Justice and Efficiency: A Non-Parametric Model for a Free and Fair Economy

Table of Links

Abstract and 1. Introduction

1. A free and fair economy: definition, existence and uniqueness

   2.1 A free economy

   2.2 A free and fair economy

2. Equilibrium existence in a free and fair economy

   3.1 A free and fair economy as a strategic form game

   3.2 Existence of an equilibrium

3. Equilibrium efficiency in a free and fair economy

4. A free economy with social justice and inclusion

   5.1 Equilibrium existence and efficiency in a free economy with social justice

   5.2 Choosing a reference point to achieve equilibrium efficiency

5. Some applications

   6.1 Teamwork: surplus distribution in a firm

   6.2 Contagion and self-enforcing lockdown in a networked economy

   6.3 Bias in academic publishing

   6.4 Exchange economies

6. Contributions to the closely related literature

7. Conclusion and References

Appendix

8 Conclusion

In this paper, we examine how elementary principles of justice and ethics, of long tradition in economic theory, affect individual incentives in a competitive environment and determine the existence and efficiency of self-enforcing social contracts. To formalize this problem, we introduce a model of a free and fair economy, in which each agent freely and non-cooperatively chooses their input from a finite set, and the surplus generated by these choices is distributed following four ideals of market justice, which are anonymity, local efficiency, unproductivity, and marginality. We show that these ideals guarantee the existence of a pure strategy Nash equilibrium. However, an equilibrium need not be unique or Pareto-efficient. We uncover an intuitive condition—strict technological monotonicity—, which guarantees equilibrium uniqueness and efficiency. Interestingly, this condition does not guarantee equilibrium efficiency (or even existence) when ideals of justice are violated in an economy. These ideals therefore lead to positive incentives, given their desirable equilibrium and efficiency properties.

\ We extend our analysis to incorporate social justice and inclusion, implemented in the form of progressive taxation and redistribution and guaranteeing a basic income to unproductive agents. In this more general setting, we generalize all of our findings. In addition, we examine how the tax policy affects efficiency, showing that there is a tax rate threshold above which an equilibrium that is Pareto-efficient always exists in the economy, even in the absence of technological monotonicity. Moreover, we show that if a free economy is able to choose its reference point, it can always do so to induce an efficient outcome that is self-enforcing, even if this economy is not monotonic.

\ By incorporating normative principles into non-cooperative game theory, we have defined a new class of finite strategic form games that always admit a pure strategy Nash equilibrium. We develop applications to some classical and recent economic problems, including the allocation of goods in an exchange economy, surplus distribution in a firm, self-enforcing lockdown in a networked economy facing contagion, and publication bias in academic publishing. This variety of applications is possible because we impose no particular assumptions on the structure of agents’ action sets, and our setting is fully non-parametric.

References

Victor Aguiar, Roland Pongou, and Jean-Baptiste Tondji. A non-parametric approach to testing the axioms of the shapley value with limited data. Games and Economic Behavior, 111:41–63, 2018.

\ Victor H Aguiar, Roland Pongou, Roberto Serrano, and Jean-Baptiste Tondji. An index of unfairness. In Handbook of the Shapley Value, Algaba, E. (Ed.), Fragnelli, V. (Ed.), S`anchezSoriano, J. (Ed.), 2020.

\ George A. Akerlof. Sins of omission and the practice of economics. Journal of Economic Literature, 58(2):405–18, 2020.

\ Siwan Anderson and Debraj Ray. Missing women: age and disease. The Review of Economic Studies, 77(4):1262–1300, 2010.

\ Aristotle. The Politics, Book III. edited and translated by Ernest Baker(New York: Oxford University Press, 1946.

\ Kenneth J. Arrow and Gerard Debreu. Existence of an equilibrium for a competitive economy. Econometrica, pages 265–290, 1954.

\ Susan Athey. Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica, 69(4):861–889, 2001.

\ Ana I. Balsa and Thomas G. McGuire. Statistical discrimination in health care. Journal of Health Economics, 20(6):881–907, 2001.

\ Hari Bapuji, Gokhan Ertug, and Jason D. Shaw. Organizations and societal economic inequality: a review and way forward. Academy of Management Annals, 14(1):60–91, 2020.

\ Marianne Bertrand and Sendhil Mullainathan. Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review, 94(4):991–1013, 2004.

\ Francis Bloch and Matthew O. Jackson. The formation of networks with transfers among players. Journal of Economic Theory, 133(1):83–110, 2007.

\ Daniel Bunn, Gustav Fritzon, and Jacob Lundberg. Taxing High Incomes: A Comparison of 41 Countries. Technical report, 2019. URL https://taxfoundation.org/ taxing-high-income-2019/. Accessed: 2021-07-23.

\ Antoni Calvo-Armengol. Job contact networks. Journal of economic Theory, 115(1):191–206, 2004.

\ Oriol Carbonell-Nicolau. On the existence of pure-strategy perfect equilibrium in discontinuous games. Games and Economic Behavior, 71(1):23–48, 2011.

\ David Card and Stefano DellaVigna. Nine facts about top journals in economics. Journal of Economic Literature, 51(1):144–61, 2013.

