Mechanism Design with Restricted Communication

We consider a Sender–Receiver environment where the sender is informed of states and the receiver chooses actions. There is a communication channel between them consisting of sets of input/output messages and a fixed transition probability. The sender reaches out to the receiver through the channel which limits communication in two ways: the number of available messages might be small, messages might be noisy. We consider a mechanism design setup whereby the receiver commits to a mechanism which selects distribution of actions and possibly monetary transfers, contingent on output messages. We aim at characterizing the joint distributions which can be implemented by communication over the channel, given the incentives of the sender. We consider both one-shot problems and series of i.i.d. problems. In particular, we show that when the sender and the receiver are engaged in a series of problems, linking decisions together is a more efficient instrument than monetary transfers.

Information Acquisition in Matching Markets: The Role of Price Discovery

We explore the acquisition and flow of information in matching markets through a model of college admissions with endogenous costly information acquisition. We extend the notion of stability to this partial information setting, and introduce regret-free stability as a refinement that additionally requires optimal student information acquisition. We show regret-free stable outcomes exist, and finding them is equivalent to finding appropriately-defined market-clearing cutoffs. To understand information flows, we recast matching mechanisms as price-discovery processes. No mechanism guarantees a regret-free stable outcome, because information deadlocks imply some students must acquire information sub optimally. Our analysis suggests approaches for facilitating efficient price discovery, by leveraging historical information or market sub-samples to estimate cutoffs. We show that mechanisms that use such methods to advise applicants on their admission chances yield approximately regret-free stable outcomes. A survey of university admission systems highlights the practical importance of providing applicants with information about their admission chances.

Unpaired Kidney Exchange: Overcoming Double Coincidence of Wants without Money

For an incompatible patient-donor pair, kidney exchanges often forbid receipt-before-donation (the patient receives a kidney before the donor donates) and donation-before-receipt, causing a double-coincidence-of-wants problem. We study an algorithm, the Unpaired kidney exchange algorithm, which eliminates this problem. In a dynamic matching model, we show that waiting time of patients under the Unpaired is close to optimal and substantially shorter than widely used algorithms. Using a rich administrative dataset from France, we show that Unpaired achieves a match rate of 63 percent and an average waiting time of 176 days for transplanted patients. The (infeasible) optimal algorithm is only slightly better (64 percent and 144 days); widely used algorithms deliver less than 40 percent and at least 232 days. We discuss a range of solutions that can address the potential practical incentive challenges of the Unpaired. In particular, we extend our analysis to an environment where a deceased donor waitlist can be integrated to improve the performance of algorithms. We show that our theoretical and empirical comparisons continue to hold. Finally, based on these analyses, we propose a practical version of the Unpaired algorithm.

Informationally Robust Cheap-Talk

We study the robustness of cheap-talk equilibria to infinitesimal private information of the receiver in a model with a binary state-space and state-independent sender-preferences. We show that the sender-optimal equilibrium is robust if and only if this equilibrium either reveals no information to the receiver or fully reveals one of the states with positive probability. We then characterize the actions that can be played with positive probability in any robust equilibrium. Finally, we fully characterize the optimal sender-utility under binary receiver’s private information, and provide bounds for the optimal sender-utility under general private information.

Should the Timing of Inspections be Predictable?

A principal hires an agent to work on a long-term project that culminates in a breakthrough or a breakdown. At each time, the agent privately chooses to work or shirk. Working increases the arrival rate of breakthroughs and decreases the arrival rate of breakdowns. To motivate the agent to work, the principal conducts costly inspections. She fires the agent if shirking is detected. We characterize the principal’s optimal inspection policy. Periodic inspections are optimal if work primarily speeds up breakthroughs. Random inspections are optimal if work primarily delays breakdowns. Crucially, the agent’s actions determine his risk attitude over the timing of punishments.

Early-Career Discrimination: Spiraling or Self-Correcting?

Do workers from social groups with comparable productivity distributions obtain comparable lifetime earnings? We study how a small amount of early-career discrimination propagates over time when workers’ productivity is revealed through employment. In breakdown learning environments that track primarily on-the-job failures, such discrimination spirals into a substantial lifetime earnings gap for groups of comparable productivity, whereas in breakthrough learning environments that track successes, early discrimination self-corrects so as to guarantee comparable lifetime earnings. This contrast is robust to large labor markets, flexible wages, inconclusive learning, investment in productivity, and misspecified employers’ beliefs.

