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What is game theory and what are some of its applications?

Mark Arnold, associate professor of mathematics, replies:

Under what conditions should a newly hatched caterpillar eat other butterfly eggs sharing its leaf? Should one ignore an insult, or is it better to reply in same, or with harsher retribution? Can a government selling radio frequencies detect whether companies are bidding fairly, or are in collusion? All of these questions have been illuminated by a branch of mathematics called game theory.

Today game theory is a fundamental tool in corporate, military and political decision making, and is a powerful explanatory tool in biology, economics, management and political science, to name a few. Modern game theory began with an ancient game: a 1913 theorem postulated by E. Zermelo about chess.

But John von Neumann was the major figure in the field from 1928 through World War II. By the 1950s, game theory had become a major branch of applied mathematics. Stephen Nash’s Nobel Prize in Economics was awarded for his work on game theory in the early 1950s.

Game theory is the study of mathematical models describing the interactions of player strategies as they relate to achieving some goal. For example, suppose you and a number of coworkers who currently make $18/hour have failed to negotiate a new contract for $20/hour, and have decided to strike. The company is offering $19/hour to anyone willing to work. A $1 raise is therefore possible for someone willing to cross the picket line, while sticking together could yield everyone a $2 raise. Management might arrive at $19 as an optimal value which inhibits cooperation among workers while minimizing labor cost.

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