We can model many political situations as zero sum, and the tools that Chapter 4 develops are thus an important part of political theory. Nevertheless, the zero-sum assumption is a restriction that precludes modeling many other situations that are central to politics. If politics concerns the collective allocation of resources, and if those resources are not fixed, as they need not be in an expanding dynamic society, then the principal political processes are necessarily nonzero sum in character. This chapter begins the exploration of the more general class of nonzero-sum, noncooperative games by focusing on a particular game, the prisoners’ dilemma. We find this focus useful for several reasons. First, prisoners’ dilemmas involving two or more persons illustrate many of the problems that one is likely to encounter in applying noncooperative game theory to politics. Second, the prisoners’ dilemma itself models a great many key political situations, including the causes of market and governmental failure, the incentives for political participation, paradoxes of vote trading, and the disincentives of people to reveal truthfully their demand for publicly provided goods and services. And with the prisoners’ dilemma as our starting point, we can introduce an additional modification of the Nash equilibrium concept, Bayes's equilibria, as well as tax schemes (called demand-revelation mechanisms) that are designed to induce truthful revelation of preferences for the goods and services that governments produce or regulate.

Nonzero-sum games

In one sense, moving from zero-sum to nonzero-sum games is not a radical theoretical departure. The representation of a situation's extensive form and the analysis of that form depend not at all on whether the game is zero sum or nonzero sum.