Price of Anarchy for Mechanisms with Risk-Averse Agents

We study the price of anarchy of mechanisms in the presence of risk-averse agents. Previous work has focused on agents with quasilinear utilities, possibly with a budget. Our model subsumes this as a special case but also captures that agents might be less sensitive to payments than in the risk-neutral model. We show that many positive price-of-anarchy results proved in the smoothness framework continue to hold in the more general risk-averse setting. A sufficient condition is that agents can never end up with negative quasilinear utility after playing an undominated strategy. This is true, e.g., for first-price and second-price auctions. For all-pay auctions, similar results do not hold: We show that there are Bayes-Nash equilibria with arbitrarily bad social welfare compared to the optimum

The Mathematics of Mutual Aid: Robust Welfare Guarantees for Decentralized Financial Organizations

Mutual aid groups often serve as informal financial organizations that don’t rely on any central authority or legal framework to resolve disputes. Rotating savings and credit associations (roscas) are informal financial organizations common in settings where communities have reduced access to formal financial institutions. In a Rosca, a fixed group of participants regularly contribute small sums of money to a pool. This pool is then allocated periodically typically using lotteries or auction mechanisms. Roscas are empirically well-studied in the development economics literature. Due to their dynamic nature, however, roscas have proven challenging to examine theoretically. Theoretical analyses within economics have made strong assumptions about features such as the number or homogeneity of participants, the information they possess, their value for saving across time, or the number of rounds. This work presents an algorithmic study of roscas. We use techniques from the price of anarchy in auctions to characterize their welfare properties under less restrictive assumptions than previous work. We also give a comprehensive theoretical study of the various Rosca formats. Using the smoothness framework of Syrgkanis and Tardos [46] and other techniques we show that the most common Rosca formats have welfare within a constant factor of the best possible. This evidence further rationalizes these organizations’ prevalence as a vehicle for mutual aid. Roscas present many further questions where algorithmic game theory may be helpful; we discuss several promising directions

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201