MIT OpenCourseWareLecture 6: Multilateral Trade Credit Set-off
MIT OpenCourseWare
Introduction To The Lecture 0:00
Tomaž Fleischman, from a company called Informal Systems, opens the lecture on Multilateral Trade Credit Set-off, or MTCS. He outlines the plan for the session: defining late payment, viewing it through obligation networks, formalizing MTCS as an algorithm, testing it on real empirical data, and finally examining network structure challenges and how liquidity injection might help.
What Late Payment Really Costs 1:30
Late payment means a business sells goods or services on credit, expects payment in a set period like 30 days, and does not get paid on time. This is far more than an inconvenience. It raises financing costs, drains cash reserves especially from small and vulnerable companies, creates administrative burdens, and hurts labor productivity. Systemically, it hides real losses behind good-looking paperwork, burdens small firms disproportionately, causes unemployment and bankruptcy, and is in fact the number one cause of business bankruptcies, killing otherwise profitable companies and blocking new firms from entering markets.
Measuring Late Payment Across Europe 4:04
Reports from Intrum Justitia show that agreed payment terms are consistently shorter than actual payment terms across European countries, with gaps like 21 days agreed versus 45 to 64 days actual in the UK in 2020. Larger companies tend to push suppliers into longer payment terms, and sentiment around late payment worsened sharply during COVID. By 2024, payment delays of around 60 days appear across many European countries and across all sectors, not just manufacturing.
Why Buyers Delay Payment 6:00
A toolkit from the English Association of Chartered Accountants sorts reasons for late payment into categories: simple unwillingness to pay, genuine default from lack of funds, regulatory or administrative slippage, and, when these combine, deliberate buyer default in bad faith, essentially payment abuse. The pattern often escalates from reluctance to demanding delayed approval to demanding discounts, a form of extortion, while the paying firm eventually faces default and must act against the non-performing customer.
Slovenia's Clearing Mechanism Data 8:30
Slovenia ran a national mechanism from 1991 onward where firms reported late payments to a public agency that also cleared them, producing a rare long-run public dataset. Reported late payment as a share of GDP was high after independence and the war economy of 1991, fell as the economy improved, spiked again during the 2008 financial crisis and during COVID, and later declined again, not because the problem shrank but because private firms began running their own clearing mechanisms and stopped sharing their data, with the largest private mechanism now bigger than the public one.
Building The Obligation Network 12:30
Using three characters, Alice, Bob, and Charlie, where Alice owes Bob 2, Bob owes Charlie 2, and Charlie owes Alice 1, the smallest amount in the cycle, 1, can be cleared multilaterally without outside money, leaving Alice owing Bob 1 and Bob owing Charlie 1. No single party can spot this alone since each only sees their own obligations, so coordination is needed. Since detecting cycles directly becomes impractical at scale, the method instead looks at each firm's net balance, adds an imaginary source of funds for those in deficit and an imaginary sink for those in surplus, finds the maximum flow from source to sink at minimum cost, and then subtracts that flow from the original network to reveal the cycle that can be cleared.
Formal Definition Of The Algorithm 18:32
The balanced network is built by adding a source node connected to every firm with a negative net position and a sink node connected to every firm with a positive net position, with edge capacities equal to those balances and, in the basic version used here, a uniform cost of one on every edge. Applying minimum cost maximum flow finds a saturating flow between source and sink while respecting flow conservation. Subtracting this flow from the network can be proven, through the balance equations, to leave every node balanced and to empty out the source and sink entirely, meaning what remains is a genuine set of cycles ready to be cleared.
The Algorithm In Practice 24:32
The pseudocode simply builds the source and sink connections based on net position, runs minimum cost maximum flow only when a source node actually exists, and then subtracts the resulting flow from the original obligations to get the cleared network. Fleischman recommends Python's NetworkX library for anyone wanting to try this, noting that its various minimum cost maximum flow algorithms perform differently mainly on very large networks. Answering a question, he explains that using a uniform cost of one simply minimizes the amount of imaginary money used, and that assigning different costs could let the model optimize for other goals such as risk levels or social priorities like food safety.
Testing On Real Italian Invoice Data 30:32
The method was applied to real data from Infocert, an Italian firm that processes invoices for VAT tax compliance, giving access to a network of about 45,000 firms and roughly 2 million transaction edges, dominated numerically by micro-companies but with the largest transaction volumes among large firms. Running MTCS monthly over two years left the remaining network at about 11 percent of its original value on average, with roughly 95 percent accuracy and notable stability even through the 2019 to 2020 COVID period, since the structure of business relationships stayed steady even as volumes dropped. Small and micro firms gained little from clearing, while medium and especially large firms, and firms in a net creditor position, benefited most, meaning the mechanism worked well as something like an accounts receivable collection service.
