Multilateral Obligation Set-off

Sharing trading information to ‘clear’ obligations with as little money as possible has a long history. According to the Bank for International Settlement’s Committee of Payment and Settlement Systems Glossary, clearing is ‘the establishment of final positions for settlement’. However, the term is often used to include settlement, and there can be a variety of steps that take place as part of clearing.

‘Scontration’ was a method for clearing debts that originated in European mediaeval market fairs, where dense trading networks made it possible to conduct large amounts of trade without requiring scarce gold and silver money. Multilateral obligation set-off is a modern accounting process that works on similar principles, and is routine in the financial and corporate sectors. Slovenia has implemented it at the national level for over thirty years, clearing invoices between businesses using a tried, tested, and optimised algorithm called TETRIS.

Businesses submit their invoices to the service provider and the algorithm detects ‘loops’ circular patterns of payments due that connect businesses with each loop an opportunity to clear debt for all participants. The simplest possible loop is Business A owes Business B, and Business B owes Business A, with the amounts exactly the same. In this case it is obvious that the two debts can be ‘set off’ from each other, leaving nothing to pay. As illustrated below, this situation is instantly recognisable from day-to-day life!

In a business-to-business context, most loops within a trading network will be longer and the amounts owed will all be different. Even so, the same principle applies – all debts in a loop share a smallest common amount, which can be cleared to reduce the size of all obligations (and eliminate the smallest entirely). The images below illustrate the simplest possible multilateral set-off (involving three participants).

Left: an invoice loop with three participants; the simplest opportunity for multilateral obligation set-off. The total debt owed is £2300. Right: when the set-off is performed, the smallest invoice amount (in this case £500 due from Eddie to Sarah) is deducted around the loop. All participants now have reduced debt (with the smallest invoice completely cleared), reducing total working capital requirements to £800 (and resolving the potential gridlock had any of them been unable to find the working capital to pay on time).

However, most loops will be even longer (such as A owes B, B owes C, ..., K owes A), and in fact participation in longer loops is associated with financial resilience. Furthermore, as the trading network grows, the number of different possible combinations of loops grows much faster still. The TETRIS algorithm therefore finds the set of loops that eliminates the maximum possible amount of debt. Participating businesses are notified of which of their invoices have been cleared, and by how much, and update their accounts payable and receivable accordingly. The images below illustrate a set of obligations from a mutual credit network in Sardinia and the loops contained therein, as detected by TETRIS.

Left: May 2019 business-to-business trade in the Sardex network. Right: trading loops detected by TETRIS, with a few examples highlighted in colour; 24.6% of total transaction value could be cleared.

As well as mitigating the effects of cash flow volatility by minimising the amount of money everyone needs for settlement, multilateral obligation set-off also resolves payment gridlocks, whereby a firm cannot pay its suppliers because it hasn’t been paid yet. Late payment is a key cause of business failure, and ‘unblocking the drain’ by resolving loops in an obligation network means that participants typically get paid faster. This both increases their resilience and improves their relationships with their suppliers, with the resulting reductions in risk far outweighing that associated with sharing the necessary data.

TETRIS helped Slovenia get through its war of independence with Yugoslavia and the aftermath of the 2008 financial crisis, with a typical reduction in participants’ mutual obligations of around 10-15% and a strong countercyclical effect on the economy as a whole. Another implementation in Bosnia and Herzegovina shows a significant reduction in firm default rates and increased sales activity. Benefits tend to increase with number and diversity (in terms of both size and sector) of participants.

In economies where trade is more localised (corresponding to denser obligation networks, and hence more loops), even greater amounts can be cleared. In addition to the near-25% figure noted above for the Sardex network, initial studies indicate that upwards of 70% could be cleared within Grassroots Economics’ Sarafu trading system in Kenya.

Because of the power-law structure associated with trading networks, the distribution of outcomes from multilateral obligation set-off is highly unequal (with the largest and best-connected firms clearing the most debt, and many less central participants seeing marginal benefit). Although clearing algorithms can be optimised for more even outcomes, without a source of liquidity to settle obligations the scope for active governance of outcomes is limited. They are therefore best used in combination with other, complementary collaborative finance tools such as mutual credit.

Mutual Credit Services is working closely with Informal Systems (the developers of an open source version of TETRIS called MTCS) to make multilateral obligation set-off widely available via our Clearing Clubs platform.

Further reading

Incredible new research: how small businesses can be saved post-Covid, Dave Darby,

Credit clearing - introduction, Tom Woodroof,

A brief history of credit clearing, with Hans-Florian Hoyer, Hans-Florian Hoyer,

Fleischman, T. et al., Liquidity-Saving through Obligation-Clearing and Mutual Credit: An Effective Monetary Innovation for SMEs in Times of Crisis, Journal of Risk and Financial Management, 2020.

Fleischman, T. and Dini, P., Mathematical Foundations for Balancing the Payment System in the Trade Credit Market, Journal of Risk and Financial Management, 2021.

Božić, M. and Zrnc, J., The Trade Credit Clearinghouse: Liquidity and Coordination, 2021.

Iosifidis, G. et al., Cyclic motifs in the Sardex monetary network, Nature Human Behaviour, 2018.

Intrum, European Payment Report 2022.