The Mathematical Foundation of Fairness: Proving Key Principles in an Economic Model

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

Appendix

Proof of Proposition 1.

Sufficiency. We show that the allocation scheme Sh satisfies ALUM.

It follows that the allocation Sh satisfies x-Anonymity for each x ∈ X. Hence, Sh satisfies Anonymity.