Game theory research reveals fragility of common resources

Game theory research reveals fragility of common resources
Shreyas Sundaram, at left, an assistant professor in Purdue University’s School of Electrical and Computer Engineering, and doctoral student Ashish Hota are performing research in game theory that harnesses the Nash equilibrium, developed by Nobel laureate John Nash, whose life was chronicled in the film “A Beautiful Mind.” . Credit: Purdue University photo/John Underwood

New research in game theory shows that people are naturally predisposed to over-use "common-pool resources" such as transportation systems and fisheries even if it risks failure of the system, to the detriment of society as a whole.

The ongoing research harnesses the Nash equilibrium, developed by Nobel laureate John Nash, whose life was chronicled in the film "A Beautiful Mind," and also applies "prospect theory," which describes how people make decisions when there is uncertainty and risk.

The research could have implications for the management of engineered systems such as the power grid, communications systems, distribution systems, and online file sharing systems, along with natural systems such as fisheries.

"We are surrounded by large-scale complex systems, and as engineers we are trying to figure out how to design systems to be more robust and secure," said Shreyas Sundaram, an assistant professor in Purdue University's School of Electrical and Computer Engineering. "One aspect would be how you could engineer systems so that the incentives for people to use them are aligned with perhaps what's best for society. As a government, what sorts of things can you do to make sure people use systems in a responsible manner?"

Doctoral student Ashish Hota is leading the research, which is the focus of his thesis.

"The main theoretical framework we are using is the language of , which concerns the analysis of decision making by multiple individuals when the benefits of their decisions depend on what other people are doing," Sundaram said. "At a Nash equilibrium, people selfishly select options that will yield the highest benefit for them, often to the detriment of their collective benefit."

Findings are detailed in a research paper that appeared in the July issue of the game-theory journal Games and Economic Behavior.

An example of a Nash equilibrium is illustrated in the so-called "prisoner's dilemma," where two robbers are caught by police and questioned independently. They would both benefit by agreeing ahead of time not to squeal on each other.

"The problem with this rational thinking is that if I know you are not going to rat me out, I stand to benefit more by ratting you out and optimizing my chances of getting away with it," Sundaram said. "So the only Nash equilibrium is for both of you to rat each other out. If your accomplice is ratting you out there is no benefit in you not ratting him out because you are going to take more of the blame for the crime."

Understanding the behavior at the Nash equilibrium can be challenging when the outcomes are uncertain. Complicating matters is that different people have different risk preferences.

"In many applications, people decide how much of a resource to use, and they know that if they use a certain amount and if others use a certain amount they are going to get some return, but at the risk that the resource is going to fail," he said.

Sundaram and Hota have analyzed the Nash equilibrium when risk preferences are modeled according to prospect theory, a Nobel-prize winning theory that captures how humans make decisions in uncertain situations.

"The key is that you have to consider how people actually perceive wins and losses, and this is where prospect theory comes in," Sundaram said. "Whereas classical models have not looked at how people actually evaluate gains and losses and probabilities, Ashish's work has been looking at what happens at the Nash equilibrium when we incorporate these more complex risk preferences. We wanted to determine the failure probability, which we refer to as the fragility of the resource, as a function of the risk preferences of the users."

In a society that tightly controls the use of resources, failure is less likely.

"This is why the notion of a Nash equilibrium ends up being key," he said. "The Nash equilibrium captures the idea that nobody is forcing you to do the right thing. You are doing just what you want to do to optimize your own benefit. If, however, it's a resource that is very carefully managed by a central authority, the failure probability is lower."

The researchers found that the resource has a higher likelihood of failure at the Nash equilibrium under prospect theory.

"This means human beings will over-utilize their resources, compared to what is predicted by classical models of ," Sundaram said.

Furthermore, people have differing, or heterogeneous, aversions to losing. In free societies, where people can exercise decisions based on their differing loss aversion, total use of a common resource is higher than otherwise.

The researchers also are studying how imposing taxes to incentivize human behavior impacts its likelihood of failure.

Future work will include research to apply the approach to cybersecurity, probing how people make decisions under risk.

"Similar reasoning can be applied to cybersecurity," Hota said. "Understanding how people perceive security risks is critical toward designing more secure systems."

The paper was authored by Hota; Siddharth Garg, an assistant professor of electrical and computer engineering at New York University; and Sundaram.

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More information: Ashish R. Hota et al, Fragility of the commons under prospect-theoretic risk attitudes, Games and Economic Behavior (2016). DOI: 10.1016/j.geb.2016.06.003
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Sep 29, 2016
Too bad people don't actually behave according to the game theoretic assumptions.

The game theory has often been used to argue for absolute private ownership of just about everything under the idea that a single owner will best manage the resource to keep from destroying their own property.

In reality people aren't completely selfish, and they practice what's called "superrationality" which can be simplified as assuming other people to think roughly on the same lines as yourself to predict their behaviour. After a number of iteration cycles, the end result is some sort of truce or agreement to stop ruining things.

The only thing that really acts like the game-theoretic person is a large corporation ran by a board of people where nobody takes personal responsibility. And economists.

Sep 29, 2016
Is this not another, or different, solution to the tragedy of the commons? I am not an economist or game theorist (as you probably surmised) but at one point in the past I had spent some time studying the tragedy of the commons. To me, it appears it is the same problem, and it is very interesting to see game theory applied to this age-old problem.

Sep 29, 2016
it is very interesting to see game theory applied to this age-old problem

It's been done a number of times. The last time the results applied became Margaret Thatcher's government.

Sep 29, 2016
The ancient, but still optimal solution to 'tragedy of the commons' is, no surprise, Common Law. Think of it as 'bottom up' coding rather than centrally established 'top down' law-making...

Sep 30, 2016
Please explain how "common law" solves the problem.

Sep 30, 2016

Game theory does not suggest that private property is the solution to all problems. Indeed Nash equilibrium suggests that free markets will be inefficient.

Oct 01, 2016
This comment has been removed by a moderator.

Oct 03, 2016

Game theory does not suggest that private property is the solution to all problems. Indeed Nash equilibrium suggests that free markets will be inefficient.

Perhaps, but that's not what the neoliberals have taken out of it.

Idea being that if common property is subject to tragedy of the commons, the obvious solution is to make it not-common : to privatize it. That is then supposed to solve the problem under the assumption that a private owner will always maximize his returns over time by not over-exploiting and therefore destroying the resource. In theory.

it doesn't reflect the actual price of raw sources for society

No, it does reflect them. It's just that not all the costs are immediately materialized, so they don't become actual costs until much much later when it can be said that the society no longer exists. Certainly not the same people.

Oct 03, 2016
This comment has been removed by a moderator.

Oct 04, 2016
Indeed Nash equilibrium suggests that free markets will be inefficient.

What's that supposed to mean, though?

The Nash equilibrium is simply when each agent makes the best possible decision by taking into account the strategies of others, which isn't the same thing as the free market. What happens on the free market will depend on how you define "best", which is usually taken to mean absolute profit maximization.

But in reality people have multiple motives, and they aren't entirely selfish either, or "rational" however you choose to define that, so the game theory breaks down. It applies to some market entities, but not all of them, and not all of the time.

Oct 04, 2016


Examples of game theory problems in which these conditions are not met:

The first condition is not met if the game does not correctly describe the quantities a player wishes to maximize. In this case there is no particular reason for that player to adopt an equilibrium strategy. For instance, the prisoner's dilemma is not a dilemma if either player is happy to be jailed indefinitely."

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