1 Introduction
There is a growing interest in economics for models of anonymous and decentralized
interaction. A possible cause for this interest is that societies have become increasingly
anonymous and the frequency of repeated interaction has declined. This interest is
reflected in the adoption of trading environments populated by a large number of
individuals who meet at random. Such frameworks are used, for example, in Diamond
(1982) to model the existence of frictions in trading, in Kiyotaki and Wright (1989) to
provide the foundations for monetary exchange, in Dixit (2003) to study economic
governance, and in Shimer (2005) to analyze unemployment. When agents interact as
strangers, as in the above settings, there exist frictions in cooperation and coordination
among agents, hence achieving optimum outcomes is a challenge.
Economic theory has shown that even in anonymous groups, cooperation is
theoretically possible as long as individuals are involved in a long-term interaction. The
theoretical foundation can be traced back to the folk theorems for infinitely repeated
games (supergames) of Friedman (1971) and the subsequent random-matching extensions
in Kandori (1992) and Ellison (1994). The basic theoretical result is that cooperation is an
equilibrium if agents are sufficiently patient. There exists very limited empirical
evidence, however, regarding the above environments.
This paper studies matching economies in an experiment where pairs of strangers
“infinitely” play a prisoners’ dilemma. Strangers are anonymous subjects who are
randomly matched in each period, and their histories are private information. In these
economies the Pareto efficient outcome is not an equilibrium in the one-shot game, but,
for an appropriate choice of parameters, it is one of the equilibria if the horizon is infinite.
Kandori (1992) and Ellison (1994) proved that the Pareto efficient outcome can be
achieved by adopting social norms of cooperation that rely on the threat of a “grim-
trigger” punishment scheme, i.e., economy-wide defection. Basically, a subject
cooperates unless someone has been caught defecting, in which case the subject should
forever defect.