Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Dynamics of Profit-Sharing Games

An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team’s profit is given by a concave function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.