Analyzing simple two-player games

Game theory is a branch of mathematics concerned with the analysis of decision-making and strategy. It has applications in economics, biology, and behavioral science. Many seemingly complex situations can be reduced to a relatively simple mathematical game that can be analyzed in a systematic way to find optimal solutions.

A classic problem in game theory is the prisoner’s dilemma, which, in its original form, is as follows: two co-conspirators are caught and must decide whether to remain quiet or to testify against the other. If both remain quiet, they both serve a 1-year sentence; if one testifies but the other does not, the testifier is released and the other serves a 3-year sentence; and if both testify against one another, they both serve a 2-year sentence. What should each conspirator do? It turns out that the best choice each conspirator can make, given any reasonable distrust of the other, is to testify. Adopting this strategy, they...