Striving for social status
Social comparisons can influence individual decisions. People compare their income and their belongings to those of people around them. Prominent scholars, such as Frank [1985], argue that increasing inequality has led to excessive spending, as people try to emulate and compete with the rich. This process accelerates as more people are exposed to the lives of the rich and what they consume. We study social comparisons and striving for status in a network context, focusing on how the status considerations and network structure influences individual outcomes and aggregate consumption of goods. We study this phenomenon in a model where agents choose a level of consumption for a good with status implications, like cars or designer clothing. Agents have a linear value for the good and a convex cost of consumption. Additionally, adopting the model of Stark andWang [2005], we assume agents suffer a status loss as they compare to themselves to those with higher consumption in their peer group. Letting e i represent the consumption level of agent i, then i suffers a loss equal to β x max{e j - e i, 0}/|N i| + 1 for each agent j in N i, i's neighborhood in the network. β parameterizes an agent's concern for status. Our primary objective is to solve for and analyze the Nash equilibria. We find that the best-response function is isotone in the lattice structure induced by consumption profiles, and so the equilibria of our game form a non-empty complete lattice. Furthermore, sequential best-response dynamics from either the min or max consumption profiles converges in polynomial time to either the min-consuming or max-consuming equilibrium. We then study how the consumption and welfare of equilibria change with respect to status considerations. We find that consumption at both the minimum-consuming and maximum-consuming equilibria increases with status considerations whereas welfare decreases, indicating that external organizations like luxury good retailers have incentives to perpetuate the perception of their goods as status symbols. Welfare, on the other hand, decreases with status concerns. Starting from any equilibrium and increasing status concerns causes agents to converge to a new equilibrium (via best-response dynamics) in which every agent has (weakly) lower welfare. This supports the intuition that attempts to "keep up with the Joneses" cause agents to over-spend. This happens for all agents, even those that don't know the Joneses, demonstrating the spillover effects of the network. We conclude with a study of the network effect on consumption and welfare. We characterize the set of equilibria by a notion of network connectivity, called cohesion. Using this, we show that adding connections can increase or decrease production (and welfare) as it alters cohesion. © 2012 Authors.
