🤖 AI Summary
This study addresses the limitations of Multiplicative Kantian Equilibrium, whose outcomes are sensitive to the arbitrary choice of strategy measurement scale due to a lack of strategic equivalence and are vulnerable to free-riding by Nash-type players. Focusing on symmetric games, the authors propose a rescaling of strategies that eliminates the free-riding advantage while preserving Pareto efficiency among Kantian agents. By integrating game-theoretic analysis, subgame perfect equilibrium concepts, and evolutionary stability (ESS) theory, they demonstrate that when types are endogenously selected, all players strictly prefer Kantian optimization. Moreover, this strategy emerges as a stable dominant strategy under both dynamic and evolutionary frameworks. The findings reveal that strategic non-equivalence—typically viewed as a drawback—can instead be leveraged to construct robust cooperative mechanisms.
📝 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.