Thank you very much for your response. Inventory games remain an important topic actively studied by game theorists. Especially in applications such as inventory pooling, cooperative models are developed to ensure fair cost allocation. In the presence of uncertainty, methods such as fuzzy or interval uncertainty are often employed in cooperative games. In this context, the concept of the core stands out as a tool for providing fair and stable solutions.
Some studies offer alternative perspectives on the concept of "uncertainty" in cooperative game theory, particularly by incorporating fuzzy set theory and interval-based approaches to model ambiguous or imprecise information in coalition formation and payoff distribution. Some of these include:
Original Message:
Sent: 06-18-2025 11:02
From: Bruce Hartman
Subject: From Coalition Insight to Ethical Foresight: Game Theory in OR-Analytics and Beyond
Gerhard, there's a history of cooperative games used in inventory, especially regarding inventory consolidation. If different entities pool their inventory (say for spare parts) there is a saving in inventory costs. But how should that saving be shared among the entities? It's proven, for instance, that with a newsvendor model (and quite a few extensions!) there is always a 'core' for the induced cooperative game on the entities. As you know, existence of a core, a set of allocations in which no subset can benefit from dropping out, is one interpretation of fairness.
I find Peleg and Sudholter's "Introduction to the theory of cooperative games" (Springer ) quite complete and thorough. It's not easy reading for me, though. The 2d edition dates from 2007; there's a lot more research since then. You could also look into Theo Driessen's work with a number of others on 1-convex cooperative games. There's a nice theorem there showing that any game is the sum of a 1-convex and a 1-concave game. The idea might be useful. The 1-convex bit is about relations with marginal contributions of coalitions.
The original newsvendor work is
Hartman, Bruce C., Moshe Dror, and Moshe Shaked. (2000) "Cores of Inventory Centralization Games." Games and Economic Behavior. 31 26-49.
An old survey is
Dror, Moshe, and Bruce C. Hartman. (2008). "Survey of Cooperative Inventory Games and Extensions." Journal of Operational Research Society. DOI: 10.1057/jors.2010.65.
Best of luck with the project!!
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Bruce Hartman
Professor
University of St. Francis
Tucson, AZ United States
bruce@ahartman.net
website: https://sites.google.com/ahartman.net/drbrucehartman/Home
blog:http://supplychainandlogistics.org
Original Message:
Sent: 06-17-2025 04:18
From: Gerhard-Wilhelm Weber
Subject: From Coalition Insight to Ethical Foresight: Game Theory in OR-Analytics and Beyond
Dear INFORMS Colleagues,
Week by week, the vibrant exchanges within our OR-MS community continue to emphasize the great responsibility we bear when transforming data into action. Today, we would like to briefly introduce an approach that we believe not only enhances operational strategies, but also encourages deeper reflection on fairness and collective value in decision-making.
Our upcoming presentation at EURO 2025 in Leeds, titled
"Unlocking Generation Z: Spatial Data and Game Theory Redefine HR Strategies,"
focuses on the application of cooperative game theory, particularly the Shapley value, to model and optimize recruitment, team formation, and salary distribution strategies for Generation Z.
While we support this framework with data-driven techniques-especially Multivariate Adaptive Regression Splines (MARS) and its advanced variants (e.g., CMARS, RCMARS)-our central innovation lies in shifting the perspective from individual optimization to coalitional fairness. By capturing spatial synergy among candidates (e.g., proximity to economic centers), we can quantify added value in team contexts and allocate it transparently and equitably.
This method, though developed in an HRM context, holds potential far beyond it. Game-theoretic coalition analysis may offer insights into other networked behaviors-such as cooperation among companies, educational institutions, or even policy planning bodies-where the distribution of shared value is critical.
However, as with all powerful analytical methods, ethical considerations are paramount. Tools that model synergy and advantage must not be misused to reinforce disparity or extract value unfairly. As such, we place strong emphasis on ethical safeguards, including data anonymization, fairness constraints, and critical interpretation of coalition dynamics.
We would be delighted to hear from others in the OR-Analytics community-where else might cooperative game theory, complemented by light-touch machine learning, bring meaningful and responsible change?
For those interested in further reading and background, we would like to reference a selection of related publications that have shaped our current work:
· Graczyk-Kucharska, M., Olszewski, R., & Weber, G.-W. (2023). The use of spatial data mining methods for modeling HR challenges of Generation Z in Greater Poland Region. Central European Journal of Operations Research, 31(1), 205–237.
· Özcan, İ., Śledziński, J. D., Gök, S. Z. A., Meca, A., Weber, G. W., Butlewski, M., & Kocadag, E. (2025). A game theory perspective on strategic profit distribution in complex IT projects. Journal of Industrial and Management Optimization, 21(2), 1503–1517.
· Özcan, İ., Śledziński, J. D., Alparslan Gök, S. Z., Butlewski, M., & Weber, G. W. (2023). Mathematical encouragement of companies to cooperate by using cooperative games with fuzzy approach. Journal of Industrial and Management Optimization, 19, 7180–7195.
· Weber, G.-W., & Özmen, A. (2014). RMARS: Robustification of multivariate adaptive regression spline under polyhedral uncertainty. Journal of Computational and Applied Mathematics, 259, 914–924. https://doi.org/10.1016/j.cam.2013.09.055.
With warm regards,
İsmail Özcan (Contact person)
PhD
📧 ismailozcanmath@gmail.com
Gerhard-Wilhelm Weber
Faculty of Engineering Management, Poznan University of Technology
📧 gerhard.weber@put.poznan.pl
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Gerhard-Wilhelm Weber
Professor
Poznan University of Technology
Poznan
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