12 - Long-run relationships and the credibility of threats and promises

Summary

The previous chapter showed that individuals may be willing to undertake otherwise wasteful “signaling” activities in order to make favorable information about themselves credible to other parties. However, that analysis presumed a one-time interaction among players. This chapter inquires into the further information transmission opportunities that are introduced when individuals interact with one another repeatedly.

In some cases at least, an individual should be able to make favorable information about himself (information that he is a high-quality or otherwise desirable trading partner) credible by actions taken in the early periods of a long-run relationship. That is, an individual should be able to develop a reputation. As we shall see, however, reputation-building may be unprofitable even when the distant future is only very mildly discounted.

The multi-period Prisoners' Dilemma

Let us begin by examining the Prisoners' Dilemma. In table 12.1 below, each individual i (i = 1,2) may choose to play either “Defect” (strategy x₁) or “Cooperate” (strategy x₂). The Prisoners' Dilemma environment is defined by the ranked payoffs in table 12.1 if e > f > g > h. Table 12.2 is a numerical example.

When the Prisoners' Dilemma is played just once, it is evident that the Defect strategy x₁ is strictly dominant for each player. The unique Nash equilibrium is therefore for both individuals to choose x₁. In the illustrative example of table 12.2, each player's payoff would be zero.