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Misinterpreting Yourself

We model an agent who stubbornly underestimates how much his behavior is driven by undesirable motives, and, attributing his behavior to other considerations, updates his view about those considerations. We study general properties of the model, and then apply the framework to identify novel implications of partially naive present bias. In many stable situations, a partially naive present-biased agent appears realistic in that he eventually predicts his behavior well. His unrealistic self-view does, however, manifest itself in several other ways. First, in basic settings he always comes to act in a more present-biased manner than a realistic agent. Second, he systematically mispredicts how he will react when circumstances change, such as when incentives for forward-looking behavior increase or he is placed in a new, ex-ante identical environment. Third, he follows empirically realistic addiction-like consumption dynamics that he does not anticipate. Fourth, he holds beliefs that — when

Accept this Paper

We explore a novel model where authors of heterogeneous papers submit to ranked journals with admission standards on noisy referee evaluations. Journal caliber reflects paper quality in a rational expectations equilibrium. In our main finding, journal rejection rates first rise and then fall in caliber, and so cannot be used to rank journals. The logic by extension applies to college rankings. This paper therefore invalidates using selectivity to rank journals and colleges. Our theory holds for all signals obeying a novel log-concavity condition that is typically met.

Building Reputations via Summary Statistics

A patient seller decides whether to build a reputation for exerting high effort in front of a sequence of consumers. Each consumer decides whether to trust the seller after she observes the number of times that the seller took each of his actions in the last K periods, but not the order with which these actions were taken. I show that (i) the seller’s payoff from building a reputation is at least his commitment payoff for all K and in all equilibria, and (ii) the seller sustains his reputation for exert high effort in all equilibria if and only if K is below some cutoff. Although a larger K allows more consumers to observe the seller’s opportunistic behavior, it weakens their incentives to punish the seller after they observe opportunistic behavior. This effect undermines the seller’s reputational incentives and lowers consumers’ welfare.

The wisdom of the crowd and higher-order beliefs

The classic wisdom-of-the-crowd problem asks how a principal can “aggregate” information about the unknown state of the world from agents without understanding the information structure among them. We propose a new simple procedure called Population-Mean-Based Aggregation to achieve this goal. The procedure only requires eliciting agents’ beliefs about the state, and also eliciting some agents’ expectations of the average belief in the population. We show that this procedure fully aggregates information: in an infinite population, it always infers the true state of the world. The procedure can accommodate correlations in agents’ information, misspecified beliefs, any finite number of possible states of the world, and only requires very weak assumptions on the information structure.

Stability and Learning in Strategic Queueing Systems

Over the last two decades we have developed good understanding how to quantify the impact of strategic user behavior on outcomes in many games (including traffic routing and online auctions) and showed that the resulting bounds extend to repeated games assuming players use a form of no-regret learning to adapt to the environment. Unfortunately, these results do not apply when outcomes in one round effect the game in the future, as is the case in many applications. In this talk, we study this phenomenon in the context of a game modeling queuing systems: routers compete for servers, where packets that do not get served need to be resent, resulting in a system where the number of packets at each round depends on the success of the routers in the previous rounds. In joint work with Jason Gaitonde, we analyze the resulting highly dependent random process. [...]

False Narratives and Political Mobilization

We present an equilibrium model of politics in which political platforms compete over public opinion. A platform consists of a policy, a coalition of social groups with diverse intrinsic attitudes to policies, and a narrative. We conceptualize narratives as subjective models that attribute a commonly valued outcome to (potentially spurious) postulated causes. When quantifi…ed against empirical observations, these models generate a shared belief among coalition members over the outcome as a function of its postulated causes. The intensity of this belief and the members’intrinsic attitudes to the policy determine the strength of the coalition’s mobilization. Only platforms that generate maximal mobilization prevail in equilibrium. Our equilibrium characterization demonstrates how false narratives can be detrimental for the common good, and how political fragmentation leads to their proliferation.

Learning in Repeated Interactions on Networks (with Wanying Huang and Omer Tamuz)

We study how long-lived, rational, exponentially discounting agents learn in a social network. In every period, each agent observes the past actions of his neighbors, receives a private signal, and chooses an action with the objective of matching the state. Since agents behave strategically, and since their actions depend on higher order beliefs, it is difficult to characterize equilibrium behavior. Nevertheless, we show that regardless of the size and shape of the network, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.
 

