<p>It is used quite a bit in machine learning. I think it's becoming a bit of an industry standard in finance.</p>
<p>My former employer used it in credit modeling. I worked there as a software developer. I cannot name them, but they are using an ML-driven credit modeling with the shap Python <a href="https://github.com/slundberg/shap" rel="nofollow noreferrer">library</a> by Scott Lundberg.</p>
<p>It's used for multiple reasons:</p>
<ul>
<li>Gave us insight into the factors influencing scoring, which helped focus efforts on high value data inputs (especially since data ingestion takes time, so one-off notebooks with one-off datasets can be used to infer if it's worth incorporating that data into a data pipelines/ingestion engine).</li>
<li>Gave customers insight into why they were approved/rejected. This was also hugely important to us, as we operated in multiple jurisdictions and paid close attention to the regulatory environment in each. For good reason, there are protected factors that one cannot use to reject an applicant. This can be accounted for in model creation, but SHAP values also helped us ensure that no unallowable data points made it into particular models.</li>
<li>It also helped us see if models were weighting particular factors too heavily, in a way that might be concerning. E.g. if a model heavily weights particular features that are known to have intermittent data quality issues, then maybe the model should be tweaked to decrease it's weight on those factors. Or we need to put more effort into cleaning/validating that data source, or to gather more data of a similar type, in order to avoid overfitting on that one feature.</li>
</ul>

CC BY-SA 4.0
2022-09-17T05:20:15.003Z
Could you please elaborate a bit on how "*SHAP values also helped us ensure that no unallowable data points made it into particular models*"? What kind of data were you calculating Shapley values from, and how did that help you with identifying when forbidden data got into a model?
Giskard
CC BY-SA 4.0
2022-09-18T22:54:14.263Z
@Giskard It was only a secondary benefit, but it provided an additional step where we checked the features the model was fitting on. Occasionally there were errors in "cleaner" steps before that point, which allowed data into the model which shouldn't have been there. Any explainability metric where you look at the most relevant features will provide this though, so it's not specific to SHAP.
David
CC BY-SA 4.0
2022-09-16T22:29:06.907Z
2022-09-17T19:12:19.883Z
2022-09-17T19:12:19.883Z
David
<p>Allegedly, Barclays uses (or once used) Shapley allocation. Quoting Mauro Cesa:</p>
<blockquote>
<p>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. <br><br> But the authors of this month’s paper, <a href="https://www.risk.net/7024151" rel="nofollow noreferrer">Reduced-form capital optimisation</a>, 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. <br><br> 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. <br><br> 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. <br><br> “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.” <br><br> 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. <br><br> “I suggested we look at Shapley allocation, which is a natural way to solve the greater-of-two problem” says Li. <br><br> 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. <br><br> 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.</p>
</blockquote>
<hr />
<ul>
<li><p>Mauro Cesa, <a href="https://www.risk.net/our-take/7041081/game-theory-plays-well-for-capital-management" rel="nofollow noreferrer">Game theory plays well for capital management</a>, Risk.net, September 30, 2019.</p>
</li>
<li><p>Yadong Li, Dimitri Offengenden, Jan Burgy, <a href="https://arxiv.org/abs/1905.05911" rel="nofollow noreferrer">Reduced form capital optimization</a>, May 15, 2019.</p>
</li>
</ul>

