Introduction to Game Theory

In the 1980’2 movie Wall St. the character Gordan Gekko (as played by Michael Douglas) proclaims that “Greed, for lack of a better word, is good.”  He claims that what is understood to be an immoral motive at the scale of an individual, is really a virtue at the scale of the organization.

This aphorism, which is understood to be derived from Adam Smith‘s Wealth of Nations, has been repeated so often it has now become the conventional wisdom, if not cliche.  The basic argument is based on the supposition that individuals respond to incentives, and when they are able to reap the rewards of their hard work, they will work harder.

Why is that good?  When individuals works harder for themselves, they produce more, create more wealth (in terms of available goods, services, or manufactured capital), driving market prices down, and enabling greater consumption (or investment).  In this way, “greedy” individuals operating in market systems can benefit all other market participants through lower prices, by acting in their own self-interest (through harder work, or innovation leading to efficiency gains).  Thus, Smith’s approach pushes back on the simpler, Judea-Christian view that greed is a vice.

However, there is a certain class of problems involving group dynamics in which the analysis described by Adam Smith is wrong.

A depicted in the biopic A Beautiful Mind, the economist John Nash discovers that when confronted with problems of competition, such as the management of common resources, actions that might seem rational at the scale of the individual can be irrational at the scale of the group.  The branch of economics that studies problems of this type is called game theory.  The essential characteristic of a game theoretic problem is the realization that any individual’s best decision depends upon what they expect other individuals to do.  Thus, game theory is capable of modeling the interaction between individuals.

The classic example of a game theoretic problem is called the Prisoner’s Dilemma:

The Prisoner’s Dilemma belongs to a class of game theoretic problems called non-cooperative.  In this class of problems, players (decision-makers) each decide independently, without the benefit of a contract or other enforcement mechanism that can hold the other party to an agreement.  The Nash Equilibrium is found where no decision-maker can improve their position unilaterally (i.e., without a change in the decisions of others).

At the Nash Equilibrium, the only way to improve the system is if the decision-makers work collectively — i.e., they have to agree to cooperate.  The difficulty is that, without a punishment mechanism for enforcing the agreement, both decision-makers have an incentive to cheat, despite the fact that in an non-cooperative game-theoretic problem like the Prisoner’s Dilemma, neither player can improve their own position without damaging the position of the other.

Cases of cheating seemingly abound, such as in sports and education.  Not all cases of cheating involve non-cooperative game theoretic problems — although they may involve collusion in covering it up.  However, several studies have documented that people are more likely to cheat when they believe that others are cheating.  In other words, cheating is contagious.

Two recent cases of cheating are noteworthy.  The first is Lance Armstrong, who was recently stripped of his cycling championship as result of the testimony of several other cyclists who claim that he used banned performance-enhancing drugs.  In this case, it is clear that all cyclists would likely be be better off if none cheated because none of them would find it necessary to incur the medical risks of blood doping.   However, if no cyclist was cheating, then the incentives would be strong among those near the top to garner a competitive advantage by being the only cyclist cheating.  Given that all top cyclists are reportedly cheating, then they all incur both medical and career risks, but none gains a competitive advantage.

The case of the Harvard University students in an Introduction to Congress class that are accused of discussing and sharing answers on a take-home exam is more complicated.  The exam itself was open book, open notes, and open Internet.  However, students were explicitly prohibited from discussing the exam.  Nevertheless, several Teaching Fellows (assistants) in the class fielded questions from the students and provided clarification of the exam questions to different degrees.  Moreover, the accused students say that the explicit rules of the exam were at odds with the culture of collaboration that characterized the course.

The accounts of the Harvard case to date seemingly ignore the fact that grading practices in modern Universities often position students in a non-cooperative game theoretic problem.  For example, when letter grades are assigned on the basis of out-performing the average score, then over-performance by one student will necessarily hurt the grades awarded to others students (by raising the average, or busting the curve).   All students might be better off if they all agreed not to study — or at least to not perform their best on the exam.  This would save the students’ effort and result in the same distribution of grades.  However, each student has an individual incentive to study as hard as they can, even knowing that their accomplishments will diminish the grades of other students.

When the cheaters like criminals or oligopolistic firms do not elicit sympathy, it hardly seems like the failure to work collectively is immoral.  In fact, the conventional wisdom is that competition benefits society.  For example, in the United States, special laws have been enacted that prohibit “racketeering” and organized crime, increasingly penalties in cases where criminals are working collectively.

However, in other instances, the failure of individuals belonging to a single bloc to work collectively can result in social costs.  In 1968, Garrett Hardin identified a class of such problems particular to management of “common pool resources“.

The classic economic solution to the problem of the commons is privatization, in which exclusive property rights are allocated to individuals, who consequently have an incentive to manage those resources wisely, thereby aligning individual and social incentives.  However, privatization is not the only mechanism by which common goods have been successfully managed.  Elinor Ostrom points out that cooperation between individuals can exist despite the incentive to cheat and in the absence of a third party (meaning someone outside the group) enforcement.  In these instances, groups typically institute their own mechanisms of enforcement.

Because some common pool resources (such as the atmosphere) are not amenable to privatization, Ostrom’s discovery of alternative mechanisms may be especially important to sustainability.  However, recognition of game-theoretic problems significantly complicates moral analysis.  Because the outcomes of an interesting game-theoretic problem depend on interaction between two or more players, where should the moral culpability for the tragedy reside?

In fact, doing the “right thing” in a non-cooperative game theoretic problem might actually encourage other players to do the wrong thing, by improving their payoffs.  The converse is also true.  Doing the wrong thing (that is, defecting or failing to cooperate), or at least the credible threat of the wrong thing, might actually turn out to be the only way to ensure that other players do the right thing, as this video from a popular British game show illustrates.

4 thoughts on “Introduction to Game Theory

  1. Pingback: Introduction to the Tragedy of the Commons | CEE300 – Engineering Business Practices

  2. Pingback: Introduction to The Tragedy of the Commons | CEE300 – Engineering Business Practices

  3. Pingback: Moral Dimensions of the Commons | Sustainability Ethics

  4. Pingback: Introduction to The Tragedy of the Commons | Sustainable Engineering Systems

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