Utilitarian Welfare Optimization in the Generalized Vertex Coloring Games: An Implication to Venue Selection in Events Planning

TL;DR

This paper studies decentralized algorithms for maximizing welfare in generalized vertex coloring games, with applications to venue selection, proposing policies with proven convergence and robustness, supported by simulations.

Contribution

It introduces a greedy Metropolis-Hastings policy for G-VCGs, proves its optimality and robustness, and extends to a robust welfare optimization framework with empirical validation.

Findings

Convergence of greedy policies under synchronous settings.

Robustness of the proposed policy in asynchronous environments.

Effective welfare optimization balancing utility and robustness.

Abstract

We consider a general class of multi-agent games in networks, namely the generalized vertex coloring games (G-VCGs), inspired by real-life applications of the venue selection problem in events planning. Certain utility responding to the contemporary coloring assignment will be received by each agent under some particular mechanism, who, striving to maximize his own utility, is restricted to local information thus self-organizing when choosing another color. Our focus is on maximizing some utilitarian-looking welfare objective function concerning the cumulative utilities across the network in a decentralized fashion. Firstly, we investigate on a special class of the G-VCGs, namely Identical Preference VCGs (IP-VCGs) which recovers the rudimentary work by \cite{chaudhuri2008network}. We reveal its convergence even under a completely greedy policy and completely synchronous settings, with a stochastic bound on the converging rate provided. Secondly, regarding the general G-VCGs, a greediness-preserved Metropolis-Hasting based policy is proposed for each agent to initiate with the limited information and its optimality under asynchronous settings is proved using theories from the regular perturbed Markov processes. The policy was also empirically witnessed to be robust under independently synchronous settings. Thirdly, in the spirit of ``robust coloring'', we include an expected loss term in our objective function to balance between the utilities and robustness. An optimal coloring for this robust welfare optimization would be derived through a second-stage MH-policy driven algorithm. Simulation experiments are given to showcase the efficiency of our proposed strategy.