CC BY-SA 4.0
2021-03-11T02:53:47.800Z
Nice! Thanks for the answer!
Herr K.
CC BY-SA 4.0
2022-09-19T10:47:14.070Z
The answer could have mentioned a few key messages and referred to the source rather than quoting it.
BrsG
CC BY-SA 4.0
2022-09-19T10:56:09.360Z
@BrsG And, then, when Risk.net erected a paywall, my answer would be useless.
Rodrigo de Azevedo
CC BY-SA 4.0
2022-09-19T13:53:40.827Z
Sorry, but a big quote dump simply isn't a good answer.
BrsG
CC BY-SA 4.0
2022-09-19T14:07:23.837Z
@BrsG Why don't you buy a lifelong subscription to Risk.net for every user of Economics SE, then?
Rodrigo de Azevedo
CC BY-SA 4.0
2021-03-10T23:58:00.787Z
2021-03-11T03:02:01.877Z
2021-03-11T03:02:01.877Z
Rodrigo de Azevedo
<p>The <a href="https://en.wikipedia.org/wiki/Shapley_value" rel="nofollow noreferrer">Shapley value</a> has been around for seven decades now. It is intuitive, tractable, and has many desirable properties. To my surprise, however, its actual applications in the real world are not readily available (as defined by a simple Google search). Most of the &quot;applications&quot; of the Shapley value I could find are theoretical/hypothetical in nature. For example, the <a href="https://www.investopedia.com/terms/s/shapley-value.asp" rel="nofollow noreferrer">Investopedia entry</a> lists the <a href="https://en.wikipedia.org/wiki/Airport_problem" rel="nofollow noreferrer">pricing of airport runway usage</a> and marketing analytics as two applications without reference to actual real world cases.</p>
<p>My question is: <strong>Are there any real world applications of the Shapley value in pricing transactions and/or allocating profits/costs among cooperating parties?</strong></p>
<p>More specifically, I'm looking for answers in any of the following forms:</p>
<ul>
<li><p>&quot;<em>As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to price its transaction with Company B and Company C.</em>&quot;</p>
</li>
<li><p>&quot;<em>As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to allocate its [R&amp;D/marketing/overhead] costs among its subsidiaries B, C and D.</em>&quot;</p>
</li>
<li><p>&quot;<em>The empirical study by Author et al. (20xx) in Publication X found that the profit/cost sharing practice within a [firm/industry/multinational enterprise] is consistent with the prediction of some model based on the Shapley Value.</em>&quot;</p>
</li>
<li><p>&quot;<em>The empirical study by Author et al. (20xx) in Publication X uses [a structural estimation/an empirical strategy] that is based on the Shapley value.</em>&quot;</p>
</li>
</ul>
<p>Please do provide links/references to the sources. Thank you.</p>
<hr />
<p><em>Note 1.</em> While I'm primarily interested in the application of the Shapley Value in a business context, pointers to its use in other domains such as politics would also be appreciated.</p>
<p><em>Note 2.</em> I found a paper by <a href="https://doi.org/10.2307/3003493" rel="nofollow noreferrer">Littlechild &amp; Thompson</a> (1977) where the authors applied the Shapley value in calculating the prices of airport runway usage based on actual data from the Birmingham Airport. It is unclear, however, whether those prices were subsequently adopted/implemented by the airport authorities.</p>

CC BY-SA 4.0
2021-03-10T20:28:27.143Z
There are many empirical papers in politics that use the Shapley value to measure power.
Michael Greinecker
CC BY-SA 4.0
2021-03-10T20:59:01.687Z
Thanks @Michael. While I'm primarily interested in the application of Shapley Value in a business context, pointers to its use in politics would also be appreciated.
Herr K.
CC BY-SA 4.0
2021-03-10T21:10:16.183Z
If you have access to it, Eyal Winter's chapter in volume 3 of the "Handbook of Game Theory and Economic Applications" by Aumann and Hart discusses several such papers.
Michael Greinecker
CC BY-SA 4.0
2021-03-10T21:40:03.273Z
@MichaelGreinecker: That's great! I'll take a look. Thank you.
Herr K.
CC BY-SA 4.0
2021-03-16T13:07:03.423Z
Shapley values, in the form of [SHAP](https://github.com/slundberg/shap) extension, are very actively used in explaining Machine Learning/AI models. Very active area of research.
Sergey Bushmanov
CC BY-SA 4.0
2021-03-16T15:06:17.010Z
@SergeyBushmanov: Thank you! This is definitely worth looking into.
Herr K.
<microeconomics><game-theory><reference-request><cooperative-game-theory>
Shapley value — any real world applications?
Herr K.
# Shapley value — any real world applications?

(Asked by: username_0 on 2021-03-10)

The [Shapley value](https://en.wikipedia.org/wiki/Shapley_value) has been around for seven decades now. It is intuitive, tractable, and has many desirable properties. To my surprise, however, its actual applications in the real world are not readily available (as defined by a simple Google search). Most of the "applications" of the Shapley value I could find are theoretical/hypothetical in nature. For example, the [Investopedia entry](https://www.investopedia.com/terms/s/shapley-value.asp) lists the [pricing of airport runway usage](https://en.wikipedia.org/wiki/Airport_problem) and marketing analytics as two applications without reference to actual real world cases.