Posterior implementability in an n-person decision problem

Posterior implementation is a solution concept for mechanism design with interdependent values. It requires that each agent’s strategy is optimal against the strategies of other agents for every possible message profile. Green and Laffont (1987) give a geometric characterization of posterior implementable social choice functions for binary collective decision problems with two agents and non-transferable utility. This paper generalizes the analysis to any finite number n of agents, with three main insights. First, posterior implementable social choice functions are posterior implementable by score voting: each agent submits a number from a set of consecutive integers; the collective decision is determined by whether or not the sum exceeds a given quota. Second, the possibility for posterior implementation depends crucially on the number of agents: in generic environments with n ≥ 3 agents, a (responsive) social choice function is posterior implementable [...]
 

Persuasion in Networks

I study strategic information disclosure in networks. When agents' preferences are sufficiently diverse, the optimal network is the line in which the agents are ordered according to their ideologies. Such optimal networks obtain as Nash equilibria of a game in which each link requires sponsorship by both connected agents, and are the unique strongly pairwise stable networks. These results overturns classical results of non-strategic information transmission in networks, where the optimal and pairwise stable network is the star.
In political economy environments such as networks of policy-makers, interest groups, or judges, these results suggest positive and normative rationales for "horizontal" links between like-minded agents in political networks, as opposed to hierarchical networks, that have been shown to be optimal in organizations where agents' preferences are more closely aligned.

Learning from Strategic Sources

This paper studies learning from multiple informed agents where each agent has a small piece of information about the unknown state of the world in the form of a noisy signal and sends a message to the principal, who then makes a decision that is not constrained by predetermined rules. In contrast to the existing literature, I model the conflict of interest between the principal and the agents more generally and consider the case where the preferences of the principal and the agents are misaligned in some realized states. I show that if the conflict of interest between the principal and the agents is moderate, there is a discontinuity: when the number of agents is large enough, adding even a tiny probability of misaligned states leads to complete unraveling in which the agents ignore their signals, in contrast to the almost complete revealing that is predicted by the existing literature. [...]

Information Aggregation in Auctions with Costly Information

We study a common-value auction in which a large number of identical, indivisible object are sold to a large number of ex-ante identical bidders with unit demand. Bidders are initially uninformed but can acquire information from multiple sources that differ in accuracy and cost. We define a cost-accuracy ratio for each available source of information. The minimum value of this cost-accuracy ratio among all information sources fully determines the limit price distribution and the information content of the auction's price. Information is aggregated if and only if the minimum cost-accuracy ratio is equal to zero. We also characterize all equilibria of the auction for posterior separable information costs with a sufficiently rich set of experiments. In this case information is aggregated if and only if the cost function is differentiable at the prior.

Non-Market Allocation Mechanisms: Optimal Design and Investment Incentives

We study how to optimally design non-market mechanisms for allocating scarce resources, taking into consideration agents' investment incentives. A principal wishes to allocate a resource of homogeneous quality, such as seats in a university, to a heterogeneous population of agents. She commits ex-ante to a possibly random allocation rule, contingent on a unidimensional characteristic of the agents she intrinsically values. The principal cannot resort to monetary transfers. Agents have a strict preference for allocation and can undertake a costly investment to improve their characteristic before it is revealed to the principal. We show that while random allocation rules have the effect of encouraging investment, especially at the top of the characteristic distribution, deterministic pass-fail allocation rules, such as exams with a pass grade, prove to be optimal.

Neutral Mechanisms: On the Feasibility of Information Sharing

The paper analyzes information sharing in neutral mechanisms when an informed party will face future interactions with an uninformed party. Neutral mechanisms are mechanisms that do not rely on (1) the provision of evidence, (2) conducting experiments, (3) verifying the state, or (4) changing the after-game (i.e., the available choices and payoffs of future interactions). They include cheap talk, long cheap talk, noisy communication, mediation, money burning, and transfer schemes, among other mechanisms. To address this question, the paper develops a reduced-form approach that characterizes the agents’ payoffs in terms of belief-based utilities. This effectively induces a psychological game, where the psychological preferences summarize information-sharing incentives. [...]

