Motivated by practical concerns in applying information design to markets and service systems, we consider a persuasion problem between a sender and a receiver where the receiver may not be an expected utility maximizer. In particular, the receiver’s utility may be nonlinear in her belief; we deem such receivers as riskconscious. Such utility models arise, for example, when the receiver exhibits sensitivity to the variability and the risk in the payoff on choosing an action (e.g., waiting time for a service). In the presence of such nonlinearity, the standard approach of using revelationprinciple style arguments fails to characterize the set of signals needed in the optimal signaling scheme. Our main contribution is to provide a theoretical framework, using results from convex analysis, to overcome this technical challenge. In particular, in general persuasion settings with riskconscious agents, we prove that the sender’s problem can be reduced to a convex optimization program. Furthermore, using this characterization, we obtain a bound on the number of signals needed in the optimal signaling scheme.
We apply our methods to study a specific setting, namely binary persuasion, where the receiver has two possible actions (0 and 1), and the sender always prefers the receiver taking action 1. Under a mild convexity assumption on the receiver’s utility and using a geometric approach,we show that the convex program can be further reduced to a linear program. Furthermore, this linear program yields a canonical construction of the set of signals needed in an optimal signaling mechanism. In particular, this canonical set of signals only involves signals that fully reveal the state and signals that induce uncertainty between two states.We illustrate our results in the setting of signaling wait time information in an unobservable queue with customers whose utilities depend on the variance of their waiting times.
more »
« less
This content will become publicly available on December 24, 2024
Markov Persuasion Processes with Endogenous Agent Beliefs
We consider a dynamic Bayesian persuasion setting where a single longlived sender persuades a stream of ``shortlived'' agents (receivers) by sharing information about a payoffrelevant state. The state transitions are Markovian and the sender seeks to maximize the longrun average reward by committing to a (possibly historydependent) signaling mechanism. While most previous studies of Markov persuasion consider exogenous agent beliefs that are independent of the chain, we study a more natural variant with endogenous agent beliefs that depend on the chain's realized history. A key challenge to analyze such settings is to model the agents' partial knowledge about the history information. We analyze a Markov persuasion process (MPP) under various information models that differ in the amount of information the receivers have about the history of the process. Specifically, we formulate a general partialinformation model where each receiver observes the history with an l period lag. Our technical contribution start with analyzing two benchmark models, i.e., the fullhistory information model and the nohistory information model. We establish an ordering of the sender's payoff as a function of the informativeness of agent's information model (with nohistory as the least informative), and develop efficient algorithms to compute optimal solutions for these two benchmarks. For general l, we present the technical challenges in finding an optimal signaling mechanism, where even determining the right dependency on the history becomes difficult. To bypass the difficulties, we use a robustness framework to design a "simple" \emph{historyindependent} signaling mechanism that approximately achieves optimal payoff when l is reasonably large.
more »
« less
 Award ID(s):
 2303372
 NSFPAR ID:
 10532237
 Publisher / Repository:
 The 19th Conference On Web And InterNet Economics (WINE 2023)
 Date Published:
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


We consider information design in spatial resource competition, motivated by ride sharing platforms sharing information with drivers about rider demand. Each of N colocated agents (drivers) decides whether to move to another location with an uncertain and possibly higher resource level (rider demand), where the utility for moving increases in the resource level and decreases in the number of other agents that move. A principal who can observe the resource level wishes to share this information in a way that ensures a welfaremaximizing number of agents move. Analyzing the principal’s information design problem using the Bayesian persuasion framework, we study both private signaling mechanisms, where the principal sends personalized signals to each agent, and public signaling mechanisms, where the principal sends the same information to all agents. We show: 1) For private signaling, computing the optimal mechanism using the standard approach leads to a linear program with 2 N variables, rendering the computation challenging. We instead describe a computationally efficient twostep approach to finding the optimal private signaling mechanism. First, we perform a change of variables to solve a linear program with O(N^2) variables that provides the marginal probabilities of recommending each agent move. Second, we describe an efficient sampling procedure over sets of agents consistent with these optimal marginal probabilities; the optimal private mechanism then asks the sampled set of agents to move and the rest to stay. 2) For public signaling, we first show the welfaremaximizing equilibrium given any common belief has a threshold structure. Using this, we show that the optimal public mechanism with respect to the senderpreferred equilibrium can be computed in polynomial time. 3) We support our analytical results with numerical computations that show the optimal private and public signaling mechanisms achieve substantially higher social welfare when compared with noinformation and fullinformation benchmarks.more » « less

We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering a service at a fixed price to a Poisson arrival of delaysensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic settings. The underlying dynamics make the problem more difficult because, in contrast to static settings, the signaling mechanism adopted by the service provider affects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). The core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelationprinciple style argument, we find that it suffices to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given fixed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold i terms of the two branches of the LambertW function. (3) Revenue comparison: Finally, we show that with the optimal choice of the fixed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal statedependent pricing mechanism in a fullyobservable queue. This implies that in settings where statedependent pricing is not feasible, the service provider can effectively use optimal signaling (with the optimal fixed price) to achieve the same revenue.more » « less

Feldman, M. (Ed.)We consider a Bayesian persuasion problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multiphase trials with different experiments conducted based on the outcomes of prior experiments. In contrast to most of the literature, we consider the problem with constraints on signals imposed on the sender. This we achieve by fixing some of the experiments in an exogenous manner; these are called determined experiments. This modeling helps us understand realworld situations where this occurs: e.g., multiphase drug trials where the FDA determines some of the experiments, startup acquisition by big firms where latestage assessments are determined by the potential acquirer, multiround job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The nondetermined experiments (signals) in the multiphase trial are to be chosen by the sender in order to persuade the receiver best. With a binary state of the world, we start by deriving the optimal signaling policy in the only nontrivial configuration of a twophase trial with binaryoutcome experiments. We then generalize to multiphase trials with binaryoutcome experiments where the determined experiments can be placed at arbitrary nodes in the trial tree. Here we present a dynamic programming algorithm to derive the optimal signaling policy that uses the twophase trial solution’s structural insights. We also contrast the optimal signaling policy structure with classical Bayesian persuasion strategies to highlight the impact of the signaling constraints on the sender.more » « less

We consider evacuation of a group of n ≥ 2 autonomous mobile agents (or robots) from an unknown exit on an infinite line. The agents are initially placed at the origin of the line and can move with any speed up to the maximum speed 1 in any direction they wish and they all can communicate when they are colocated. However, the agents have different wireless communication abilities: while some are fully wireless and can send and receive messages at any distance, a subset of the agents are senders, they can only transmit messages wirelessly, and the rest are receivers, they can only receive messages wirelessly. The agents start at the same time and their communication abilities are known to each other from the start. Starting at the origin of the line, the goal of the agents is to collectively find a target/exit at an unknown location on the line while minimizing the evacuation time, defined as the time when the last agent reaches the target. We investigate the impact of such a mixed communication model on evacuation time on an infinite line for a group of cooperating agents. In particular, we provide evacuation algorithms and analyze the resulting competitive ratio (CR) of the evacuation time for such a group of agents. If the group has two agents of two different types, we give an optimal evacuation algorithm with competitive ratio CR = 3+2√2. If there is a single sender or fully wireless agent, and multiple receivers we prove that CR ∈ [2+√5,5], and if there are multiple senders and a single receiver or fully wireless agent, we show that CR ∈ [3,5.681319]. Any group consisting of only senders or only receivers requires competitive ratio 9, and any other combination of agents has competitive ratio 3.more » « less