Learning to Coordinate over Networks with Bounded Rationality

2026-04-08

AI Summary

This study investigates how boundedly rational agents achieve efficient coordination in binary Stag Hunt games over networks. By integrating Logit response dynamics with Gibbs measure theory, and leveraging Markov chain steady-state analysis on K-regular graphs, the work establishes that the probability of coordination increases monotonically with both the rationality parameter and network connectivity. The main contributions include a novel method for approximating the Gibbs partition function using the moment-generating function of a Gaussian distribution, a proof that K-regular networks maximize the steady-state coordination probability among all possible topologies, and the derivation of a tight upper bound on the minimal rationality required to attain a desired coordination level—thereby significantly enhancing the reliability of cooperation in multi-agent systems under bounded rationality.

Abstract

Network coordination games are widely used to model collaboration among interconnected agents, with applications across diverse domains including economics, robotics, and cyber-security. We consider networks of bounded-rational agents who interact through binary stag hunt games, a canonical game theoretic model for distributed collaborative tasks. Herein, the agents update their actions using logit response functions, yielding the Log-Linear Learning (LLL) algorithm. While convergence of LLL to a risk-dominant Nash equilibrium requires unbounded rationality, we consider regimes in which rationality is strictly bounded. We first show that the stationary probability of states corresponding to perfect coordination is monotone increasing in the rationality parameter $β$. For $K$-regular networks, we prove that the stationary probability of a perfectly coordinated action profile is monotone in the connectivity degree $K$, and we provide an upper bound on the minimum rationality required to achieve a desired level of coordination. For irregular networks, we show that the stationary probability of perfectly coordinated action profiles increases with the number of edges in the graph. We show that, for a large class of networks, the partition function of the Gibbs measure is well approximated by the moment generating function of Gaussian random variable. This approximation allows us to optimize degree distributions and establishes that the optimal network - i.e., the one that maximizes the stationary probability of coordinated action profiles - is $K$-regular. Consequently, our results indicate that networks of uniformly bounded-rational agents achieve the most reliable coordination when connectivity is evenly distributed among agents.

Problem

• bounded rationality
• network coordination
• stag hunt game
• Log-Linear Learning
• Gibbs measure

Innovation

• bounded rationality
• network coordination
• Log-Linear Learning
• Gibbs measure
• regular graphs