Centro de Matemática e Aplicaçōes (CMA), FCT, UNL, Campus da Caparica, 2829-516 Caparica, Portugal

2. 

Facultad de Economía y Empresa, Universidad de Salamanca, Campus Miguel de Unamuno, 37007 Salamanca, Spain

3. 

Department of Economics, Vanderbilt University, Nashville, TN 37235, United States

Received  June 2013 Revised  November 2013 Published  March 2014

Bergstrom, Blume and Varian [4] provides an elegant game-theoretic model of an economy with one private good and one public good. Strategies of players consist of voluntary contributions of the private good to public good production. Without relying on first order conditions, as in prior literature, the authors demonstrate existence of Nash equilibrium. The assumption of one-private good greatly facilities the results. We provide an analogue of the Bergstrom, Blume and Varian result in a model allowing multiple private and public goods. In addition, we relate the strategic market game equilibrium to the private-provision equilibrium of Villanacci and Zenginobuz [17], which provides a counter-part to the Walrasian equilibrium for a public goods economy. To obtain our results we introduce a model of a strategic market game with public goods. Our approach also incorporates, into the strategic market game literature, economies with production.
Citation: Marta Faias, Emma Moreno-García, Myrna Wooders. A strategic market game approach for the private provision of public goods. Journal of Dynamics & Games, 2014, 1 (2) : 283-298. doi: 10.3934/jdg.2014.1.283
References:
[1]

R. Amir and F. Bloch, Comparative statics in a simple class of strategic market games,, Games and Economic Behavior, 65 (2009), 7. doi: 10.1016/j.geb.2007.09.002.

[2]

J. Andreoni, Privately provided public goods in a large economy: The limits of altruism,, Journal of Public Economics, 35 (1988), 57. doi: 10.1016/0047-2727(88)90061-8.

[3]

J. Andreoni, Impure altruism and donations to public goods: A theory of warm-glow giving,, The Economic Journal, 100 (1990), 464. doi: 10.2307/2234133.

[4]

T. Bergstrom, L. Blume and H. Varian, On the private provision of public goods,, Journal of Public Economics, 29 (1986), 25. doi: 10.1016/0047-2727(86)90024-1.

[5]

P. Dubey and J. Geanakoplos, From nash to walras via shapley-shubik,, Journal of Mathematical Economics, 39 (2003), 391. doi: 10.1016/S0304-4068(03)00012-0.

[6]

M. Faias, E. Moreno-García and M. Wooders, A Strategic Market Game Approach for the Private Provision of Public Goods,, Working-paper CMA 4-2012. Universidade Nova de Lisboa., (): 4.

[7]

M. Florenzano, Walras-Lindahl-Wicksell: What Equilibrium Concept for Public Goods Provision? I - The Convex Case,, CES Working Papers 2009.09. Documents de Travail du Centre d'Economie de la Sorbonne, (2009).

[8]

D. Foley, Lindahl's solution and the core of an economy with public goods,, Econometrica, 38 (1970), 66. doi: 10.2307/1909241.

[9]

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

[10]

M. C. Kemp, A note on the theory of international transfers,, Economics Letters, 14 (1984), 259. doi: 10.1016/0165-1765(84)90092-2.

[11]

L. C. Koutsougeras, Non-walrasian equilibria and the law of one price,, Journal of Economic Theory, 108 (2003), 169. doi: 10.1016/S0022-0531(02)00014-5.

[12]

L. C. Koutsougeras, Convergence to no arbitrage equilibria in market games,, Journal of Mathematical Economics, 39 (2003), 401. doi: 10.1016/S0304-4068(03)00013-2.

[13]

T. J. Muench, The Core and the Lindahl equilibrium of an economy with a public good: An example,, Journal of Economic Theory, 4 (1972), 241. doi: 10.1016/0022-0531(72)90151-2.

[14]

K. Peck, J. Shell and S. E. Spear, The market game: Existence and structure of equilibrium,, Journal of Mathematical Economics, 21 (1992), 271. doi: 10.1016/0304-4068(92)90005-R.

[15]

P. Samuelson, The pure theory of public expenditure,, The Review of Economics and Statistics, 36 (1954), 387. doi: 10.2307/1925895.

[16]

L. S. Shapley and M. Shubik, Trade using one commodity as a means of payment,, Journal of Political Economy, 85 (1977), 937. doi: 10.1086/260616.

[17]

A. Villanacci and Ü. Zenginobuz, Existence and regularity of equilibria in a general equilibrium model with private provision of a public good,, Journal of Mathematical Economics, 41 (2005), 617. doi: 10.1016/j.jmateco.2004.12.005.

