We study a decentralized trading model as in , where a finite number of heterogeneous capacity-constrained sellers compete for a finite number of homogeneous buyers, by posting prices. This "directed search" model is known to admit symmetric equilibria; yet, uniqueness has proved elusive. This study makes two contributions: a substantive contribution is to establish uniqueness of symmetric equilibrium; a methodological contribution is to develop a tool based on directional derivatives to characterize equilibrium.
Kim, Jaehong, and Gabriele Camera. "Uniqueness of equilibrium in directed search models." Journal of Economic Theory 151 (2014): 248-267. doi: 10.1016/j.jet.2013.11.004
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