13 - Delays and Payoff Externalities

Summary

It takes two to tango.

Agents optimize their decisions over time with externalities of information and in payoffs. Examples of strategic substitutability include learning about the capacity of demand in a market, the marginal cost of production of a new technology, or the potential capacity of supply. When there are strategic complementarities, coordination may be easier to achieve in the multiperiod setting if the number of agents is finite, but it may be impossible if the number of agents is large. An example of strategic complementarity is the diffusion of contraceptives in some countries.

When agents can choose the timing of their actions, they have an incentive to delay in order to gain information. We have seen in Chapter 6 that the information externalities can generate strategic substitutabilities or complementarities. In this chapter, we reconsider the issue of delays with the introduction of payoff externalities. Given the current state of the literature, the problem of coordination, which was the main one in the previous two chapters, is assumed away here. Agents coordinate on a Nash equilibrium. If such an equilibrium is not unique, some ad hoc rule will be followed for its choice.

STRATEGIC SUBSTITUTABILITY

Payoff externalities have been shown to be a source of delays in the abundant literature on wars of attrition. An example is the private provision of a public good. Harris and Nalebuff (1982) describe a hot room with people who each would like the window to be opened. The open window is a public good that benefits all, but each person shuns the embarrassment of standing up in front of others and going to open the window. Everyone is waiting for someone else to go.