Beyond Nash: The Case for Mixed Objective Equilibrium - Part 1
The work of John Nash and the concept of the Nash Equilibrium rightfully stand as a monumental achievement in the history of strategic thought. Game theory gives us a powerful language to model conflict and cooperation, and its insights are foundational to everything from economics to evolutionary biology. Classical game theory, however, often built its elegant models on a crucial simplifying assumption: that a rational agent is ruthlessly optimizing for a single, pure utility function - typically profit.
But the real world is far messier.
Consider a multi-table poker tournament. The standard Game Theory Optimal (GTO) approach, based on the Independent Chip Model (ICM), seeks to maximize a player's real-dollar equity ($EV) in the prize pool. Yet, any experienced player knows this is an incomplete picture of their own decision-making. At any given moment, a player is simultaneously trying to:
Maximize their $EV.
Maximize their simple survival probability.
Maintain a large enough stack to apply pressure on weaker opponents.
Avoid high-variance spots against stronger opponents.
These are not parallel goals; they are often in direct conflict. A decision that maximizes short-term $EV might drastically increase your risk of elimination. A play that ensures survival might force you to pass up on a profitable opportunity. The player is not solving for a single objective; they are solving for a mix of them.
This gap between pure, single-objective theory and the messy, multi-objective reality is the focus of my primary research project: the development of a new framework I am calling Mixed Objective Equilibrium (MOE).
This post is not intended to detail the mathematics of the solution. Instead, its purpose is to introduce the problem. The ambition of MOE is to formalize a class of equilibrium where agents are optimizing for a blended and often competing set of objectives. The goal is not to replace the foundational concept of the Nash Equilibrium, but to build upon it, extending its power to better model the complex, multi-faceted incentive structures that drive real-world strategic decisions.
This is a long-term, ambitious project. The initial work will involve defining the mathematical structure of these blended utility functions and exploring solutions in simplified toy games. I will be documenting my progress, challenges, and insights on this topic here in The Lab.
While the initial models will focus on tournament poker, the scope of MOE extends far beyond the felt. Any domain where agents navigate competing incentives - from corporate strategy to AI alignment - stands to benefit from a richer equilibrium framework.