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

A note on the efficiency of position mechanisms with budget constraints

We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey–Clarke–Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria

Revenue Guarantee Equivalence

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders\u27 values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017a). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered