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The mathematical study of cooperation and conflict, in cases where all actors are assumed to be rational, is called game theory. It was pioneered by John von Neumann, Oskar Morgenstern, John Nash, and others in mid-20th century, and has subsequently grown into a major academic area of study.

A key concept of game theory is the Nash Equilibrim. If all players have chosen a strategy and no player can benefit from changing their strategy unless other players also change their strategy, we are in a Nash equilibrium.

As an illustration, consider the problem known as “the prisoner’s dilemma.” Two suspects face imprisonment, but can get a reduced sentence by betraying each other. However, if neither of them betrays each other, they get a shorter sentence than if both do.

Payoff MatrixPrisoner B stays silent (cooperates)Prisoner B betrays (defects)
Prisoner A stays silent (cooperates)Each serve 1 yearPrisoner A: 3 years; Prisoner B: goes free
Prisoner A betrays (defects)Prisoner A: goes free; Prisoner B: 3 yearsEach serves 2 years

Conditional on both prisoners’ expected utility functions being such that they each gain utility from getting a shorter prison sentence, but not from the other prisoner getting a shorter prison sentence, both defecting is a Nash equilibrium, even though that is worse for both than both cooperating.

One real-world analogy to the prisoner’s dilemma is climate change mitigation, where it may not be rational for countries to reduce their carbon emissions if they cannot ensure that other countries will as well. Such cases illustrate the usefulness of group decision-making procedures.

Further reading

Alexander, Scott. 2014. Meditations on Moloch.

Ross, Don. 2014. Game theory. In Edward Zalta (ed.), Stanford Encyclopedia of Philosophy.

Wikipedia. 2016. Game theory.

Wikipedia. 2016. Prisoner’s dilemma.

Wikipedia. 2016. Tragedy of the commons.

Wikipedia. 2016. Nash equilibrium.