Signaling Games with Costly Monitoring

TL;DR

This paper investigates how small monitoring costs affect signaling game equilibria, showing that certain pooling equilibria with non-zero index persist when monitoring costs are minimal.

Contribution

It proves that for sufficiently small monitoring costs, pooling equilibria with non-zero index remain stable close to the original equilibrium.

Findings

Pooling equilibria with non-zero index survive small monitoring costs

Monitoring costs do not alter equilibria with zero information gain

The stability of equilibria depends on the size of the monitoring cost

Abstract

If in a signaling game the receiver expects to gain no information by monitoring the signal of the sender, then when a cost to monitor is implemented he will never pay that cost regardless of his off-path beliefs. This is the argument of a recent paper by T. Denti (2021). However, which pooling equilibrium does a receiver anticipate to gain no information through monitoring? This paper seeks to prove that given a sufficiently small cost to monitor any pooling equilibrium with a non-zero index will survive close to the original equilibrium.