In May, Tata Steel formally took control of Bhushan Steel, settling nearly two-thirds of the non-performing loans of the bankrupt steelmaker. While this is a heartening success story, overall, the process of resolution in the Insolvency and Bankruptcy Code (IBC) is marked with a certain degree of churn. We abstract the sound and fury and set out axiomatic principles for the central challenge of the process—the determination of the losses or “haircuts" of different creditors whose claims cannot be simultaneously fulfilled in entirety. This is referred to as the “bankruptcy problem" in game theory.

Currently, the allocations of different creditors are decided by the proportional division rule. For instance, in case the asset is valued at 100 units and the secured creditors are owed 120 units, with 115 units being held by company A and 5 units being held by company B, then A will get a payout of 96, and B will get a payout of 4 units.

Apart from the proportional division rule, there are two other rules that are commonly used. The constrained equal-awards rule divides equally the asset among the agents under the condition that nobody gets more than her claim. In the problem mentioned above, imagine money being distributed equally between company A and company B, till both get 5 units each, at which point company B has received its entire claim. After that only company A is given money, and ends up with 95 units.

The constrained equal-losses rule, on the other hand, divides equally the difference between the aggregate claim and the asset, with the proviso that no agent ends up with a negative transfer. In the problem above, the value of the claims exceeds the value of the asset by 20 units. Company B’s claim is lower than the average loss of 10 units. Hence, it would get nothing and company A would get the entire asset.

A paper by game theorists Carmen Herrero and Antonio Villar identifies five properties that only these three rules satisfy. These properties include equal treatment of equals, and scale invariance (this means that if the claims and the asset are suddenly expressed in dollars instead of rupees, the payout should not change).

Next, Herrero and Villar define the properties of exemption and exclusion to distinguish these rules. The property of exemption states that all creditors whose claim is less than the average amount available for each creditor—100 divided by 2 = 50, in our example, will get an allocation equal to their claim. Thus, company B would get 5 units and company A would get 95 units. This property aligns with the view that small claimants correspond to relatively financially weaker companies for whom the claims represent a larger fraction of their wealth. Hence their claims are accorded priority.

The property of exclusion states that all creditors whose claims are lower than the average loss, which in our example is 20/2 = 10, would get nothing. This implies that company B gets nothing and company A gets 100 units. From a geometric viewpoint, this way of solving the problem amounts to maximizing “efficiency" by selecting that point in the feasible set which is closest to the vector of claims. In general, the constrained equal-losses rule is compatible with exclusion but not exemption, while the reverse is true for the constrained equal-awards rule.

Robert Aumann and Michael Maschler have defined a fourth division rule drawn from an analysis of a bankruptcy problem in the Babylonian Talmud. This rule, which satisfies neither exemption nor exclusion, represents a compromise between the constrained equal-awards and the constrained equal-losses rules. It acts exactly like the constrained equal-awards rule for that part of the available asset that is less than 50% of the claims. After the asset breaches the halfway mark of the claims, the rule allocates the remaining asset in accordance with the constrained equal-losses rule. In our example, both companies would first get 50% of their claims—company A would get 57.5 and company B would get 2.5. The remaining 40 units of the asset would be divided according the constrained equal-losses rule. The residual claims of the creditors amount to 60 units and yield an average loss of 10 units. Since the remaining claim of company B (2.5 units) is lower than the average loss, it would get nothing more, ending up with 2.5 units while company A gets 97.5 units. Note this allocation is the midpoint of the allocations as per the constrained equal-awards and constrained equal-losses rules.

The Talmudic rule embodies the principle of “more than half is like the whole, whereas less than a half is like nothing". Thus it focuses attention on equitable distribution till everyone receives at least half their claim, and thereafter, attempts to minimize the distance of the payout from the claim—adopts the constrained equal-losses rule.

Thus, from an axiomatic point of view, it may represent a happy compromise. Those concerned that this rule has resulted in a lower payout to the smaller creditor than the proportional division rule should note that this need not generally be the case.

At this nascent stage of the IBC, where different types of stakeholders are learning the ropes and attempting to maximize their payouts, a non-cooperative game theoretic approach as opposed to an axiomatic approach may be required to understand the possibilities for reform. This problem we reserve for a future column.

Rohit Prasad and Yogesh B. Mathur are, respectively, a professor at MDI, Gurgaon, and author of Blood Red River, and a senior adviser-restructuring and former CFO at several major Indian/international groups. Game Sutra is a fortnightly column based on game theory.