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

Table of Links

Abstract and 1. Introduction

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

   2.1 A free economy

   2.2 A free and fair economy

3. 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

4. Equilibrium efficiency in a free and fair economy

5. 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

6. 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

7. Contributions to the closely related literature

8. 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).