Strategy Rescaling and the Stability of Kantian Optimization

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.