Social status in a social structure: noisy signaling in networks

How do incentives to engage in costly signaling depend on social structure? This paper formalises and extends Thorstein Veblen’s theory of how costly signaling by conspicuous consumption depends on social structure. A noisy signaling game is introduced in which spectators observe signals only imperfectly, and use Bayesian updating to interpret the observed signals. It is shown that this noisy signaling game has (under some weak regularity conditions) a unique plausible Perfect Bayesian Nash equilibrium. Then, a social information network is introduced as a second source of information about a player’s type. Equilibrium signaling depends in the resulting game on the relative quality of the substitute sources of information, which depends again on the social network. For some highly stylised networks, the dependence of equilibrium costly signaling on network characteristics (network size, density and connectedness, the centrality of the consumer in the network) is studied, and a simple dominance result for more arbitrary networks is suggested.