Shapley Value - Any Real World Applications?
Allegedly, Barclays uses (or once used) Shapley allocation. Quoting Mauro Cesa:

The basic objective of every bank is to find an optimal business strategy that maximises return on capital (ROC). To this end, banks will allocate more capital to desks that generate the highest ROC, while those with lower ROC receive a smaller share of available capital. This is an intuitive and seemingly sensible solution.  But the authors of this month’s paper, Reduced-form capital optimisation, argue that ranking business units by ROC might not result in an optimal allocation of capital. The approach ignores the correlation between businesses and will deliver the optimal allocation only if the correlation is zero – an assumption for which there is little evidence in the real world.  The problem is further complicated by the Basel III capital rules, which are primarily based on two ratios: risk-weighted assets (RWAs) and leverage balance sheet (LBS). The minimum capital requirement for each legal entity under the same parent bank is the greater of the two.  To optimise its ROC, a legal entity must hold RWA and LBS capital in equal measure. The selection of RWA or LBS, as directed by the greater-of-the-two rule, introduces non-linearities that are difficult to deal with in an optimisation context.  “This is a huge, unsolved problem for banks,” says Yadong Li, managing director of quantitative analytics at Barclays, and one of the authors of the paper. “The bank as a whole ultimately needs to deploy the resources to different business units. This is a key part of senior management’s job.”  Dimitri Offengenden, a Tel Aviv-based managing director of quantitative strategy at Barclays, joined the bank in 2017 specifically to work on the capital allocation problem. He consulted with Li, who has worked on related issues in the past.  “I suggested we look at Shapley allocation, which is a natural way to solve the greater-of-two problem” says Li.  Shapley allocation is well known in game theory and has been widely applied in economics and business decision making. It attributes a value to the contribution of each agent in a system where agents co-operate and share the costs and gains of their activity. In essence, it measures the marginal contribution of each agent by observing the difference the agent’s presence or absence makes to the activity. Based on that, a portion of the shareable pie is allocated to each agent. In the case of a bank, the agents are individual business units and the pie is the overall capital stock.  Offengenden, Li and Jan Burgy, a quant strategist at Barclays, realised that regressing the overall allocation of capital on the selection of RWAs and LBS obtained from the application of the Shapley method resulted in an almost perfect approximation.



Mauro Cesa, Game theory plays well for capital management, Risk.net, September 30, 2019.

Yadong Li, Dimitri Offengenden, Jan Burgy, Reduced form capital optimization, May 15, 2019.