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 non-linear in her belief; we deem such receivers as risk-conscious. 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 non-linearity, the standard approach of using revelation-principle 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 risk-conscious 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 per-suasion, 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.
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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 long-lived sender persuades a stream of ``short-lived'' agents (receivers) by sharing information about a payoff-relevant state. The state transitions are Markovian and the sender seeks to maximize the long-run average reward by committing to a (possibly history-dependent) 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 partial-information model where each receiver observes the history with an l period lag. Our technical contribution start with analyzing two benchmark models, i.e., the full-history information model and the no-history information model. We establish an ordering of the sender's payoff as a function of the informativeness of agent's information model (with no-history 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{history-independent} signaling mechanism that approximately achieves optimal payoff when l is reasonably large.
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- Award ID(s):
- 2303372
- NSF-PAR 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
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