John von Neumann and Oskar Morgenstern published this in 1944 and it created game theory as a field. Its ambition was to supply economics with a mathematical foundation appropriate to situations where outcomes depend on the interacting decisions of multiple parties.
The book's first substantial contribution is the axiomatic derivation of expected utility. Von Neumann and Morgenstern set out axioms describing consistent preferences over lotteries and show that anyone satisfying them behaves as if maximising the expected value of a utility function. This became the foundation of decision theory under uncertainty and of every subsequent model in financial economics.
The game theory itself covers two-person zero-sum games, where the minimax theorem von Neumann had proved in 1928 establishes that a solution in mixed strategies always exists, and then n-person and cooperative games, where the authors develop coalition analysis and the concept of a stable set. The cooperative theory occupies most of the book and has proved less influential than the two-person material and than the non-cooperative equilibrium concept that John Nash introduced six years later. The book is long, difficult and written in a mathematical style that few economists could read at the time. Its influence came through others: the expected utility axioms and the minimax theorem entered economics immediately, while game theory itself took several decades to become central.
Readers who want the founding text of game theory and of expected utility, understanding that its influence came through work that followed it.
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