My question is: **Are there any real world applications of the Shapley value in pricing transactions and/or allocating profits/costs among cooperating parties?**

More specifically, I'm looking for answers in any of the following forms:

* "*As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to price its transaction with Company B and Company C.*"
* "*As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to allocate its [R&D/marketing/overhead] costs among its subsidiaries B, C and D.*"
* "*The empirical study by Author et al. (20xx) in Publication X found that the profit/cost sharing practice within a [firm/industry/multinational enterprise] is consistent with the prediction of some model based on the Shapley Value.*"
* "*The empirical study by Author et al. (20xx) in Publication X uses [a structural estimation/an empirical strategy] that is based on the Shapley value.*"

Please do provide links/references to the sources. Thank you.

---

*Note 1.* While I'm primarily interested in the application of the Shapley Value in a business context, pointers to its use in other domains such as politics would also be appreciated.

*Note 2.* I found a paper by [Littlechild & Thompson](https://doi.org/10.2307/3003493) (1977) where the authors applied the Shapley value in calculating the prices of airport runway usage based on actual data from the Birmingham Airport. It is unclear, however, whether those prices were subsequently adopted/implemented by the airport authorities.

**Tags:** microeconomics, game-theory, reference-request, cooperative-game-theory

> **Comments:**
> **username_1**: There are many empirical papers in politics that use the Shapley value to measure power.  
> **username_0**: Thanks @Michael. While I'm primarily interested in the application of Shapley Value in a business context, pointers to its use in politics would also be appreciated.  
> **username_1**: If you have access to it, Eyal Winter's chapter in volume 3 of the "Handbook of Game Theory and Economic Applications" by Aumann and Hart discusses several such papers.  
> **username_0**: @MichaelGreinecker: That's great! I'll take a look. Thank you.  
> **username_2**: Shapley values, in the form of [SHAP](https://github.com/slundberg/shap) extension, are very actively used in explaining Machine Learning/AI models. Very active area of research.  
> **username_0**: @SergeyBushmanov: Thank you! This is definitely worth looking into.  

---

## 2 answers

### Answer by username_3 on 2022-09-16. Score: 3

It is used quite a bit in machine learning. I think it's becoming a bit of an industry standard in finance.

My former employer used it in credit modeling. I worked there as a software developer. I cannot name them, but they are using an ML-driven credit modeling with the shap Python [library](https://github.com/slundberg/shap) by Scott Lundberg.

It's used for multiple reasons:

* Gave us insight into the factors influencing scoring, which helped focus efforts on high value data inputs (especially since data ingestion takes time, so one-off notebooks with one-off datasets can be used to infer if it's worth incorporating that data into a data pipelines/ingestion engine).
* Gave customers insight into why they were approved/rejected. This was also hugely important to us, as we operated in multiple jurisdictions and paid close attention to the regulatory environment in each. For good reason, there are protected factors that one cannot use to reject an applicant. This can be accounted for in model creation, but SHAP values also helped us ensure that no unallowable data points made it into particular models.
* It also helped us see if models were weighting particular factors too heavily, in a way that might be concerning. E.g. if a model heavily weights particular features that are known to have intermittent data quality issues, then maybe the model should be tweaked to decrease it's weight on those factors. Or we need to put more effort into cleaning/validating that data source, or to gather more data of a similar type, in order to avoid overfitting on that one feature.

> **Comments:**
> **username_4**: Could you please elaborate a bit on how "*SHAP values also helped us ensure that no unallowable data points made it into particular models*"? What kind of data were you calculating Shapley values from, and how did that help you with identifying when forbidden data got into a model?  
> **username_3**: @username_4 It was only a secondary benefit, but it provided an additional step where we checked the features the model was fitting on. Occasionally there were errors in "cleaner" steps before that point, which allowed data into the model which shouldn't have been there. Any explainability metric where you look at the most relevant features will provide this though, so it's not specific to SHAP.  

---

### Answer by username_5 on 2021-03-10. Score: 3

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](https://www.risk.net/7024151), 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](https://www.risk.net/our-take/7041081/game-theory-plays-well-for-capital-management), Risk.net, September 30, 2019.
* Yadong Li, Dimitri Offengenden, Jan Burgy, [Reduced form capital optimization](https://arxiv.org/abs/1905.05911), May 15, 2019.

> **Comments:**
> **username_0**: Nice! Thanks for the answer!  
> **username_6**: The answer could have mentioned a few key messages and referred to the source rather than quoting it.  
> **username_5**: @username_6 And, then, when Risk.net erected a paywall, my answer would be useless.  
> **username_6**: Sorry, but a big quote dump simply isn't a good answer.  
> **username_5**: @username_6 Why don't you buy a lifelong subscription to Risk.net for every user of Economics SE, then?  

---

