How Wasteful is Signaling?

TL;DR

This paper quantifies the inefficiency of signaling by defining a waste ratio as the proportion of private surplus dissipated in a separating equilibrium. It shows that with multiplicative costs, the waste ratio is invariant to the scale of costs (stakes) and to the difficulty of signaling, and, within an isoelastic class where $V(\hat{\theta})=sB(\hat{\theta})$ with $B(\theta)=\theta^{\beta}$ and $C(a,\theta)=D(a)\theta^{-\sigma}$, the waste ratio is a constant across types: $W=\frac{\beta}{\beta+\sigma}$. The analysis further links signaling to contest theory by applying the result to signaling tournaments, where the waste ratio for $N$ candidates is $W_N=\frac{N-1}{N}$, matching the rent dissipation rate in symmetric Tullock contests. The findings imply that increasing signaling difficulty or stakes may not reduce waste unless the isoelastic structure or the number of competitors changes; this framework provides a tractable benchmark for evaluating signaling inefficiency and its policy implications.

Abstract

Signaling is wasteful. But how wasteful? We study the fraction of surplus dissipated in a separating equilibrium. For isoelastic environments, this waste ratio has a simple formula: $β/(β+σ)$, where $β$ is the benefit elasticity (reward to higher perception) and $σ$ is the elasticity of higher types' relative cost advantage. The ratio is constant across types and independent of other parameters, including convexity of cost in the signal. A constant waste ratio characterizes the isoelastic class. In winner-take-all signaling tournaments with $N$ candidates, exactly $(N-1)/N$ of the surplus dissipates -- the same as in Tullock contests.

Theorems & Definitions (10)

• Definition 1
• Definition 2
• Theorem 1
• Example 1
• Theorem 2
• Proposition 1
• Proposition 2
• Example 2
• Example 3
• Lemma 1