Cooperative Game Theory

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= "a theory of cooperative games that ... sheds light on ways economic surplus arises from people working together within organizations".


Kyle Birchard:

"We will use a specific area of study, cooperative games, as a jumping off point for our discussion of ecological and data-driven economic systems, with a particular focus on the developments emerging from Regen Network.

IBM-owned Weather Underground reports weather data obtained from roughly 280,000 connected devices in the United States. While the data from any individual weather station is worth little by itself, transformative value emerges when those data are combined with information and analysis from other sources.

The value of weather information, if fully monetized, has been estimated at roughly $14 billion per year in the United States. This amounts to an average value of $50,000 per station for the network. Even at current levels of weather data monetization, roughly $2 billion per year in the U.S., over $7,000 per year in revenues can be attributed to an “average” weather station (yes, I’m aware of the limitations of that definition) — but only if the network is considered as a whole.

This phenomenon was recognized by some of the pioneers in game theory, namely Lloyd Shapley and Martin Shubik who, in a remarkable string of articles dating from the early 1950s, helped develop a theory of cooperative games that, in contrast to zero-sum or adversarial contests such as the Prisoner’s Dilemma, shed light on ways economic surplus arises from people working together within organizations, and how seemingly insignificant participants in a system can organize in ways that make an outsized impact.

In the sense used here, a Cooperative Game is comprised of coalitions of individuals working toward a common goal. While those early papers often considered business decision makers, in the present day, we might also model these actors as households, firms, sensors, data owners, personal AI agents, DAOs, and other entities that haven’t yet been invented.

The key feature of coalitional forms is that working together creates a larger surplus than the sum of any of the individual actors. In one sense, this is almost too obvious to mention, but one of the important contributions of game theory is a formal representation of “cooperation” that gives us ways to measure this surplus in quantitative terms and to embed rules in code that can be deployed, for example, in Ecological Contracts executed over the Ecological State Protocols envisioned by Regen Network.

Other properties we are interested in with cooperative game theory are functions that are superadditive (the whole is greater than the sum of its parts) and supermodular (joining a coalition yields increasing returns as the coalition size gets larger, i.e., increasing returns).

This is a good time to introduce the Shapley Value, a measure of the contributions made by the individuals that comprise a coalition. Introduced by Lloyd Shapley in a seminal 1953 paper, this value presents a dynamic allocation mechanism that reflects the value contributed by the entities participating in a coalition at any given time.

Until recently, the Shapley Value was largely of theoretical interest because it is so computationally expensive: the number of computations grows as a factorial of the number of agents in the coalition. So, for example, if you have 20 members of a coalition, you would need to compute 20! combinations for each of the 20 members (or 2,432,902,008,176,640,000 computations each). Improvements in processor power and new approximation methods have made it possible to compute values for larger groups, and the Shapley Value has recently been used to study coalition formation in automated negotiation systems, the economics of peer-to-peer networks, and even the contributions of individual players to an English soccer club. Given some of its interesting properties, the Shapley Value and its variants could see important application to data valuation in cryptoeconomic settings." (


Cooperative vs Non-Cooperative Games

Kyle Birchard:

"Cooperative Games: Imagine an interaction for which it is the case that everything that both is affected by the actions of the players and is of concern to any of the players is subject to binding (meaning costlessly enforceable) agreement. This is termed a cooperative game. The term does not refer to the feelings of the parties about each other but simply to the institutional arrangements governing their interactions.

Non-cooperative Games: More commonly, however, something about the interaction is not subject to binding agreement. Such situations are modeled as noncooperative games.

Notice how this doesn’t necessarily refer to the ability or desire to cooperate, Cooperative Games simply refer to the enforcement level found in binding vs non-binding agreements.

In the social arrangement between an employer and employee, part of the interaction may be addressed cooperatively, as when an employer and an employee bargain over a wage and working hours. Other aspects of the same interaction may be noncooperative because of the impossibility of writing or enforcing the relevant contracts.

Examples include how hard the worker works or whether the employer will invest the resulting profits back into the company. When the employer is measuring productivity, he/she plays a cooperative game if he/she has a ticker at the door that tracks when the employee walks in and out. However, if the employer can’t verify the quality of work or effort put in, then the game is non-cooperative.

In technology jobs, and inside startups especially, it’s often difficult and costly to track worker productivity at work → making it a non-cooperative game. This is why we hear so often about ‘company culture’ and establishing a common ‘mission’. When an employer has no way enforce certain agreements, and rational employees can slack off without repercussions, therefore a narrative of ‘culture’ is used to imprint made-up social contracts.

Most commonly, social interactions are categorized based on whether the game representing it is cooperative or noncooperative and whether the payoffs of the game are common interest or conflict." (