55 Pages Posted: 1 Apr 2020 Last revised: 4 Jan 2022
Date Written: Jan 2, 2021
We consider a network of socially connected newsvendors facing random demand for a product who need to commit to a stocking level before demand realizes. A newsvendor can share her ex post excess stock to fulfill the unsatisfied demand of a connected newsvendor. The amount of shared supply that a newsvendor anticipates receiving from her network is affected by two factors: sharing magnitude and tie strength. Sharing magnitude (resp., tie strength) measures the portion of excess stock that a newsvendor will share (resp., the likelihood that a newsvendor will share her excess supply) with a neighboring newsvendor. We adopt a Bayesian game framework with incomplete information about the network structure, where a newsvendor has private information about the number of connections she has (as her type) but does not know her neighbors' types, which she believes are consistent with a network's known degree distribution. First, we demonstrate that with more sharing activity (i.e., greater sharing magnitude or stronger social ties) within a fixed network, all newsvendors decrease their stocking levels regardless of their types, which implies that the total consumption level drops. Second, we show that when tied with the number of connections a newsvendor has, the sharing magnitude has a first-order effect on the mean of the shared supply, while the social tie has a second-order effect on the variability of the shared supply. As the degree distribution of the network increases in the sense of usual stochastic dominance, we show that the two factors may have opposite effects on the equilibrium stocking levels. The effect of sharing magnitude is to increase the equilibrium stocking levels. But the effect of tie strength is such that for a high-fractile product, the population's expected consumption level increases, while it is the other way around for a low-fractile product. Lastly, we extend the supply-sharing base model to complete network information under specific networks and to demand sharing, where unsatisfied demand at one newsvendor can be referred to a neighbor in her network.
Keywords: newsvendor, network game
JEL Classification: A14, C72, D85
Suggested Citation: Suggested Citation