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.

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:::info Authors:

(1) Ghislain H. Demeze-Jouatsa, Center for Mathematical Economics, University of Bielefeld (demeze [e-mail]);

(2) Roland Pongou, Department of Economics, University of Ottawa ([e-mail]);

(3) Jean-Baptiste Tondji, Department of Economics and Finance, The University of Texas Rio Grande Valley ([e-mail]).

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

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