Economics

We study collusion in a second-price auction with two bidders in a dynamic environment. One bidder can make a take-it-or-leave-it collusion proposal, which consists of both an offer and a request of bribes, to the opponent. We show that there always exists a robust equilibrium in which the collusion success probability is one. In the equilibrium, for each type of initiator the expected payoff is generally higher than the counterpart in any robust equilibria of the single-option model (Esö and Schummer (2004)) and any other separating equilibria in our model.

I propose a cheap-talk model in which the sender can use private messages and only cares about persuading a subset of her audience. For example, a candidate only needs to persuade a majority of the electorate in order to win an election. I find that senders can gain credibility by speaking truthfully to some receivers while lying to others. In general settings, the model admits information transmission in equilibrium for some prior beliefs. The sender can approximate her preferred outcome when the fraction of the audience she needs to persuade is sufficiently small. I characterize the sender-optimal equilibrium and the benefit of not having to persuade your whole audience in separable environments. I also analyze different applications and verify that the results are robust to some perturbations of the model, including non-transparent motives as in Crawford and Sobel (1982), and full commitment as in Kamenica and Gentzkow (2011).

A principal can restrict an agent's information (the persuasion problem) or restrict an agent's discretion (the delegation problem). We show that these problems are generally equivalent - solving one solves the other. We use tools from the persuasion literature to generalize and extend many results in the delegation literature, as well as to address novel delegation problems, such as monopoly regulation with a participation constraint.

This paper extends the sequential search model of Wolinsky (1986) by allowing firms to choose how much match value information to disclose to visiting consumers. This restores the Diamond paradox (Diamond 1971): there exist no symmetric equilibria in which consumers engage in active search, so consumers obtain zero surplus and firms obtain monopoly profits. Modifying the scenario to one in which prices are advertised, we discover that the no-active-search result persists, although the resulting symmetric equilibria are ones in which firms price at marginal cost.

Persuasion is an exceedingly difficult task. A leading cause of this difficulty is the misalignment of preferences, which is studied extensively by the literature on persuasion games. However, the difficulty of communication also has a first order effect on the outcomes and welfare of agents. Motivated by this observation, we study a model of Bayesian Persuasion in which the communication between the sender and the receiver is constrained. This is done by allowing the cardinality of the signal space to be less than the cardinality of the action space and the state space, which limits the number of action recommendations that the sender can make. Existence of a maximum to the sender's problem is proven and its properties are characterized. This generalizes the standard Bayesian Persuasion framework, in which existence results rely on the assumption of rich signal spaces. We analyze the sender's willingness to pay for an additional signal as a function of the prior belief, which can be interpreted as the value of precise communication. We provide an upper bound for this value which applies to all finite persuasion games. While increased precision is always better for the sender, we show that the receiver might prefer coarse communication. We show this by analyzing a game of advice seeking, where the receiver has the ability to choose the size of the signal space.

We introduce a new family of mechanisms for one-sided matching markets, denoted pick-an-object (PAO) mechanisms. When implementing an allocation rule via PAO, agents are asked to pick an object from individualized menus. These choices may be rejected later on, and these agents are presented with new menus. When the procedure ends, agents are assigned the last object they picked. We characterize the allocation rules that can be sequentialized by PAO mechanisms, as well as the ones that can be implemented in a robust truthful equilibrium. We justify the use of PAO as opposed to direct mechanisms by showing that its equilibrium behavior is closely related to the one in obviously strategy-proof (OSP) mechanisms, but includes commonly used rules, such as Gale-Shapley DA and Top Trading Cycles, which are not OSP-implementable. We run laboratory experiments comparing truthful behavior when using PAO, OSP, and direct mechanisms to implement different rules. These indicate that individuals are more likely to behave in line with the theoretical prediction under PAO and OSP implementations than their direct counterparts.

Cross-group externalities and network effects in two-sided platform markets shape market structure and competition policy, and are the subject of extensive study. Less understood are the within-group externalities that arise when the platform designs many-to-many matchings: the value to agent i of matching with agent j may depend on the set of agents with which j is matched. These effects are present in a wide range of settings in which firms compete for individuals' custom or attention. I characterize platform-optimal matchings in a general model of many-to-many matching with within-group externalities. I prove a set of comparative statics results for optimal matchings, and show how these can be used to analyze the welfare effects various changes, including vertical integration by the platform, horizontal mergers between firms on one side of the market, and changes in the platform's information structure. I then explore market structure and regulation in two in-depth applications. The first is monopolistic competition between firms on a retail platform such as Amazon. The second is a multi-channel video program distributor (MVPD) negotiating transfer fees with television channels and bundling these to sell to individuals.

Player-Compatible Equilibrium (PCE) imposes cross-player restrictions on the magnitudes of the players' "trembles" onto different strategies. These restrictions capture the idea that trembles correspond to deliberate experiments by agents who are unsure of the prevailing distribution of play. PCE selects intuitive equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We show that rational learning and weighted fictitious play imply our compatibility restrictions in a steady-state setting.

We introduce a model of polarization in networks as a unifying framework for the measurement of polarization that covers a wide range of applications. We consider a sufficiently general setup for this purpose: node- and edge-weighted, undirected, and connected networks. We generalize the axiomatic characterization of Esteban and Ray (1994) and show that only a particular instance within this class can be used justifiably to measure polarization in networks.

An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close approximations of the subject's preference, even when the limiting (countably infinite) data are enough to infer the preference perfectly. We provide sufficient conditions on the set of alternatives, preferences, and sequences of pairs so that the observation of finitely many choices allows the experimenter to learn the subject's preference with arbitrary precision. While preferences can be identified under our sufficient conditions, we show that it is harder to identify utility functions. We illustrate our results with several examples, including consumer choice, expected utility, and preferences in the Anscombe-Aumann model.