Relationship Design for Socially-Aware Behavior in Static Games

TL;DR

This paper introduces a novel model for socially-aware decision-making in static games, incorporating bounded rationality and inter-agent relationships, and proposes algorithms to optimize social costs at equilibrium.

Contribution

It presents a new relationship game model and mechanism design approach for socially-aware behavior in static games, addressing equilibrium multiplicity and social cost minimization.

Findings

Algorithms effectively reach equilibria with desired social costs.

Numerical results validate the approach in congestion scenarios.

The model captures social behaviors in autonomous agent decision-making.

Abstract

Autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. We present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. We capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. For each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. We address the multiplicity of equilibria by presenting the problem in two forms: Min-Max and Min-Min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. We compute the quantal response equilibrium by solving a least-squares problem defined with its Karush-Kuhn-Tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. Numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.