The role of cooperative game theory in macroeconomics

Cooperative game theory itself is designed to comprehend scenarios where players form groups (i.e., ‘coalitions’) as compared to acting on their own. As one of the most highly studied branches of game theory, this framework helps focus on how the benefits and costs of collaboration can be fairly divided among coalitions, ensuring that the maximum payoff is achieved while maintaining fairness throughout the game.

In cooperative games, the core features of a coalition are straightforward¹. Players voluntarily form coalitions based on shared interests, exchange information, and work together to achieve both individual and collective goals. They also establish binding agreements (such as contracts or other institutional mechanisms) to ensure that each member fulfills their role. 

Cooperative games are analyzed to evaluate the potential costs and benefits of different choices among players, taking into account how those decisions impact others within the coalition¹. Of the various solution concepts available, two stand out as particularly influential:

Shapley value

The Shapley value was introduced in the 1950s by American mathematician Lloyd Shapley², used to calculate how to fairly divide rewards in cooperative games. It follows some key fairness principles³: (1) all the value is shared (efficiency); (2) players who contribute the same amount get the same share (symmetry); (3) results from different situations can be combined (additivity); and (4) anyone who doesn’t contribute doesn’t receive a share (dummy player rule). However, calculation using the Shapley value becomes increasingly complex as the number of participants grows, making it more suitable for scenarios with a smaller group of players⁴.

The core

The core is a solution concept in cooperative game theory used to identify stable outcomes, where no group of players (or coalition) has an incentive to break away and form a better deal on their own³. First introduced by Francis Y. Edgeworth in the 1880s⁵ as “final settlements” and later formalized in game theory by Donald B. Gillies in 1959⁶, the core represents payoff distributions where every coalition is satisfied with the outcome. However, in some games, the core can be empty, meaning that no stable agreement exists, and every proposed distribution can be blocked by a dissatisfied coalition. 

Binding agreements

Cooperative game theory assumes that players can be trusted to uphold the promises and agreements they enter into. This assumption is central in macroeconomics, where international treaties, fiscal pacts, or monetary unions require credible and enforceable commitments to shared policies.

A strong real-world example is the Paris Agreement⁷ on climate change, a legally binding international treaty that came into force in November 2016. Nearly 200 countries have committed to reducing their greenhouse gas emissions and working together to achieve this through various national climate action plans and regular progress reviews. Even though each country sets its own climate goals (called Nationally Determined Contributions (NDCs)), the agreement legally requires them to report regularly on their progress and update their plans. This transparency and frequent monitoring of both individual and collective progress build trust among countries and encourage stronger commitments over time. Together, these elements ensure the Paris Agreement is a genuine, cooperative effort that countries are expected to uphold⁸.

Coalitions

At its core, cooperative game theory is all about players forming groups to work together. In the scope of macroeconomics, this means countries, companies, or even different parts of an economy might decide to coordinate policies or combine their resources to achieve goals they simply couldn't reach on their own.

A prime illustration of this in action is the Eurozone debt crisis, particularly the complex dynamic between Germany, Greece, and other EU members. While there was clear competition and conflicting interests, their interactions can be powerfully understood through a "coopetitive" lens, as explored by academics David Carfì and Daniele Schilirò back in 2011⁹. Instead of just competing, these Eurozone members engaged in forming coalitions and intense negotiations over debt restructuring. The goal was to find mutually beneficial financial outcomes, even if it meant, for instance, exploring how Germany could boost demand for Greek exports to create a win-win scenario amidst the crisis. This shows how, even in tough times, cooperation can lead to shared stability.

Joint payoff

In cooperative game theory, the collective value generated by a coalition often exceeds the mere sum of individual payoffs. This synergistic effect arises from efficiencies gained through collaboration, such as the reduction of transaction costs, effective risk sharing, or enhanced bargaining power.

