Computational aspects of optimal information revelation

Abstract

2017-08-28Strategic interactions often take place in environments rife with uncertainty and information asymmetry. Understanding the role of information in strategic interactions is becoming more and more important in the age of information we live in today. This dissertation is motivated by the following question: What is the optimal way to reveal information, and how hard is it computationally to find an optimum? We study the optimization problem faced by an informed principal, who must choose how to reveal information in order to induce a desirable equilibrium, a task often referred to as information structure design, signaling or persuasion. ❧ Our exploration of optimal signaling begins with Bayesian network routing games. This widely studied class of games arises in several real-world settings. For example, millions of people use navigation services like Google Maps every day. Is it possible for Google Maps (the principal) to partly reveal the traffic conditions to reduce the latency experienced by selfish drivers? We show that the answer to this question is two-fold: (1) There are scenarios where the principal can improve selfish routing, and sometimes through the careful provision of information, the principal can achieve the best-coordinated outcome; (2) Optimal signaling is computationally hard in routing games. Assuming P ≠ NP, there is no polynomial-time algorithm that does better than full revelation in the worst case. ❧ We next study the optimal signaling problem in one of the most fundamental classes of games: Bayesian normal form games. We settle the complexity of (approximately) optimal signaling in normal form games: We give the first quasipolynomial time approximation scheme for signaling in normal form games; and complementing this, we show that a fully polynomial time approximation scheme for optimal signaling is NP-hard, and rule out any polynomial time approximation scheme assuming the planted clique conjecture. It is worth noting that our algorithm works for games with a constant number of players, and for a large and natural class of objective functions including social welfare, while our hardness results hold even in the simplest Bayesian two-player zero-sum games. ❧ Complementing our results for signaling in normal form games, we continue to investigate the optimal signaling problem in two special cases of succinct games: (1) Second-price auctions in which the auctioneer wants to maximize revenue by revealing partial information about the item for sale to the bidders before running the auction; and (2) Majority voting when the voters have uncertainty regarding their utilities for the two possible outcomes, and the principal seeks to influence the outcome of the election by signaling. We give efficient approximation schemes for all these problems under one unified algorithmic framework, by identifying and solving a common optimization problem that lies at the core of all these applications. Finally, we present the currently best algorithm (asymptotically) for computing Nash equilibria in complete-information anonymous games. Compared to all other games we study in this thesis, anonymous games are the only class of games whose complexity of equilibrium computation is still open. We present the currently best algorithm for computing Nash equilibria in anonymous games, and we also provide some evidence suggesting our algorithm is essentially tight