Why The Network Resists Clearing 35:31
Fleischman explains why only about 10 to 12 percent of obligations clear despite this method. Invoice amounts follow a power law distribution, meaning most invoices are small, typically 183 euros on average or 332 for large firms, while very large amounts are rare outliers, so a cycle's clearable amount is capped by its smallest link, usually a small one. Similarly, the number of business partners per firm follows a power law, so most firms in a cycle have only a few connections, which further constrains flow. This scale-free topology arises from a preferential attachment process, where new connections in a growing network favor already well-connected players, a pattern he notes is identical mathematically to things like protein interaction networks in yeast or village economies in Kenya.
Engineering Liquidity Into The Network 40:31
Since the topology itself limits clearing, the response is to inject engineered liquidity, some accepted token of value that isn't real money, which could be a bank instrument, mutual credit, or crypto. Returning to Alice, Bob, and Charlie, if Alice holds two units of something Charlie is willing to accept, running the same MTCS algorithm with this engineered asset resolves Alice's full debt to Bob and Bob's debt to Charlie, leaving only a partial remainder, in this case Bob still owing Charlie 1, because there wasn't quite enough engineered liquidity in the system to clear everything completely.
Extending Liquidity Injection Beyond Three Firms 43:31
The same source-and-target framework used for Alice, Bob, and Charlie extends to larger networks, with source and target joined to represent an engineered source of liquidity. In the experiments, every participant faced the same liquidity restriction, set by a parameter called gamma, ranging from 0 (no engineered liquidity) to 1 (full liquidity). Results show that even at gamma zero, some debt clears through existing cycles. As gamma rises, clearing rises steeply at first, then levels off toward a roughly linear relationship, with diminishing extra benefit near full liquidity. A striking finding is that injecting just 20 percent of required liquidity can clear close to 50 percent of total indebtedness, showing a strong network multiplier effect. This pattern held stably across twelve months of real data. Breaking results down by firm size showed that small and micro firms depend heavily on engineered liquidity, while larger firms benefit even more from the network effect. Applied back to late payment, increasing engineered liquidity sharply reduces the late-payment problem, with contributions arriving both through multi-step chains across the network and through single-hop transfers. The mechanism proves most valuable during liquidity crises, as seen in Slovenia's wartime economy and during COVID, and could also help specific liquidity-constrained regions even when the wider economy is healthy.
Multiple Liquidity Sources and Flow Conservation 49:32
Using real data from Sardex, a mutual credit community in Sardinia, the speaker showed how three different liquidity sources, such as bank deposits, mutual credit, cryptocurrency, or vouchers, can be engineered simultaneously without ever exchanging with one another. Because the algorithm follows flow conservation and balance principles, each liquidity type stays self-contained, so a flow never converts from Bitcoin into dollars or into mutual credit. When questioned whether this separateness makes the system less efficient, the speaker explained that it actually resolves more cycles, since interaction happens through the network's obligations rather than through trade or exchange between asset types. He described this as "exchange without trade," an idea still being actively developed. He framed the broader point as a challenge to the assumption that markets alone drive economic efficiency, arguing that collaboration, layered alongside competition rather than replacing it, adds real value without interfering with markets.
Blockchain Implementation Through Cycles Protocol 54:31
The speaker's company, moving from Informal Systems toward a new venture called Cycles Protocol, plans to build this idea on blockchain as a shared source of truth. Users encrypt their payment obligations as "intents," which go on-chain, get decrypted and solved by the clearing algorithm, then get re-encrypted with an attestation and zero-knowledge proof confirming the process was done correctly. Verifiers check this and post results on-chain, letting users read outcomes while the underlying network structure stays fully private, since exposing debt networks would hand competitors valuable information.
History of Clearing and Design Questions 57:32
The idea of clearing dates back to European Renaissance merchant fairs, where traders avoided carrying cash through dangerous travel by writing notes and settling collectively during a two-day "banking fair" choreography, physically linking arms until cycles of debt were found and reduced. English banking clearing clubs later carried this tradition forward. In discussion, the professor clarified how liquidity is solicited from net debtors like Alice, who might voluntarily escrow a fraction of what she owes, with gamma representing that fraction; full liquidity means no network multiplier, while zero means no clearing happens at all. The speaker described plans to incentivize early payment through small premiums or discounts, noting that factoring can cost firms 5 to 10 percent, making even a 1 percent network incentive attractive. Adoption hinges on integration with existing accounting and ERP systems, since the data driving this process comes directly from standard accounting records. Responding to questions on timing, the speaker noted that flows within a chosen time window are treated as equal, though weights could reflect timestamp differences, and that systems like CHAPS already run comparable clearing every 15 seconds. Finally, comparing netting to multilateral setoff using the Alice, Bob, and Charlie example, he explained that netting can introduce novation, creating new risk relationships between parties who never dealt with each other directly, whereas setoff only reduces original debts without redistributing risk, making it safer for large, loosely trusting trade credit networks.
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