\ David Card, Stefano DellaVigna, Patricia Funk, and Nagore Iriberri. Are referees and editors in Economics gender neutral? The Quarterly Journal of Economics, 135(1):269–327, 2020.

\ Guilherme Carmona and Konrad Podczeck. Pure strategy nash equilibria of large finite-player games and their relationship to non-atomic games. Journal of Economic Theory, page 105015, 2020.

\ Kerwin Kofi Charles and Jonathan Guryan. Prejudice and wages: an empirical assessment of Becker’s the economics of discrimination. Journal of Political Economy, 116(5):773–809, 2008.

\ Tommaso Colussi. Social ties in academia: A friend is a treasure. Review of Economics and Statistics, 100(1):45–50, 2018.

\ Partha Dasgupta and Eric Maskin. The existence of equilibrium in discontinuous economic games, I: Theory. The Review of economic studies, 53(1):1–26, 1986a.

\ Partha Dasgupta and Eric Maskin. The existence of equilibrium in discontinuous economic games, II: Applications. The Review of economic studies, 53(1):27–41, 1986b.

\ H. David and Mark G. Duggan. The growth in the social security disability rolls: a fiscal crisis unfolding. Journal of Economic perspectives, 20(3):71–96, 2006.

\ Geoffroy De Clippel and Kareen Rozen. Fairness through the lens of cooperative game theory: An experimental approach. Cowles Foundation Discussion Paper, 2013.

\ Geoffroy De Clippel and Roberto Serrano. Marginal contributions and externalities in the value. Econometrica, 76(6):1413–1436, 2008.

\ Gerard Debreu. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences, 38(10):886–893, 1952.

\ Glenn Ellison. Evolving standards for academic publishing: A q-r theory. Journal of Political Economy, 110(5):994–1034, 2002.

\ Andrew M Francis and Maria Tannuri-Pianto. The redistributive equity of affirmative action: Exploring the role of race, socioeconomic status, and gender in college admissions. Economics of Education Review, 31(1):45–55, 2012.

\ David Gale. A theory of n-person games with perfect information. Proceedings of the National Academy of Sciences of the United States of America, 39(6):496, 1953.

\ Irving L. Glicksberg. A further generalization of the kakutani fixed point theorem, with application to Nash equilibrium points. Proceedings of the American Mathematical Society, 3(1):170–174, 1952.

\ Claudia Goldin, Sari Pekkala Kerr, Claudia Olivetti, and Erling Barth. The expanding gender earnings gap: Evidence from the LEHD-2000 Census. American Economic Review, 107(5): 110–14, 2017.

\ Sanjeev Goyal and Sumit Joshi. Unequal connections. International Journal of Game Theory, 34 (3):319–349, 2006.

\ Douglas Grbic, David J. Jones, and Steven T. Case. The role of socioeconomic status in medical school admissions: validation of a socioeconomic indicator for use in medical school admissions. Academic Medicine, 90(7):953–960, 2015.

\ Rema Hanna and Benjamin A. Olken. Universal basic incomes versus targeted transfers: Antipoverty programs in developing countries. Journal of Economic Perspectives, 32(4):201–26, 2018.

\ James J Heckman and Sidharth Moktan. Publishing and promotion in Economics: the tyranny of the top five. Journal of Economic Literature, 58(2):419–70, 2020.

\ James J. Heckman, George Akerlof, Angus Deaton, Drew Fudenberg, and Lars Hansen. Publishing and promotion in economics: the curse of the top five. AEA Roundatble Discussion at ASSA in Chicago, 2017. URL https://www.aeaweb.org/webcasts/2017/curse.php.

\ Bengt Holmstrom. Moral hazard in teams. The Bell Journal of Economics, pages 324–340, 1982.

\ Marie Hyland, Simeon Djankov, and Pinelopi Koujianou Goldberg. Gendered laws and women in the workforce. American Economic Review: Insights, 2(4):475–490, 2020.

\ Matthew O. Jackson and Asher Wolinsky. A strategic model of social and economic networks. Journal of Economic Theory, 71(1):44–74, 1996.

\ Reinoud Anna Maria Gerardus Joosten. Dynamics, equilibria, and values. PhD thesis, Maastricht University, 1996.

\ M. Ali Khan and Yeneng Sun. Pure strategies in games with private information. Journal of Mathematical Economics, 24(7):633–653, 1995.

\ Marlene Koffi. Gendered citations at top economic journals. AEA Papers and Proceedings, 111: 60–64, 2021.

\ Marlene Koffi and Leonard Wantchekon. Racial justice from within? diversity and inclusion in Economics. Econometric Society World Congress Monograph, Forthcoming.

\ Michael W. Kraus, Brittany Torrez, Jun Won Park, and Fariba Ghayebi. Evidence for the reproduction of social class in brief speech. Proceedings of the National Academy of Sciences, 116 (46):22998–23003, 2019.

\ David N. Laband and Michael J. Piette. Favoritism versus search for good papers: Empirical evidence regarding the behavior of journal editors. Journal of Political Economy, 102(1):194– 203, 1994.

