The Full Pareto Frontier as Kantian Equilibria

TL;DR

This paper demonstrates that the full Pareto frontier can be achieved as Kantian equilibria by strategic space adjustments, separating efficiency from fairness in social dilemmas.

Contribution

It proves that any Pareto-efficient point can be realized as a Kantian equilibrium through strategic parametrization, providing a constructive geometric proof.

Findings

Achievable Kantian equilibria span the entire Pareto frontier.

Strategic non-equivalence is key to attaining different equilibrium outcomes.

The method separates efficiency considerations from fairness criteria.

Abstract

Multiplicative Kantian equilibrium explains cooperative behavior in social dilemmas without abandoning methodological individualism. However, its outcomes depend critically on the parametrization of the strategy space - the property of strategic non-equivalence. We investigate what fraction of the Pareto frontier can be attained by varying the strategy space. We show that the set of achievable Kantian equilibria is the entire Pareto frontier: for any interior Pareto-efficient point there exists a shift of coordinates - imposing lower bounds on actions - that makes it a Multiplicative Kantian equilibrium. The proof is constructive and relies on a intuitive geometric property: moving the origin to a point on the common tangent to players' indifference curves. This result separates the problem of efficiency from the problem of fairness, allowing any normative criterion to be implemented without loss of Pareto optimality.