Designing the Optimal Menu of Tests

A decision-maker must accept or reject a privately informed agent. The agent always wants to be accepted, while the decision-maker wants to accept only a subset of types. The decision-maker has access to a set of feasible tests and, prior to making a decision, requires the agent to choose a test from a menu, which is a subset of the feasible tests. By offering a menu, the decision-maker can use the agent's choice as an additional source of information. I characterise the decision-maker's optimal menu for arbitrary type structures and feasible tests. I then apply this characterisation to various environments. When the domain of feasible tests contains a most informative test, I characterise when only the dominant test is offered and when a dominated test is part of the optimal menu. I also characterise the optimal menu when types are multidimensional or when tests vary in their difficulty.

Prove yourself: Dynamic delegation in promotion contests

I study how organizations assign tasks to identify the best candidate to promote among a pool of workers. When only non-routine tasks are informative about a worker’s potential and non-routine tasks are scarce, the organization’s preferred promotion system is an index contest. Each worker is assigned a number that depends only on his own potential. The principal delegates the non-routine task to the worker whose current index is the highest and promotes the first worker whose type exceeds a threshold. Each worker’s threshold depends only on his own type. In this environment, task allocation and workers’ motivation interact through the organization’s promotion decisions. The organization designs the workers’ careers to both screen and develop talent. So competition is mediated by the allocation of tasks: who gets the opportunity to prove themselves is a determinant factor in promotions. [...]

Efficient Mechanisms under Unawareness

We study the design of mechanisms under asymmetric awareness and asymmetric information. Unawareness refers to the lack of conception rather than the lack of information. With limited awareness, an agent's message space is type-dependent because an agent cannot misrepresent herself as a type that she is unaware of. Nevertheless, we show that the revelation principle holds.
The revelation principle is of limited use though because a mechanism designer is hardly able to commit to outcomes for type profiles of which he is unaware. Yet, the mechanism designer can at least commit to properties of social choice functions like efficiency given ex post awareness. Assuming quasi-linear utilities, private values, and welfare isotonicity in awareness, we show that if a social choice function is utilitarian ex post efficient, then it is implementable under pooled agents’ awareness in conditional dominant strategies. That is, it is possible to reveal all asymmetric awareness among agents and implement the welfare maximizing social choice function in conditional dominant strategies without the need of the social planner being fully
aware ex ante. To this end, we develop dynamic versions of the Groves and Clarke mechanisms along which true types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. 

Simultaneous bidding in second-price auctions

In this paper, we analyze a model of competing sealed-bid second-price auctions where bidders have unit demand and can bid on multiple auctions simultaneously. We show that there is no symmetric pure equilibrium with strictly increasing strategies, unlike in standard auction games. However, a symmetric mixed-strategy equilibrium exists, where all bidders will bid on all available auctions with probability one. This holds true for any mixed equilibrium. We then focus on two specific scenarios: one with two auctions and three bidders, and the other with two auctions and two bidders. For the case of three bidders, we identify a pure equilibrium. In contrast, for the case of two bidders, we find a continuum of mixed equilibria.

Informing to Divert Attention

We study a multidimensional Sender-Receiver game in which Receiver can acquire limited information after observing the Sender's signal. Depending on the parameters describing the conflict of interest between Sender and Receiver, we characterise optimal information disclosure and the information acquired by Receiver as a response. We show that in case of partial conflict of interests (aligned on some dimensions and misaligned on others) Sender uses multidimensionality of the environment to divert Receiver's attention away from the dimensions of misalignment of interests. Moreover, there is negative value of information in the sense that Receiver would be better off if she could commit not to extract private information or to have access to information of lower quality. We present applications to informational lobbying and optimal bonus policies.

Incentives and Efficiency in Constrained Allocation Mechanisms

We study private-good allocation mechanisms where an arbitrary constraint delimits the set of feasible joint allocations. This generality provides a unified perspective over several prominent examples that can be parameterized as constraints in this model, including house allocation, roommate assignment, and social choice. We characterize the set of two-agent strategy- roof and Pareto efficient mechanisms, showing that every mechanism is a form of “local dictatorship.” For more agents, we show that an N-agent mechanism is group strategy-proof if and only if all its two-agent marginal mechanisms (defined by holding fixed all but two agents’ preferences) are individually strategy-proof and Pareto efficient, allowing us to leverage the two-agent characterization for more general problems. To illustrate their usefulness, we apply these results to the roommates problem to provide the first characterization of all group strategy-proof and Pareto efficient mechanisms, that turn out to be sequential dictatorships. Our results also yield a novel proof of the Gibbard–Satterthwaite Theorem. We finally introduce a new class of mechanisms, that we call “local priority” mechanisms, that exists for all constraints and subsumes many important classes of existing mechanisms.

