Distance-based Equilibria in Normal-Form Games

TL;DR

This paper introduces a new class of equilibrium concepts in normal-form games based on agents' uncertainty modeled by distance from actual strategies, analyzing their properties, relationships, and existence.

Contribution

It proposes a simple uncertainty modification in agent behavior leading to distance-based equilibria, connecting them to existing concepts and establishing their existence.

Findings

Distance-based equilibria generalize existing solution concepts.

Existence of these equilibria is proven for certain classes of games.

Some distance-based equilibria can yield better outcomes than traditional solutions.

Abstract

We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of "possible profiles" that are within a certain distance from the actual action profile. We investigate the various instantiations in which the agent chooses her strategy using well-known rationales e.g., considering the worst case, or trying to minimize the regret, to cope with such uncertainty. Any such modification in the behavioral model naturally induces a corresponding notion of equilibrium; a distance-based equilibrium. We characterize the relationships between the various equilibria, and also their connections to well-known existing solution concepts such as Trembling-hand perfection. Furthermore, we deliver existence results, and show that for some class of games, such solution concepts can actually lead to better outcomes.