Results 1  10
of
10
Bayes Correlated Equilibrium and the Comparison of Information Structures
, 2013
"... The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Baye ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures which we call individual sufficiency under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative de…nitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell’s for the single player case.
Privacy and Mechanism Design
"... This paper is a survey of recent work at the intersection of mechanism design and privacy. The connection is a natural one, but its study has been jumpstarted in recent years by the advent of differential privacy, which provides a rigorous, quantitative way of reasoning about the costs that an agen ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
This paper is a survey of recent work at the intersection of mechanism design and privacy. The connection is a natural one, but its study has been jumpstarted in recent years by the advent of differential privacy, which provides a rigorous, quantitative way of reasoning about the costs that an agent might experience because of the loss of his privacy. Here, we survey several facets of this study, and differential privacy plays a role in more than one way. Of course, it provides us a basis for modeling agent costs for privacy, which is essential if we are to attempt mechanism design in a setting in which agents have preferences for privacy. It also provides a toolkit for controlling those costs. However, perhaps more surprisingly, it provides a powerful toolkit for controlling the stability of mechanisms in general, which yields a set of tools for designing novel mechanisms even in economic settings completely unrelated to privacy.
Bayes Correlated Equilibrium and
, 2015
"... A game of incomplete information can be decomposed into a basic game and an information structure. The basic game de
nes the set of actions, the set of payo ¤ states the payo ¤ functions and the common prior over the payo ¤ states. The information structure refers to the signals that the players rec ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
A game of incomplete information can be decomposed into a basic game and an information structure. The basic game de
nes the set of actions, the set of payo ¤ states the payo ¤ functions and the common prior over the payo ¤ states. The information structure refers to the signals that the players receive in the game. We characterize the set of outcomes that can arise in Bayes Nash equilibrium if players observe the given information structure but may also observe additional signals. The characterization corresponds to the set of (a version of) incomplete information correlated equilibria which we dub Bayes correlated equilibria. We identify a partial order on many player information structures (individual su ¢ ciency) under which more information shrinks the set of Bayes correlated equilibria. This order captures the role of information in imposing (incentive) constraints on behavior.
Algorithmic Bayesian Persuasion
, 2015
"... We consider the Bayesian Persuasion problem, as formalized by Kamenica and Gentzkow [27], from an algorithmic perspective in the presence of high dimensional and combinatorial uncertainty. Specifically, one player (the receiver) must take one of a number of actions with apriori unknown payoff; ano ..."
Abstract
 Add to MetaCart
(Show Context)
We consider the Bayesian Persuasion problem, as formalized by Kamenica and Gentzkow [27], from an algorithmic perspective in the presence of high dimensional and combinatorial uncertainty. Specifically, one player (the receiver) must take one of a number of actions with apriori unknown payoff; another player (the sender) is privy to additional information regarding the payoffs of the various actions for both players. The sender can commit to revealing a noisy signal regarding the realization of the payoffs of various actions, and would like to do so as to maximize her own payoff in expectation assuming that the receiver rationally acts to maximize his own payoff. This models a number of natural strategic interactions, in domains as diverse as ecommerce, advertising, politics, law, security, finance, and others. When the payoffs of various actions follow a joint distribution (the common prior), the sender’s problem is nontrivial, and its complexity depends on the representation of the prior. Assuming a Bayesian receiver, we study the sender’s problem with an algorithmic and approximation lens. We show two results for the case in which the payoffs of different actions are i.i.d and given explicitly: a polynomialtime (exact) algorithmic solution, and a “simple”
Representations of Information Structures
"... Abstract — In many problems of design of mechanisms and multiagent systems, the system designer has control over the information environment. What is the optimal design given the goals of the system designer? We discuss several ways of representing information structures. Each representation sim ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract — In many problems of design of mechanisms and multiagent systems, the system designer has control over the information environment. What is the optimal design given the goals of the system designer? We discuss several ways of representing information structures. Each representation simplifies a particular class of optimization problems over information structures; we discuss current and potential applications of these representations. I.