[18]

A. Villanacci and Ü. Zenginobuz, On the neutrality of redistribution in a general equilibrium model with public goods,, Journal of Public Economic Theory, 9 (2007), 183. doi: 10.1111/j.1467-9779.2007.00303.x.

[19]

A. Villanacci and Ü. Zenginobuz, Subscription equilibrium with production: Non-neutrality and constrained suboptimality,, Journal of Economic Theory, 147 (2012), 407. doi: 10.1016/j.jet.2010.08.012.

[20]

P. G. Warr, The private provision of a public good Is independent of the distribution of income,, Economics Letters, 13 (1983), 207. doi: 10.1016/0165-1765(83)90087-3.

show all references

References:
[1]

R. Amir and F. Bloch, Comparative statics in a simple class of strategic market games,, Games and Economic Behavior, 65 (2009), 7. doi: 10.1016/j.geb.2007.09.002.

[2]

J. Andreoni, Privately provided public goods in a large economy: The limits of altruism,, Journal of Public Economics, 35 (1988), 57. doi: 10.1016/0047-2727(88)90061-8.

[3]

J. Andreoni, Impure altruism and donations to public goods: A theory of warm-glow giving,, The Economic Journal, 100 (1990), 464. doi: 10.2307/2234133.

[4]

T. Bergstrom, L. Blume and H. Varian, On the private provision of public goods,, Journal of Public Economics, 29 (1986), 25. doi: 10.1016/0047-2727(86)90024-1.

[5]

P. Dubey and J. Geanakoplos, From nash to walras via shapley-shubik,, Journal of Mathematical Economics, 39 (2003), 391. doi: 10.1016/S0304-4068(03)00012-0.

[6]

M. Faias, E. Moreno-García and M. Wooders, A Strategic Market Game Approach for the Private Provision of Public Goods,, Working-paper CMA 4-2012. Universidade Nova de Lisboa., (): 4.

[7]

M. Florenzano, Walras-Lindahl-Wicksell: What Equilibrium Concept for Public Goods Provision? I - The Convex Case,, CES Working Papers 2009.09. Documents de Travail du Centre d'Economie de la Sorbonne, (2009).

[8]

D. Foley, Lindahl's solution and the core of an economy with public goods,, Econometrica, 38 (1970), 66. doi: 10.2307/1909241.

[9]

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

[10]

M. C. Kemp, A note on the theory of international transfers,, Economics Letters, 14 (1984), 259. doi: 10.1016/0165-1765(84)90092-2.

[11]

L. C. Koutsougeras, Non-walrasian equilibria and the law of one price,, Journal of Economic Theory, 108 (2003), 169. doi: 10.1016/S0022-0531(02)00014-5.

[12]

L. C. Koutsougeras, Convergence to no arbitrage equilibria in market games,, Journal of Mathematical Economics, 39 (2003), 401. doi: 10.1016/S0304-4068(03)00013-2.

[13]

T. J. Muench, The Core and the Lindahl equilibrium of an economy with a public good: An example,, Journal of Economic Theory, 4 (1972), 241. doi: 10.1016/0022-0531(72)90151-2.

[14]

K. Peck, J. Shell and S. E. Spear, The market game: Existence and structure of equilibrium,, Journal of Mathematical Economics, 21 (1992), 271. doi: 10.1016/0304-4068(92)90005-R.

[15]

P. Samuelson, The pure theory of public expenditure,, The Review of Economics and Statistics, 36 (1954), 387. doi: 10.2307/1925895.

[16]

L. S. Shapley and M. Shubik, Trade using one commodity as a means of payment,, Journal of Political Economy, 85 (1977), 937. doi: 10.1086/260616.

[17]

A. Villanacci and Ü. Zenginobuz, Existence and regularity of equilibria in a general equilibrium model with private provision of a public good,, Journal of Mathematical Economics, 41 (2005), 617. doi: 10.1016/j.jmateco.2004.12.005.

[18]

A. Villanacci and Ü. Zenginobuz, On the neutrality of redistribution in a general equilibrium model with public goods,, Journal of Public Economic Theory, 9 (2007), 183. doi: 10.1111/j.1467-9779.2007.00303.x.

[19]

A. Villanacci and Ü. Zenginobuz, Subscription equilibrium with production: Non-neutrality and constrained suboptimality,, Journal of Economic Theory, 147 (2012), 407. doi: 10.1016/j.jet.2010.08.012.

[20]

P. G. Warr, The private provision of a public good Is independent of the distribution of income,, Economics Letters, 13 (1983), 207. doi: 10.1016/0165-1765(83)90087-3.

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