Almost-Nash Sequential Bargaining

In a 2017 paper, later presented at the Web and Internet Economics conference, titled ``Sequential Deliberation for Social Choice", the authors propose a mechanism in which a series of agents, are tasked to negotiate over a set of decisions S. Building on assumptions of Nash Bargaining and assuming the decision space follows the median graph, the authors constructed a robust algorithm which approximates the decision which minimizes the social cost to the entire population. In this paper, we give a brief overview of the background theory which this paper builds upon from foundational work from Nash, and social choice results which hold true in Condorcet mechanisms. Following this analysis, we consider the stability of the results in the paper with different deviations from Nash equilibrium. These deviations could be pessimal, in the context of unequal bargaining power (say in a labor market) or constructive, as in the context of opinion dynamics. Our analysis is observatory, in the context of simulations, and we hope to formalize the results of these simulations to get an understanding of more general properties in spaces beyond our simulation.