Rationality and connectivity in stochastic learning for networked coordination games

TL;DR

This paper investigates how network connectivity and bounded rationality influence the convergence to optimal strategies in stochastic learning for networked coordination games, revealing that higher connectivity can compensate for less rational agents.

Contribution

It introduces a framework analyzing bounded rationality in networked coordination games and demonstrates the relationship between connectivity and rationality for convergence.

Findings

Higher connectivity allows less rational agents to still converge to near-optimal strategies.

The framework establishes that the game is a potential game, facilitating analysis.

Connectivity can offset bounded rationality, promoting collective coordination.

Abstract

Coordination is a desirable feature in many multi-agent systems such as robotic and socioeconomic networks. We consider a task allocation problem as a binary networked coordination game over an undirected regular graph. Each agent in the graph has bounded rationality, and uses a distributed stochastic learning algorithm to update its action choice conditioned on the actions currently played by its neighbors. After establishing that our framework leads to a potential game, we analyze the regime of bounded rationality, where the agents are allowed to make sub-optimal decisions with some probability. Our analysis shows that there is a relationship between the connectivity of the network, and the rationality of the agents. In particular, we show that in some scenarios, an agent can afford to be less rational and still converge to a near optimal collective strategy, provided that its connectivity degree increases. Such phenomenon is akin to the wisdom of crowds.