Metastrategies in Large-Scale Bargaining Settings

Abstract

This article presents novel methods for representing and analyzing a special class of multiagent bargaining settings that feature multiple players, large action spaces, and a relationship among players’ goals, tasks, and resources. We show how to reduce these interactions to a set of bilateral normal-form games in which the strategy space is significantly smaller than the original settings while still preserving much of their structural relationship. The method is demonstrated using the Colored Trails (CT) framework, which encompasses a broad family of games and has been used in many past studies. We define a set of heuristics (metastrategies) in multiplayer CT games that make varying assumptions about players’ strategies, such as boundedly rational play and social preferences. We show how these CT settings can be decomposed into canonical bilateral games such as the Prisoners’ Dilemma, Stag Hunt, and Ultimatum games in a way that significantly facilitates their analysis. We demonstrate the feasibility of this approach in separate CT settings involving one-shot and repeated bargaining scenarios, which are subsequently analyzed using evolutionary game-theoretic techniques. We provide a set of necessary conditions for CT games for allowing this decomposition. Our results have significance for multiagent systems researchers in mapping large multiplayer CT task settings to smaller, well-known bilateral normal-form games while preserving some of the structure of the original setting.