\ Kevin Lang and Michael Manove. Education and labor market discrimination. American Economic Review, 101(4):1467–96, 2011.

\ Indrajit Mallick. On the existence of pure strategy Nash equilibria in two person discrete games. Economics Letters, 111(2):144–146, 2011.

\ Andreu Mas-Colell. On a theorem of Schmeidler. Journal of Mathematical Economics, 13(3): 201–206, 1984.

\ Dov Monderer and Lloyd S. Shapley. Potential games. Games and economic behavior, 14(1): 124–143, 1996.

\ John Nash. Non-cooperative games. Annals of mathematics, pages 286–295, 1951.

\ John Nash. Two-person cooperative games. Econometrica, pages 128–140, 1953.

\ Rabia Nessah and Guoqiang Tian. On the existence of Nash equilibrium in discontinuous games. Economic Theory, 61(3):515–540, 2016.

\ Martin J. Osborne and Ariel Rubinstein. A course in game theory. MIT press, 1994.

\ Roland Pongou. The economics of fidelity in network formation. PhD thesis, Brown University, 2010.

\ Roland Pongou and Roberto Serrano. Fidelity networks and long-run trends in HIV/AIDS gender gaps. American Economic Review, 103(3):298–302, May 2013. doi: 10.1257/aer.103.3.298.

\ Roland Pongou and Roberto Serrano. Volume of trade and dynamic network formation in twosided economies. Journal of Mathematical Economics, 63:147–163, 2016.

\ Roland Pongou and Jean-Baptiste Tondji. Valuing inputs under supply uncertainty : The Bayesian Shapley value. Games and Economic Behavior, 108:206–224, 2018.

\ Eric A. Posner and E. Glen Weyl. Radical markets: Uprooting capitalism and democracy for a just society. Princeton University Press, 2018.

\ John Rawls. A theory of justice. Harvard university press, 1971.

\ Cordelia W. Reimers. Labor market discrimination against hispanic and black men. The Review of Economics and Statistics, pages 570–579, 1983.

\ Philip J. Reny. On the existence of pure and mixed strategy nash equilibria in discontinuous games. Econometrica, 67(5):1029–1056, 1999.

\ Philip J. Reny. Nash equilibrium in discontinuous games. Economic Theory, 61(3):553–569, 2016.

\ John E Roemer. Theories of distributive justice. Harvard University Press, 1998.

\ Robert W Rosenthal. A class of games possessing pure-strategy nash equilibria. International Journal of Game Theory, 2(1):65–67, 1973.

\ Jean-Jacques Rousseau. Le contrat social; ou, principes du droit politique. (Rreprinted: Paris, Gamier, 1966), 1762.

\ Michael J. Sandel. Justice: What’s the right thing to do? Macmillan, 2010.

\ Heather Sarsons. Recognition for group work: Gender differences in academia. American Economic Review, 107(5):141–45, 2017.

\ David Schmeidler. Equilibrium points of nonatomic games. Journal of statistical Physics, 7(4): 295–300, 1973.

\ Amartya Sen. Missing women. BMJ: British Medical Journal, 304(6827):587, 1992.

\ Amartya Sen. The idea of justice. Harvard University Press, 2009.

\ Roberto Serrano. Top5itis. Technical report, Working Paper, 2018.

\ Roberto Serrano. Sixty-seven years of the Nash Program: Time for retirement? Brown Orlando Bravo Center for Economic Research Working Paper, (2020-020), 2020.

\ Lloyd S. Shapley. A value for n-person games. Contributions to the Theory of Games, 2(28): 307–317, 1953.

\ Lloyd S. Shapley and Martin Shubik. An example of a trading economy with three competitive equilibria. Journal of Political Economy, 85(4):873–875, 1977.

\ Mario L. Small and Devah Pager. Sociological perspectives on racial discrimination. Journal of Economic Perspectives, 34(2):49–67, 2020.

\ William Thomson. Fair allocation. New York, Oxford University Press, 2016.

\ Graham Thornicroft, Diana Rose, and Aliya Kassam. Discrimination in health care against people with mental illness. International Review of Psychiatry, 19(2):113–122, 2007.

\ Leon Walras. Elements of pure Economics. London: Allen and Unwing, 1954.

\ Robert E. Wright and John F. Ermisch. Gender discrimination in the british labour market: a reassessment. The Economic Journal, 101(406):508–522, 1991.

\ H. Peyton Young. Monotonic solutions of cooperative games. International Journal of Game Theory, 14(2):65–72, 1985.

\ Abderrahmane Ziad. Pure strategy nash equilibria of non-zero-sum two-person games: non-convex case. Economics Letters, 62(3):307–310, 1999.

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:::info Authors:

(1) Ghislain H. Demeze-Jouatsa, Center for Mathematical Economics, University of Bielefeld (demeze jouatsa@uni-bielefeld.de);

(2) Roland Pongou, Department of Economics, University of Ottawa (rpongou@uottawa.ca);

(3) Jean-Baptiste Tondji, Department of Economics and Finance, The University of Texas Rio Grande Valley (jeanbaptiste.tondji@utrgv.edu).

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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