Screening: A Unified Geometric Perspective

We investigate single-agent mechanism design with arbitrary restrictions on the agent’s vNM preferences over a finite set of outcomes. This covers many standard problems with or without transfers, including the (multi-good) monopolistic seller problem. We characterize incentive-compatible mechanisms through their associated delegation sets, convex bodies within the unit simplex. Every extreme point of the set of incentive-compatible mechanisms grants the agent a veto, allowing them to choose, for any outcome, a lottery that excludes it. Determining whether a veto mechanism is an extreme point corresponds to solving the indecomposability problem for convex bodies as introduced by Gale (1954). In one-dimensional type spaces, we find that the principal’s ex-ante expected utility is maximized by offering a menu with at most three options. However, for multi-dimensional type spaces, no such simplification exists: the set of (exposed) extreme points is dense in the set of veto-granting mechanisms. We apply these insights to derive known and novel results about the monopolistic seller problem.

A Robust Characterization of Nash Equilibrium

We give a robust characterization of Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies consequentialism, consistency, and rationality. It follows that every equilibrium refinement violates at least one of these properties. We moreover show that every solution concept that approximately satisfies consequentialism, consistency, and rationality returns approximate Nash equilibria. The latter approximation can be made arbitrarily good by increasing the approximation of the axioms. This result extends to various natural subclasses of games such as two-player zero-sum games, potential games, and graphical games.

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The Timing of Complementary Innovations

This paper studies the dynamic completion of interrelated projects. A decision maker allocates, at each point in time, a fixed unit of attention to projects that are completed in the form of breakthroughs. The agent's final payoff depends on the set of completed projects at the chosen stopping time. After completing a project, the agent might regret the attention that was already allocated to an incomplete project. I construct a partial order in the set of allocation policies that is based on regret, and show that the expected payoff of an allocation policy is increasing in such order. Moreover, I provide sufficient conditions in the distribution of completion times such that the optimal policy for complementary projects is regret-free. I apply these results to study the canonical problem of two complementary projects with uncertain but constant rate of completion and characterise the optimal attention allocation policy in that case.

Costly Persuasion by a Partially Informed Sender

I study a model of costly Bayesian persuasion by a privately and partially informed sender who conducts a public experiment. I microfound the cost of an experiment via a Wald's sequential sampling problem and show that it equals the expected reduction in a weighted log-likelihood ratio function evaluated at the sender's belief. I focus on equilibria that satisfy the D1 criterion. The equilibrium outcome depends on the relative costs of drawing good and bad news in the experiment. If bad news is more costly, there exists a unique separating equilibrium outcome, and the receiver unambiguously benefits from the sender's private information. If good news is sufficiently more costly, the single-crossing property fails. There exists a continuum of pooling equilibria, and the receiver strictly suffers from sender private information in some pooling equilibria.

Smart Contracts and the Coase Conjecture

This paper reconsiders the problem of a durable-good monopolist who cannot make intertemporal commitments. The buyer’s valuation is binary and his private information. The seller has access to dynamic contracts and, in each period, decides whether deploy the previous period’s contract or to replace it with a new one. Our main result is that the Coase Conjecture fails: the monopolist’s payoff is bounded away from the low valuation irrespective of the discount factor.

Optimal Insurance: Dual Utility, Random Losses and Adverse Selection

We study a generalization of the classical monopoly insurance problem under adverse selection where we allow for a random distribution of losses, possibly correlated with the agent's risk parameter that is private information. Our main purpose is to provide a convenient analytical model that explains both the pattern of observed customer behavior and the pattern of insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs, or menus of insurance with coverage limits- premium pairs. The main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional.