At the macroeconomic level, this principle is especially evident in transnational infrastructure investments, such as cross-border railways or integrated energy grids, where multiple countries contribute resources and share both costs and benefits. Notable examples include the critical challenge of space debris removal around the world¹⁰ and the Nile Basin Initiative¹¹ for regional water management across ten African countries that share the river, as well as the development of interconnected European energy networks¹². Cooperative game theory, particularly the Shapley value, can guide fair value allocation across participants and support the long-term stability of these joint efforts.

Negotiation and commitment

Once a group has created a collective gain in a cooperative scenario, participants must then figure out how to distribute it. For this cooperation to last, it relies on having reliable ways to ensure commitment and a fair sharing of benefits and costs. This approach prevents any smaller group from feeling it would be better off breaking away to form its separate alliance.

In this context, Lloyd Shapley's contributions, especially the Shapley value, provide key understanding into how fair and stable outcomes can be negotiated. These ideas aren't just theoretical; they help design practical solutions in areas such as school admissions and the placement of medical residents. Within macroeconomic settings, similar sharing rules can help manage financial transfers among member countries in economic unions or guide the distribution of development funding between partners of varying wealth. As seen during the Eurozone crisis, the success of any coordinated financial action depended not just on political desire, but importantly on whether the sharing of costs and benefits was perceived as fair. 

Within macroeconomics, trust, fairness, and commitment take on heightened importance, as numerous parties are involved and the potential consequences operate on a vast scale. This is precisely where the study of cooperative game theory has significantly aided in addressing various global challenges, offering both the theoretical foundation and practical tools for designing more effective collective actions. Whether for climate change, cross-country resource allocation, or other shared challenges, these analytical insights reveal deeper meaning in complex data and facilitate tangible impacts for the greater good.

References

1. Muros FJ. Cooperative Game Theory Tools in Coalitional Control Networks. 1st ed. Cham: Springer; 2019. p. 9–11. ISBN: 978-3-030-10488-7.
   
2. UBS. Lloyd Shapley [Internet]. Nobel Perspectives. [cited 2025 Jun 16]. Available from:https://www.ubs.com/microsites/nobel-perspectives/en/laureates/lloyd-shapley.html
   
3. Serrano R. Cooperative games: Core and Shapley value. Working Paper No. 2007-11. Providence (RI): Brown University, Department of Economics; 2007.
   
4. ScienceDirect. Cooperative game theory [Internet]. [cited 2025 Jun 16]. Available from:https://www.sciencedirect.com/topics/computer-science/cooperative-game-theory
   
5. Edgeworth FY. Mathematical Psychics. London: Kegan Paul Publishers; 1881. Reprinted in: Newman P, editor. F.Y. Edgeworth’s Mathematical Psychics and Further Papers on Political Economy. Oxford: Oxford University Press; 2003.
   
6. Gillies DB. Solutions to General Zero-Sum Games. In: Tucker A, Luce R, editors. Contributions to the Theory of Games IV. Princeton (NJ): Princeton University Press; 1959. p. 47–85.
   
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8. Quartz. Game theory says the Paris Agreement might be a climate winner [Internet]. [cited 2025 Jun 17]. Available from:https://qz.com/2099301/game-theory-says-the-paris-agreement-might-be-a-climate-winner
   
9. Carfì D, Schilirò D. A framework of coopetitive games: applications to the Greek crisis. AAPP Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali. 2012 Jun;90(1):A1. p. 1–32.
10. Games. Cooperative Game Theory: Core and Shapley Value [Internet]. MDPI. 2016 [cited 2025 Jun 17];7(3):20. Available from:https://www.mdpi.com/2073-4336/7/3/20
    
11. International Waters Governance. Nile River Basin Initiative [Internet]. [cited 2025 Jun 17]. Available from:http://www.internationalwatersgovernance.com/nile-river-basin-initiative.html
    
12. The European Files. Interconnection of European Energy Networks: Foundation of Energy Security [Internet]. [cited 2025 Jun 17]. Available from:https://www.europeanfiles.eu/energy/interconnection-of-european-energy-networks-foundation-of-energy-security