Game theory is a relatively young branch of mathematics that goes back to the publication of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern in 1944.

Game theory undertakes to build mathematical models and draw conclusions from these models in connection with interactive decision-making: situations in which a group of people not necessarily sharing the same interests are required to make a decision.

The choice of the topics reflects our purpose: we wanted to present material that does not require mathematical prerequisites and yet involves deep game-theoretic ideas and some mathematical sophistication. Thus, we ruled out topics from non-cooperative game theory, which requires some knowledge of probability, matrices, and point-set topology.

Broadly speaking, the topics chosen are all related to the various meanings that can be given to the concept of “fair division. ” The four chapters illustrate this.

The first, “Mathematical Matching, ” concerns, among other things, the problem of assigning applicants to institutions of higher learning. Each applicant ranks the universities according to his scale of preferences. The institutions of higher learning, in turn, rank the applicants for admission according to their own scale of preferences. The question is how to effect the “matching” between the applicants and the universities. The reader will discover that this problem leads to unexpected solutions.