# Non-Cooperative Games with Uncertainty

arXiv: https://arxiv.org/abs/2503.01889 · HTML: https://mlsanity.com/paper/2503.01889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 27 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Abstract (arXiv)

This paper introduces a framework for finite non-cooperative games where each player faces a globally uncertain parameter with no common prior. Every player chooses both a mixed strategy and projects an emergent subjective prior to the uncertain parameters. We define an "Extended Equilibrium" by requiring that no player can improve her expected utility via a unilateral change of strategy, and the emergent subjective priors are such that they maximize the expected regret of the players. A fixed-point argument -- based on Brouwer's fixed point theorem and mimicking the construction of Nash -- ensures existence. Additionally, the "No Fictional Faith" theorem shows that any subjective equilibrium prior must stay non-concentrated if the parameter truly matters to a player. This approach provides a framework that unifies regret-based statistical decision theory and game theory, yielding a tool for handling strategic decision-making in the presence of deeply uncertain parameters.