Game Theoretic Analysis of a Problem of Government of People

The general problem of control of a set of individuals to achieve the objective of a controller is common to many areas such as business and government. This paper attempts a mathematical formulation and analysis of such problems. It is assumed that each individual is a rational being acting in his own self-interest. The interests of different individuals are, in general, conflicting, thus leading to a competitive situation which can be analyzed using Game Theory notions. An important aim of mathematical analysis of such a situation will be to study the effectiveness of various kinds of power that a controller might have over the individuals. Most of the results in this paper are concerning a class of “coordination problems” where the controller's objective is to maximize the total utility to the whole group of individuals and where competition arises due to constraints on strategies. The analysis indicates that in such cases the simple power to accept or reject strategies which violate the constraints may be sufficient to realize the controller's goals.