π€ AI Summary
This study quantifies the social surplus waste induced by signaling in separating equilibria. Focusing on isoelastic environments, the authors employ game-theoretic analysis and elasticity-based modeling to derive a general expression for the waste ratioβΞ²/(Ξ²+Ο)βwhich depends solely on the elasticity of benefits and the elasticity of relative cost advantage, and remains constant across equilibria. The framework is further extended to an N-player, winner-take-all signaling contest, where it is shown that the social surplus is exactly dissipated by a factor of (Nβ1)/N, aligning precisely with the classic Tullock contest result. This work not only uncovers the structural origins of efficiency loss in signaling but also establishes a universal quantitative framework for assessing resource wastage in competitive signaling environments.
π 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: $\beta/(\beta+\sigma)$, where $\beta$ is the benefit elasticity (reward to higher perception) and $\sigma$ 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.