Game theory is an immensely powerful mathematical tool for, among other things, helping us to uncover the hidden drivers and impulses that cause people to form connections and networks in a social and economic context. From the formation of relationships between governmental entities to the way in which a sporting league is organized, our decisions about human connections are informed by a deeply rooted set of principles, both psychological and rational. The game theory of network formation allows us to peer inside the workings of these dynamic systems, and better inform our decision-making ability as we build relationships in a rapidly changing world.
What is the Game Theory of Network Formation?
Game theory is a branch of investigation that seeks to understand the outcomes of strategic interactions between separate actors. Using mathematical games as models, these theories can help us to better understand how people, irrational as they often may be, come together in order to form dynamic networks. Like pieces on a chessboard, these actors must find a way to maneuver in order to reach their desired ends, and game theory helps us to better predict their movements and behavior. The game theory of network formation looks to uncover the mechanics and incentives that influence the formation of systems of relationship in our modern world.
In the words of Nobel Prize-winning economist, John Harsanyi, “Game theory enables us to construct alternative models of social environments and to investigate their logical consequences by means of formal methods…by comparing the model with observations of real-world behavior, the researcher can often find the elements that are most relevant in an empirical context.”1 It is exactly this notion that has spawned some of the greatest leaps forwards in the understanding of social dynamics and human behavior.
How Does Game Theory Help Us Understand How Networks of Social and Economic Relationships Might Form?
Applying principles from game theory to network formation can bring a deeper level of insight than simply observing external behaviors in group dynamics. By understanding the motivations at play within large networks of interaction, game theorists are better able to deconstruct the patterns that manifest over time. This can include anything from the way the internet is structured to the incentive structures that drive certain tax regimes in different countries.
Game theory is also used to understand the emergence of certain patterns in the behavioral sciences. From studying how groups interact and how they form alliances, as well as how they contrast and oppose each other, game theory can help us to navigate the psychological and interpersonal considerations that drive the formation of certain relationships and networks.
To borrow a phrase from the late physicist Stephen Hawking, “Game theory takes us a step closer to understanding the complexity of human interaction and decision-making, and how this can be used to our advantage.”2 By understanding the mathematics that underpin network formation, game theorists are better able to observe and exploit the evolution of a system over time, and are able to make more informed decisions about our interactions.
What Are Some of the Most Important Factors to Consider When Designing a Network?
When it comes to designing a network, the most important goal is to create incentives for rational actors to participate in the network. By recognizing that each agent has their own objectives and motivations, and by creating an environment in which those actors are able to better meet their aims through collective action, a network will be more successful in the long run.
Put simply, network design should focus on creating an infrastructure that incentivizes rational actors to cooperate and work together towards a common end. Key considerations should include the need for self-organization, the capability for dynamic communication, and the need for a strong and effective governance framework that is capable of responding quickly to changing dynamics.
Furthermore, it is important to create an economic system that encourages constructive competition and rewards innovation. By providing incentives for entrepreneurs and innovators, it is possible to foster a rich and diverse climate that will foster beneficial relationships.
Lastly, it is important to keep an eye on the overall stability of the network. In times of instability, networks often fragment into individual fragments, which can lead to a collapse of the system or even war. By designing a network that is aware of all potential points of failure, it will be more resilient in times of crisis and less likely to fail in the face of external stressors.
The game theory of network formation is an invaluable mathematical tool for uncovering the secrets of our social and economic production systems. By understanding the motivations at work in our decisions about the formation of relationships, it is possible to better inform our interactions and decisions in a rapidly changing world.
References
1 Harsanyi, J. (1955). Games with Incomplete Information Played by Bayesian Players. Management Science, 4(1), 159–182.
2 Hawking, S. (2009). On quantum theory. IEEE Annals of the History of Computing, 31(2), 49–60.