Super-Nash Performance A New Benchmark and the Optimin Solution Concept
📝 Original Paper Info
- Title: Super-Nash Performance- ArXiv ID: 1912.00211
- Date: 2025-10-23
- Authors: Mehmet S. Ismail
📝 Abstract
In this paper, I introduce a novel benchmark in games, super-Nash performance, and a solution concept, optimin, whereby players maximize their minimal payoff under unilateral profitable deviations by other players. Optimin achieves super-Nash performance in that, for every Nash equilibrium, there exists an optimin where each player not only receives but also guarantees super-Nash payoffs under unilateral profitable deviations by others. Further, optimin generalizes Nash equilibrium in n-person constant-sum games and coincides with it when n=2. Finally, optimin is consistent with the direction of non-Nash deviations in games in which cooperation has been extensively studied.💡 Summary & Analysis
This paper introduces a new concept in game theory called "super-Nash performance" and the methodology to achieve it through something called "optimin". Optimin is designed so that each player maximizes their minimum payoff even under unilateral profitable deviations by other players. This provides a more stable state than traditional Nash equilibrium, especially in games where cooperative behavior plays an essential role.The core issue addressed here is finding a new kind of equilibrium beyond the traditional Nash equilibrium, one where players can ensure their minimal payoffs are guaranteed while maintaining stability. The methodology introduced involves designing strategies that maximize minimum payoff under any circumstances, ensuring that even if another player acts to benefit themselves unilaterally, the other players’ minimum payoffs remain secure.
The key achievement is that optimin generalizes Nash equilibrium and coincides with it in two-person constant-sum games. It also maintains consistent behavior regarding non-Nash deviations in cooperative games, providing a robust solution concept for stable game states.
This work is significant because it introduces a new stability concept in game theory that can be applied to diverse scenarios where ensuring minimal payoffs and maintaining stability are critical. This is particularly important in fields requiring collaborative actions, as optimin provides a framework for creating fairer and more stable gaming environments.