Strategically Robust Aggregative Games

TL;DR

This paper introduces a new equilibrium concept called strategically robust Wardrop equilibrium for aggregative games, providing a way for agents to protect against uncertain aggregate behaviors and improving decision-making in multiagent systems.

Contribution

It proposes a novel equilibrium concept that interpolates between standard and robust strategies, with existence proofs and computational methods for convex aggregative games.

Findings

Strategically robust Wardrop equilibria exist in convex aggregative games.

Robust equilibria lead to better decisions and lower costs for agents.

Robustification can induce a coordination effect among agents.

Abstract

In many multiagent settings, such as electric vehicle charging and traffic routing, agents must make decisions in the face of uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, such as incomplete information, limited computation, or bounded rationality, ultimately impacting the aggregate behavior. To tackle this challenge, we follow recent work on strategically robust game theory and postulate that agents seek protection directly against deviations around the emergent behavior, as opposed to explicitly modeling all sources of uncertainty. Specifically, we propose that each agent protects itself against the worst-case aggregate behavior within an optimal-transport-based ambiguity set centered at the emergent aggregate population behavior. This leads to a novel equilibrium concept, called strategically robust Wardrop equilibrium, that enables one to interpolate between standard Wardrop equilibria (no robustness) and security strategies (maximum robustness). In the setting of convex aggregative games, we establish the existence of a pure strategically robust Wardrop equilibrium and provide tractable computational tools for computing it. Through an application in electric vehicle charging, we demonstrate that strategically robust Wardrop equilibria lead to better decisions, protecting agents against the uncertain aggregate behavior of the population. Remarkably, we also observe that strategic robustness can lead to lower equilibrium costs for all agents, uncovering a "coordination-via-robustification" effect.