Markets, Bargaining, and Networks with Heterogeneous Agents

Abstract

The paper proposes an intertemporal model of bargaining among heterogeneous buyers and sellers placed on a bipartite network. First, it characterizes conditions on the network under which its trading restrictions are inessential and the outcome is arbitragefree. Instead, when the system is segmented in different trading components, we show how these come about and how prices are determined in each of them. Second, we turn to the issue of network endogeneity, focusing on those networks that are Pairwise Stable. Such networks are shown to always exist and be arbitrage-free. In the latter respect, therefore, they satisfy one of the key properties displayed by frictionless markets. We identify, however, a sharp contrast regarding another key feature: Pairwise-Stable networks are generically inefficient if the matching process is genuinely decentralized. This uncovers a fundamental incompatibility between individual incentives and social welfare in endogenous trading networks. We explain that such incompatibility is not only due to buyer/seller heterogeneity but is also caused by the incentives underlying network formation in a trading context.

Matching structure and bargaining outcomes in buyer–seller networks

“…The role of the Structure Theorem does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values [see, e.g., Polanski and Vega Redondo (2013) for a generalization of the Manea (2011) model in this direction].…”

Strategic formation of homogeneous bargaining networks

“…In this light, Polanski and Vega-Redondo (2013) argue that the discrepancy between pairwise stability and efficiency in their model is due to the ex-ante heterogeneity between players. In the following we establish that in our model the two sets of pairwise stable and efficient networks do not coincide in general either though players are ex-ante homogeneous.…”

“…Most other papers studying strategic network formation in a bargaining context again focus on buyerseller networks, which is complementary to our general approach. Kranton and Minehart (2001) and Polanski and Vega-Redondo (2013) are prominent examples for this, whereby the latter also does not involve explicit linking costs.…”

Strategic Formation of Homogeneous Bargaining Networks

“…From the perspective of a social planner it is of particular interest to understand the connection between pairwise stable network structures on the one hand and efficient ones on the other. Polanski and Vega-Redondo (2013) argue that the discrepancy between pairwise stability and efficiency in their model is due to the ex-ante heterogeneity between players. Insofar, we would expect that in our model the set of efficient networks coincides with the one of the pairwise stable, which we have characterized in Section 3.…”

“…Most other papers studying strategic network formation in a bargaining context again focus on buyer-seller networks, which is complementary to our general approach. Kranton and Minehart (2001) and Polanski and Vega-Redondo (2013) are prominent examples for this, whereby the latter also does not involve explicit linking costs.…”