Piotr Dworczak

The Simple Economics of Optimal Persuasion

We study Bayesian persuasion problems in which the Senders preferences depend only on the mean of posterior beliefs. We show that, given a price schedule for posterior means, the Sender faces a consumer-like choice problem, purchasing posterior means using the prior distribution as her endowment. Prices are determined in equilibrium of a Walrasian economy with the Sender as the only consumer and a production technology that garbles the state. Welfare theorems provide a verification tool for optimality of a persuasion scheme, and characterize the structure of prices that support the optimal solution. This price-theoretic approach yields a tractable solution method for persuasion problems with infinite state spaces. Moreover, we show that the approach extends to the general case with no restrictions on Senders utility.

Mechanism Design with Aftermarkets: Cutoff Mechanisms

I study a mechanism design problem in which a designer allocates a single good to one of several agents, and the mechanism is followed by an aftermarket -- a post-mechanism game played between the agent who acquired the good and third-party market participants. The designer has preferences over final outcomes, but she cannot design the aftermarket. However, she can influence its information structure by disclosing information elicited from the agents by the mechanism. I introduce a class of allocation and disclosure rules, called cutoff rules, that disclose information about the buyers type only by revealing information about the realization of a random threshold (cutoff) that she had to outbid to win the object. When there is a single agent in the mechanism, I show that the optimal cutoff mechanism offers full privacy to the agent. In contrast, when there are multiple agents, the optimal cutoff mechanism may disclose information about the winners type; I provide sufficient conditions for optimality of simple designs. I also characterize aftermarkets for which restricting attention to cutoff mechanisms is without loss of generality in a subclass of all feasible mechanisms satisfying additional conditions.

Deferred Acceptance with Compensation Chains

I introduce a class of algorithms called Deferred Acceptance with Compensation Chains (DACC). DACC algorithms generalize the DA algorithms by Gale and Shapley (1962) by allowing both sides of the market to make offers. The main result is a characterization of the set of stable matchings: a matching is stable if and only if it is the outcome of a DACC algorithm.

Redistribution through Markets

Even when global income redistribution is not feasible, market designers can seek to mitigate inequality within individual markets. If sellers are systematically poorer than buyers, for example, they will be willing to sell at relatively low prices. Yet a designer who cares about inequality might prefer to set higher prices precisely when sellers are poor -- effectively, using the market as a redistributive tool. In this paper, we seek to understand how to design goods markets optimally in the presence of persistent inequality. Using a mechanism design approach, we find that redistribution through markets can indeed be optimal. When there is substantial inequality across sides of the market, the designer uses a tax-like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump-sum payments. When there is significant within-side inequality, meanwhile, the designer imposes price controls even though doing so induces rationing.

Mechanism Design with Aftermarkets: On the Optimality of Cutoff Mechanisms

I study a mechanism design problem of allocating a single good to one of several agents. The mechanism is followed by an aftermarket, that is, a post-mechanism game played between the agent who acquired the good and a third-party market participant. The designer has preferences over final outcomes, but she cannot redesign the aftermarket. However, she can influence its information structure by disclosing information elicited by the mechanism, subject to providing incentives for agents to report truthfully.A companion paper (Dworczak, 2016) introduces a class of cutoff mechanisms, characterizes their properties, and derives the optimal mechanism within the class. In this paper, under the assumption that the aftermarket payoffs are determined by a binary decision of the third party, I provide sufficient conditions for optimality of cutoff mechanisms.I also analyze a version of the model in which cutoff mechanisms are sometimes suboptimal. I derive robust payoff bounds on their performance, and show that by using a cutoff mechanism the designer can often guarantee a large fraction of the payoff of the optimal (non-cutoff) mechanism.I study a mechanism design problem of allocating a single good to one of several agents. The mechanism is followed by an aftermarket, that is, a post-mechanism game played between the agent who acquired the good and a third-party market participant. The designer has preferences over final outcomes, but she cannot redesign the aftermarket. However, she can influence its information structure by disclosing information elicited by the mechanism, subject to providing incentives for agents to report truthfully.A companion paper (Dworczak, 2016) introduces a class of cutoff mechanisms, characterizes their properties, and derives the optimal mechanism within the class. In this paper, under the assumption that the aftermarket payoffs are determined by a binary decision of the third party, I provide sufficient conditions for optimality of cutoff mechanisms.I also analyze a version of the model in which cutoff mechanisms are sometimes suboptimal. I derive robust payoff bounds on their performance, and show that by using a cutoff mechanism the designer can often guarantee a large fraction of the payoff of the optimal (non-cutoff) mechanism.

Mechanism Design with Aftermarkets: On the Impossibility of Pure Information Intermediation

A mediator, with no prior information and no control over the market protocol, attempts to redesign the information structure in the market by running an information intermediation mechanism with transfers that first elicits information from an agent, and then discloses information to another market participant (third party). The note establishes a general impossibility result: If the third party has full bargaining power in the interaction with the agent, all incentive-compatible information intermediation mechanisms are uninformative about the agents type.