Robust Equilibria in Generic Extensive-Form Games

We prove the 2-player, generic extensive-form case of the conjecture of Govindan and Wilson (1997a,b) and Hauk and Hurkens (2002) stating that an equilibrium component is essential in every equivalent game if and only if the index of the component is nonzero. This provides an index-theoretic characterization of the concept of hyperstable components of equilibria in generic extensive-form games, first formulated by Kohlberg and Mertens (1986). We explore the consequences of the result for the literature on refinements.

Antipartisanship - an explanation for extremism? (brown bag)

I adapt the Hotelling-Downs model with three parties and add an ''antipartisan''-component. Antipartisans vote for the party located furthest away from the party they dislike. While the standard game without antipartisanship has no equilibrium in pure strategies, antipartisanship allows for three types of outcomes: in equilibrium, parties spread over the spectrum, locate on extreme positions, or no equilibrium exists.
The model provides a theoretical explanation for phenomena as those observed in Brazil in 2018: an exogenous increase in the share of antipartisans, followed by relocation on the spectrum towards the extrema. I characterise conditions under which such relocations can be explained by antipartisanship only.

Competition in News Media

I investigate competition between news media firms under the assumptions that consumers get their information about political topics from these firms and that consumers prefer news that validates their views. I show that for topics where the consumers have sufficiently heterogeneous opinions, news media firms may withhold information which can lead to a polarization of political parties. In particular, the median voter theorem does not necessarily apply.

Endogenous Information Acquisition in Cheap-Talk Games

This paper studies costly information acquisition and transmission. An expert communicates with a decision-maker about a state of nature by sending a cheap-talk message. In efficient equilibria, the expert generally reveals all acquired information to the decision-maker. I show the existence of efficient equilibria under general conditions. For the class of posterior separable cost structures, I derive properties of efficient experiments. Under posterior-mean preferences, any cheap-talk problem is solved by a convex combination of two bi-pooling policies. The best bi-pooling policies are characterized for the uniform-quadratic case. Contrary to existing cheap-talk models, monotone partitions are not always optimal.

The Fragility of Specialized Advice

We consider a multi-sender cheap talk model, where the receiver faces uncertainty over whether senders have aligned or state-independent preferences. This uncertainty generates a tradeoff between giving sufficient weight to the most informed aligned senders and minimizing the influence of the unaligned. We show that preference uncertainty diminishes the benefits from specialization, i.e., senders receiving signals with more dispersed accuracy. When preference uncertainty becomes large, it negates them entirely, causing qualified majority voting to become the optimal form of communication. Our results demonstrate how political polarization endangers the ability of society to reap the benefits of specialization in knowledge.

Political Competition and Misperceived Voters

I study the effect of misspecified communication among voters in a political competition setting. Parties advertise by sending information about their candidate's type to voters, who subsequently can share this information with neighbors. I assume that voters misperceive the likelihood that other voters obtained information. Introducing this misperception has effects both on policy outcomes as well as communication between voters. Compared to a benchmark of no misperception, parties choose extreme candidates more often and advertise moderate candidates to a lesser extent. Further, strategic communication between voters results in higher thresholds for truthful communication.

Explaining Sniping via Reference-Dependent Utility in Online Auctions

Sniping/last-minute bidding is an unusual bidding technique that has been extensively studied in empirical studies of eBay auctions, where bidders compete in a modified sealed-bid, second-price auction format and depart from the predictions of standard economic theory. Using Kőszegi and Rabin’s (2006) theory of reference-dependent preferences, I build a game theoretic model that explains not only late bidding but also overbidding in a private-value eBay auction setting involving a sophisticated, rational bidder and a naive, loss-averse bidder. The latter suffers from pseudo-endowment effect which causes willingness to pay (WTP) for the item to increase while the auction runs. By reserving her bid for late in the game, a rational bidder can prevent intermediate information revelation about relative valuation structure to her opponent. This discourages re-bidding for the loss-averse bidder, thereby preventing higher prices and justifying sniping.

Information Design In Selection Problems

I study information design in selection problems. There is a receiver who selects one out of many alternatives and takes an action, and a sender who transmits information about the viability of alternatives to persuade the receiver to select a favorable alternative and take a favorable action. The main theorem characterizes which distributions of posterior beliefs about the favorable alternative conditional on selection can be induced by some signal structure. This theorem facilitates a decomposition of the multi-dimensional information design problem into a selection persuasion problem and an action persuasion problem. I analyze applications of the model to advertising and lobbying.