Christopher Sandmann wille defend his thesis on June 29th at 3:00 PM
Title: « Essays in Economic Theory »
By videoconferencing (TSE)
Supervisor: Thomas Mariotti
To attend the meeting, please contact Elvire JALRAN
- Marina Halac, Professor, Yale University
- Lucas Maestri, Professor, FGV EPGE
- Leeat Yariv, Professor, Princeton University
- Bruno Jullien, Senior researcher, CNRS
- Thomas Mariotti, Senior researcher, CNRS
This dissertation studies several seemingly disparate problems in economic theory: chapters 2 and 3 (written jointly with Nicolas Bonneton) investigate how (non-stationary, i.e., time-varying) search frictions affect positive assortative matching (PAM), chapter 4 studies higher-order belief uncertainty and their manipulation in games of incomplete information, chapter 1 questions the optimality of second-order price discrimination by a monopolist seller.
Economists view choices—taking the form of individual match acceptance decisions (as in chapter 2 and 3), coordination issues in investment games (as in chapter 4), or consumer purchase and subsequent pricing decisions (as in chapter 1)—as solutions to constrained optimization problems. Comparative properties of payoffs determine whether one agent is more accepting to match with a less desirable partner than another agent, whether investment decisions are mutually encouraging, or to what extent one can decrease quality and price to buyers of lower valuation without sacrificing the demand of high valuation buyers for high quality products.
What binds these disparate essays together is that they identify (as in chapters 1, 2 and 3) or make use of (as in chapter 4) comparative properties of payoffs under which equilibrium behavior is particularly well understood: sorting under random search matching obtains (see chapters 2 and 3); we gain insights into the information structure which guarantees the highest probability of coordination across all equilibria (chapter 4); instead of charging distinct prices for separate qualities or times of purchase, the monopolist posts a single price for the highest level of quality only (chapter 1).
In the context of monopolistic second-degree price discrimination (see chapter 1) I derive a condition under which a single posted price as opposed to sophisticated discriminatory pricing is profit-maximizing. The weakest sufficient condition for this to arise posits a ranking on the concavity of preferences. Under second-degree price discrimination this requires that high valuation buyers’ utilities are more concave than low valuation buyers’ utilities. Intuitively, this is the case when consuming per-se, not quality is what matters to buyers of greater valuation. This generalizes findings by Anderson and Dana (2009) and Stokey (1979).
In the context of matching absent bargaining (the NTU paradigm), see chapter 2, we identify comparative properties of payoffs under which more highly ranked individuals are choosier with whom they accept to match, thereby stipulating PAM—even in the presence of search frictions. Answers to this question have been provided in the steady state where entry and exit exactly balance each other at every point in time. Our analysis encompasses non-stationary dynamics instead, where the pool of agents searching fluctuates over time. To sustain sorting we find that more desirable individuals must be less risk-averse than lesser ranked individuals. The intuition is straightforward: the decision to reject a certain match payoff today is a revealed preference for a risky, random match payoff some time in the future. What is then perhaps most surprising is that this ranking on risk-preferences is not required to ensure PAM in the steady state (see Morgan (1994) and Smith (2006)). The reason is that risk-preferences only come to full bearing in the presence of the risk of future worsening match prospects, inherent to non-stationary dynamics.
In chapter 3, we extend our analysis of non-stationary sorting to an environment where match payoffs are determined via bargaining (the TU paradigm, previously studied by Shimer and Smith (2000) and Atakan (2006)). More fundamentally, chapter 3 broadens the definition of assortative matching to allow for individual heterogeneity. In doing so, chapter 3 identifies a novel force which upsets
assortative matching under bargaining – irrespective of match complementarities: frictions disproportionately erode the value of search and hence the bargaining power of more productive agents. At the extreme, when the market is thin so that meetings are rare, agents unanimously exhibit the greatest match surplus when matched with the most productive individuals, and not with individuals of similar characteristics.
In addition, the thesis makes several technical contributions. First, chapter 2 formulates general conditions under which deterministic non-stationary dynamic equilibria of the search and matching economy exist. Here we considered a continuum of agents and infinite time horizon. Motivated by the fact that finite player games are known to be prone to equilibrium multiplicity, i.e., they can coordinate on equilibria in which all agents are more or less accepting of others, chapter 3 then shows that in a framework with aggregate uncertainty and terminal-time, an equilibrium does not only exist but is also unique. The reason is that aggregate uncertainty makes it impossible to coordinate on an equilibrium, when such strategy can only be optimal if one reaches a far-fetched pessimistic (or optimistic) state with few (many) agents in the search pool. More succinctly, aggregate uncertainty impedes coordination.
Finally, chapter 4 proposes a novel approach to information design in games (going beyond the single-receiver case studied by Kamenica and Gentzkow (2011)). An example thereof is the investment game where a sender seeks to encourage several investors to invest amid an unknown state of nature. Central to this novel approach is a new explicit representation of higher-order beliefs which allows for greater tractability than the representation proposed thus far in the literature. As an application, I provide a unified and hopefully clarifying perspective on the oft-invoked infection argument. Here, the sender sends a chain of messages alternating between players such that one message inducing a low action is contagious for another player to likewise choose the low action. I introduce a new distinction based on whether the information structure manipulates first-order beliefs only, or creates uncertainty over higher-order beliefs at all orders.