Different sellers often sell the same good at different prices. Using a strategic bargaining model, I characterize how the equilibrium prices of a good depend on the interaction between its sellers’ costs, its buyers’ values, and a network capturing various frictions associated with trading it. In contrast to the standard random-matching model of bargaining in stationary markets, I allow agents to strategically choose whom to make offers to, which qualitatively changes how the network shapes prices. As in the random-matching model, the market decomposes into different submarkets, and—in the limit as bargaining frictions vanish—the law of one price holds within but not across them. But strategic choice of partners changes both how the market decomposes into different submarkets and the determinants of each submarket’s price.
Simple games serve as abstract representations of voting systems and other group-decision procedures. A stable set (or von Neumann-Morgenstern solution) of a simple game represents a “standard of behavior” that satisfies certain internal and external stability properties. Compound simple games are built out of component games, which are, in turn, “players” of a quotient game. I describe a method to construct fair (or symmetry-preserving) stable sets of compound simple games from fair stable sets of their quotient and components. This method is closely related to the composition theorem of Lloyd Shapley (1963) and contributes to the answer of a question that he formulated: what is the set G of simple games that have a fair stable set? In particular, this method shows that G includes all simple games whose factors--or quotients in their “unique factorization” of Shapley (1967)--are in G. This suggests a path to characterize the set G of all simple games that have a fair stable set.
Outside options shape bargaining outcomes, but understanding how they are determined is often challenging, because one's outside options depend on others' outside options, which depend, in turn, on others' outside options, and so on. This paper describes a non-cooperative theory of coalition formation that shows how the classical Nash bargaining solution uniquely pins down both the sharing rule and the relevant outside options in each coalition. This provides a tractable framework to investigate how different economic shocks propagate via outside options.
In many settings, heterogenous agents make non-contractible investments before bargaining over both who matches with whom and the terms of trade. In thin markets, the holdup problem---that is, underinvestment caused by agents receiving only a fraction of the returns from their investments---is ubiquitous. Using a non-cooperative investment and bargaining game, we show that holdup need not be a problem in markets with dynamic entry---even if they are thin at every point in time. This provides non-cooperative foundations for the standard price-taking assumption in matching markets, and shows that intertemporal competition can perfectly substitute for intratemporal competition.
Risk compensation can undermine the ability of partially-effective vaccines to curb infectious-disease epidemics: Vaccinated agents may optimally choose to engage in more risky interactions and, as a result, may increase everyone’s infection probability. We show how—in contrast to the prediction of standard models—things can be worse than that: Free and perfectly safe but only partially effective vaccines can harm everyone, and hence fail to satisfy—in a strong sense—the fundamental principle of “first, do no harm.” Our main departure from standard economic epidemiological models is that we allow agents to strategically choose their partners, which we show creates strategic comple- mentarities in risky interactions. As a result, the introduction of a partially-effective vaccine can lead to a much denser interaction structure—whose negative externalities overwhelm the beneficial direct effects of this intervention.
In a wide variety of social settings (e.g. crime, education, political activism, technology adoption), players’ returns to their efforts depend on how much effort others exert. Modeling these situations as a network game with strategic complementarities, we show that a player’s cycle centrality—a weighted sum of the number of network cycles that she is in—determines the extent to which she benefits from her complementarities with others. In contrast to the widely-used Bonacich centrality—which measures how efforts propagate through the network—cycle centrality measures how the variance of efforts propagates through the network. A utilitarian social planner who can incentivize one player’s effort targets the one with the highest cycle centrality.