Strategy Rescaling and the Stability of Kantian Optimization

TL;DR

This paper analyzes the stability of Kantian equilibrium in symmetric games, revealing how strategy rescaling impacts outcomes and proposing methods to promote stable cooperation through Kantian optimization.

Contribution

It demonstrates the strategic non-equivalence of Kantian best-responses and introduces a rescaling approach to stabilize cooperation and evolutionary stability.

Findings

Kantian best-response is not invariant under strategy rescaling.

Rescaling can neutralize free-rider advantages in mixed Kantian-Nasher games.

Kantian optimization is shown to be evolutionarily stable.

Abstract

This study investigates the properties and stability of the Multiplicative Kantian Equilibrium (MKE) in symmetric games. We first demonstrate that MKE lacks strategic equivalence: the Kantian best-response function is not invariant under monotonic strategy rescaling. This strategic non-equivalence implies that the choice of measurement scale - a subjective interpretation of the game - materially impacts equilibrium outcomes. Exploiting this non-equivalence, in a game where players may be Kantian or Nasher, we propose an efficient strategy rescaling that allows Kantians to neutralize the free-rider advantage of Nashers, while preserving Pareto-efficient outcomes among themselves. In a dynamic framework, we show that the subgame-perfect Nash equilibrium with endogenous choice of optimization type leads all players to prefer Kantian optimization over Nash optimization. In an evolutionary setup, we show that Kantian optimization is an evolutionarily stable strategy (ESS). Our results suggest that the inherent strategic non-equivalence of Kantian optimization provides a robust pathway to stable cooperation.