The Monotonicity Theorem: How a Simple Condition Guarantees Equilibrium Uniqueness and Efficiency

Further demonstrating that if the economy is strictly monotonic, the equilibrium is not only Pareto-efficient but also unique, providing a critical condition for ruling out multiple equilibria.


This content originally appeared on HackerNoon and was authored by Tokenomy

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

4 Equilibrium efficiency in a free and fair economy

\

\ We have the following result.

\

\ In Theorem 2, we show that each weakly monotonic free and fair economy admits an equilibrium that is Pareto-efficient. Consider the strategic form game described in Table 5 below. The latter is derived from a free and fair economy with the profile o = (c, a) as the reference point. The economy admits two equilibria, namely, outcomes (c, a) and (d, b). The profile (d, b) is Pareto-efficient and it dominates the outcome (c, a).

\ Table 5: A 2-agent free and fair economy with a Pareto-dominated equilibrium

\ Table 6: A 2-agent strictly monotonic free and unfair economy

\

\

:::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).

:::

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

:::

\


This content originally appeared on HackerNoon and was authored by Tokenomy


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