A Higher-order Framework for Decision Problems and Games

TL;DR

This paper presents a unified, flexible framework for modeling decision problems and finite games using quantifiers and selection functions, allowing for more nuanced agent goals and behaviors beyond traditional utility maximization.

Contribution

It introduces a novel, compositional framework that generalizes Nash equilibrium to include context-dependent goals and non-maximizing heuristics, enhancing game modeling.

Findings

Framework accommodates incomplete preferences and heuristics.

Generalized Nash equilibrium captures context-dependent goals.

Modular and easily exchangeable game components.

Abstract

We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions. We show that the canonical utility maximisation is one special case of a quantifier and that our more abstract framework provides several additional degrees of freedom in modelling. In particular, incomplete preferences, non-maximising heuristics, and context-dependent motives can be taken into account when describing an agent's goal. We introduce a suitable generalisation of Nash equilibrium for games in terms of quantifiers and selection functions. Moreover, we introduce a refinement of Nash that captures context-dependency of goals. Modelling in our framework is compositional as the parts of the game are modular and can be easily exchanged. We provide an extended example where we illustrate concepts and highlight the benefits of our alternative modelling approach.