Title

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

Degree Year

2021

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Computer Science

Advisor(s)

Adam Eck
Samuel Taggart

Keywords

Algorithmic game theory, Auction theory, Development economics, Mutual aid, Price of anarchy

Abstract

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.

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