10.1 Introduction

Although the Prisoner's Dilemma was originally developed and analyzed as a two-person interaction, many of the most important applications of what we might loosely call “Prisoner's Dilemma thinking” involve issues in the social sciences that are concerned with much larger numbers. This fact immediately poses a question: How does the two-person version differ from the large number Prisoner's Dilemma? Do the lessons of (and intuitions arising from) the two-person case carry over to larger scale social applications?

The general consensus in the economics literature is that the differences are very considerable – amounting to something like a qualitative difference between small-number and large-number situations. Consider, for example, the case of market provision of so-called “public goods.” As Richard Tuck observes in the epigraph, virtually all the classic writers on public goods provision make two points: first, that the public goods problem is very like the Prisoner's Dilemma problem in certain critical respects; and second, that small-number cases are unlike large-number cases in that voluntary action is much more likely to secure satisfactory levels of public goods provision in the small-number setting. Buchanan, for example, observes:

There is in short consensus that numbers make a difference; but much less consensus concerning exactly how and why they do.