An Algorithmic Introduction to Savings Circles

[Original paper by Rediet Abebe, Adam Eck, Christian Ikeokwu and Samuel Taggart]

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Overview: Rotating savings and credit associations (roscas) are informal financial organizations common in contexts where communities have little access to formal financial services. This paper builds on tools from algorithmic game theory to show that roscas are effective at allocating financial resources; this property helps explain their prevalence.

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Introduction

Rotating savings and credit associations (roscas) are informal financial organizations common in contexts where communities have little access to formal financial services. Examples include low-income countries, refugee/immigrant communities and other economically vulnerable populations. In a rosca, participants regularly meet and contribute small sums of money into a common pot. At regular intervals,  pot is then allocated to one of the members. Roscas are empirically well-studied in economics. They are, however, challenging to study theoretically since they unfold dynamically, and the pot is often allocated according to complex procedures such as auctions. In this work, we initiate an algorithmic study of roscas. Building on techniques from the price of anarchy literature we derive robust guarantees on the welfare of rosca participants. We do this under a wide range of assumptions on types of rosca participants and allocation formats, and are able to analyze a wide variety of formats used in practice. Our welfare guarantees help explain the prevalence of roscas and serve as proof of concept for techniques from algorithms and artificial intelligence to the study of informal finance and mutual aid.

Key Insights

Why study roscas?

Roscas play important roles in the lives of numerous individuals globally. Their use has been recorded in over 85 countries and 5+ continents (Aredo 2004; Bouman 1995a; Klonner 2002; La Ferrara 2002; Raccanello and Anand 2009) for variety of purposes such as to purchase durable goods (e.g., farming equipment, appliances, and vehicles), to buffer shocks (e.g. an unexpected medical expense), or to pay off loans. Roscas account for about one-half of Cameroon’s national savings. Likewise, over one in six households in Ethiopia’s highlands participate in roscas (Bouman 1995a).

Roscas often exist outside of legal frameworks and do not typically have a central authority to resolve disputes or enforce compliance. Instead, they provide a decentralized mechanism for peer-to-peer lending, where members who receive the pot earlier borrow from those who receive it later. To understand algorithmic-decision making and the impact of new financial technologies in low-access contexts, it is necessary to understand existing allocation mechanisms. 

Due to their ability to provide quick, targeted support within communities, roscas and other mutual aid organizations often play an instrumental role when communities experience shocks and disasters, such as during the covid-19 pandemic. (Chevée 2021; Mesch et al. 2020; Travlou 2020). Thus, roscas are a programmatic cornerstone for large development NGOs such as Care International (Care International 2019) who use them to create a structure for mutual support and community empowerment.

Previous work and Limitations

Roscas are well-studied in the economics literature, with economic theory on the subject pioneered by Besley, Coate, and Loury (1993); Kovsted and Lyk-Jensen (1999) and Kuo (1993). However, studies in economics are typically constrained in two main ways. The standard approach in economics predicts participants’ behaviors by solving mathematically for game-theoretic equilibria. Deriving these equilibria  is difficult due to the complexity of decision-making in roscas. Second, much of the existing theory focuses on coarse comparisons between the performance of roscas and other mechanisms for allocating credit. In part due to these coarse comparisons, this work often concludes that roscas allocate credit suboptimally, still leaving open the question of why roscas are prevalent in practice. 

Viewing roscas through the lens of approximation algorithms and using techniques from the price of anarchy literature, we study the welfare properties of rosca outcomes without directly solving for them and obtain quantifiable welfare guarantees that are within a constant factor of the best possible allocation mechanism.

We specifically quantify the allocative efficacy of roscas: how well do roscas coordinate saving and lending among agents with heterogeneous investment opportunities? We show roscas enable a group’s lending and borrowing in a way that approximately maximizes the groups’ total utility. We do so under a wide range of assumptions on both participants’ values for investment and the mechanisms used for allocating the pots. This robustness may provide one explanation for their prevalence.

Framework

A rosca consists of n agents and takes place over n discrete and fixed time periods, or rounds. During each round three things occur: (1) each member contributes a pre-agreed amount into the rosca common pot, (2) a winner for the pot is decided among those who have not yet won by some allocation mechanism, and (3) the winning participant is allocated the entire pot.

A variety of different pot allocation mechanisms are common in practice (see Ardener 1964; Bouman 1995b) and we analyze the welfare properties of typical pot allocation mechanisms. In a “swap rosca”, agents are given an initial (e.g. random) allocation and then swap positions in an after-market through bilateral trade agreements. We study the outcomes of these bilateral trade agreements. In auction-based roscas, during each meeting, members bid to decide a winner among those who have not yet received a pot and the bids are redistributed to others as rebates. During each round, participants must weigh the value of investing earlier against the utility loss from spending to win that round. We study the Nash equilibria of the rosca-sequential auctions. 

Main Results

Our technical contributions are as follows: For swap roscas, we prove that all outcomes guarantee at most a factor 2 loss from the optimal allocation. For auction-based roscas, we give full-information constant price of anarchy (PoA) bounds: we study second-price and first-price  sequential roscas and more and show they lose at most a constant factor of the optimal welfare. 
Our work provides new applications of and extensions to the smoothness framework of Syrgkanis and Tardos (2013) which has previously been used to analyze partial information auctions, auction revenue Hartline, Hoy and Taggart (2014), large games Feldman et al. (2016), and more (c.f Roughgarden, Syrgkanis, and Tardos (2017)). However, since participants can only win once and all payments are redistributed to members (i.e the auctions have no “seller”) in a rosca, standard smoothness arguments do not work in our setting.  Our welfare guarantees also hold under varying levels of risk-aversion and we use simulations to show that typical rosca instances perform much better than the theoretical guarantees.  

Between the lines

Roscas are complex and varied social institutions, significant for their integral role in allocating financial resources worldwide. While there are many open directions for further research we highlight two directions we are most excited about. First, our work focused on the savings aspect of roscas, but roscas are also used as insurance. Participants experiencing unanticipated needs may bid to obtain the pot earlier than they may have otherwise planned (Calomiris and Rajaraman 1998; Klonner 2003, 2001). There remain many gaps in our understanding of roscas when participants’ values and incomes evolve stochastically over time. 

The other challenge is understanding the tension between allocative efficiency and wealth inequality. Participants with valuable investment opportunities might not bid as aggressively if their low wealth causes them to value cash highly. Ethnographic work shows that altruism might play a role in alleviating this tension (Klonner 2008; Sedai, Vasudevan, and Pena 2021); roscas often serve a dual role of community-building institutions participants tend to observe signals about each others’ needs and act with mutual aid in mind (Klonner 2008; Mequanent 1996).