Bayesian persuasion is the study of information sharing policies among strategic agents. A prime example is signaling in online ad auctions: what information should a platform signal to an advertiser regarding a user when selling the opportunity to advertise to her? Practical considerations such as preventing discrimination, protecting privacy or acknowledging limited attention of the information receiver impose constraints on information sharing. In this work, we propose and analyze a simple way to mathematically model such constraints as restrictions on Receiver's admissible posterior beliefs.
We consider two families of constraints - ex ante and ex post, where the latter limits each instance of Sender-Receiver communication, while the former more general family can also pose restrictions in expectation. For the ex ante family, Doval and Skreta establish the existence of an optimal signaling scheme with a small number of signals - at most the number of constraints plus the number of states of nature; we show this result is tight and provide an alternative proof for it. For the ex post family, we tighten a bound of Vølund, showing that the required number of signals is at most the number of states of nature, as in the original Kamenica-Gentzkow setting. As our main algorithmic result, we provide an additive bi-criteria FPTAS for an optimal constrained signaling scheme assuming a constant number of states; we improve the approximation to single-criteria under a Slater-like regularity condition. The FPTAS holds under standard assumptions; relaxed assumptions yield a PTAS. Finally, we bound the ratio between Sender's optimal utility under convex ex ante constraints and the corresponding ex post constraints. This bound applies to finding an approximately welfare-maximizing constrained signaling scheme in ad auctions.
Politecnico di Milano（米兰理工大学）；University of Southampton（南安普顿大学）
We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the case where the receivers interact in a sequential game with imperfect information, wit…
We study the problem of allocating indivisible goods among agents with additive valuations. When randomization is allowed, it is possible to achieve compelling notions of fairness such as envy-freeness, which states that no agent should prefer any other agent's allocation to her own. When allocations must be deterministic, achieving exact fairness is impossible but approximate notions such as envy-freeness up to one good can be guaranteed. Our goal in this work is to achieve both simultaneously, by constructing a randomized allocation that is exactly fair ex-ante and approximately fair ex-post…
We present a polynomial-time algorithm that computes an ex-ante envy-free lottery over envy-free up to one item (EF1) deterministic allocations. It has the following advantages over a recently proposed algorithm: it does not rely on the linear programming machinery including separation oracles; it is SD-efficient (both ex-ante and ex-post); and the ex-ante outcome is equivalent to the outcome returned by the well-known probabilistic serial rule. As a result, we answer a question raised by Freeman, Shah, and Vaish (2020) whether the outcome of the probabilistic serial rule can be implemented by…
We consider the problem of maximizing revenue for a monopolist offering multiple items to multiple heterogeneous buyers. We develop a simple mechanism that obtains a constant factor approximation under the assumption that the buyers' values are additive subject to a feasibility constraint and independent across items. Importantly, different buyers in our setting can have different constraints on the sets of items they desire. Our mechanism is a sequential variant of two-part tariffs. Prior to our work, simple approximation mechanisms for such multi-buyer problems were known only for the specia…
Smart Lotteries in School Choice: Ex-ante Pareto-Improvement with Ex-post Stability
UNSW Sydney（新南威尔士大学）；ELTE Centre for Economic and Regional Studies（布达佩斯经济区域研究中心）；Department of Quantitative Economics, Maastricht University（马斯特里赫特大学数量经济学系）；HUN-REN Institute for Computer Science and Control（匈牙利科学院计算机与控制研究所）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
A basic lesson from game theory is that strategic behavior often renders the equilibrium outcome inefficient. The recent literature of information design -- a.k.a. signaling or persuasion -- looks to improve equilibria by providing carefully-tuned information to players in order to influence their actions. Most previous studies have focused on the question of designing optimal signaling schemes. This work departs from previous research by considering a descriptive question and looks to quantitatively characterize the power of signaling (PoS), i.e., how much a signaling designer can improve her…
This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling scheme and participants form a posterior belief about the state of the network based on prior beliefs and the received signal. They subsequently select routes minimizing their individual expected travel time under their posterior beliefs, giving rise to a Wardrop equilibrium. We investigate how the TIS can infer the prior beliefs held by the participants by des…