Information and Market Power
, 2015
"... We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We establish our results by providing a characterization of the ..."
Abstract
 Add to MetaCart
We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We establish our results by providing a characterization of the set of all joint distributions over demands and payo ¤ states that can arise in equilibrium under any information structure. In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot competition. We find that the first and second moments of the equilibrium distribution respond very di¤erently to the private information of the agents under these two market structures. The first moment of the equilibrium demand, the average demand, is more sensitive to the nature of the private information in demand function competition, reecting the strategic impact of private information. By contrast, the second moments are less sensitive to the private information, reecting the common conditioning on the price among the agents.
FIRST PRICE AUCTIONS WITH GENERAL INFORMATION STRUCTURES: IMPLICATIONS FOR BIDDING AND REVENUE By
, 2015
"... This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In part ..."
Abstract
 Add to MetaCart
This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others ’ values. Revenue is minimized when buyers are uncertain about whether they will win or lose and incentive constraints are binding for all upward bid deviations. We provide further analytic results on possible welfare outcomes and report computational methods which work when we do not have analytic solutions. Many of our results generalize to asymmetric value distributions. We apply these results to study
Price Discrimination and Public Policy in the U.S. College Market
, 2014
"... In the United States, a form called the Free Application for Federal Student Aid, or FAFSA, is used to determine eligibility for federal aid. The FAFSA collects extensive financial information, checks it for accuracy against several government databases, including the IRS, and then shares the inform ..."
Abstract
 Add to MetaCart
In the United States, a form called the Free Application for Federal Student Aid, or FAFSA, is used to determine eligibility for federal aid. The FAFSA collects extensive financial information, checks it for accuracy against several government databases, including the IRS, and then shares the information with colleges. I demonstrate that sharing the FAFSA with colleges enables them to engage in substantial price discrimination with widespread repercussions for the cost of a college education as well as the equilibrium sorting of students into colleges. I build a structural model of college pricing and price discrimination, and show that the model is identified from studentlevel data on prices and student characteristics. Reduced form estimates are consistent with several predictions of the model. According to my structural estimates, on average elite colleges capture 70 % of the studentcollege match surplus through their studentspecific prices. Withholding FAFSA information would lower prices for middle and highincome students while raising them for lowincome students. On average prices would fall by $825, and the withincollege price variance would also drop by 17%. By using the FAFSA to price discriminate, elite colleges effectively levy a 1.9 % tax on adjusted gross income coupled with a $709 lump sum rebate. However, with less information to
Privacy Games
"... The problem of analyzing the effect of privacy concerns on the behavior of selfish utilitymaximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss [Xia13, GR11, NOS12, CCK+13]. Such priva ..."
Abstract
 Add to MetaCart
The problem of analyzing the effect of privacy concerns on the behavior of selfish utilitymaximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss [Xia13, GR11, NOS12, CCK+13]. Such privacy aware agents prefer to take a randomized strategy even in very simple games in which nonprivacy aware agents play pure strategies. In some cases, the behavior of privacy aware agents follows the framework of Randomized Response, a wellknown mechanism that preserves differential privacy. Our work is aimed at better understanding the behavior of agents in settings where their privacy concerns are explicitly given. We consider a toy setting where agent A, in an attempt to discover the secret type of agent B, offers B a gift that one type of B agent likes and the other type dislikes. As opposed to previous works, B’s incentive to keep her type a secret isn’t the result of “hardwiring ” B’s utility function to consider privacy, but rather takes the form of a payment between B and A. We investigate three different types of payment functions and analyze B’s behavior in each of the resulting games. As we show, under some payments, B’s
Harvard University
"... Abstract. The problem of analyzing the effect of privacy concerns on the behavior of selfish utilitymaximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss [24,13,19,4]. Such privacy aw ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The problem of analyzing the effect of privacy concerns on the behavior of selfish utilitymaximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss [24,13,19,4]. Such privacy aware agents prefer to take a randomized strategy even in very simple games in which nonprivacy aware agents play pure strategies. In some cases, the behavior of privacy aware agents follows the framework of Randomized Response, a wellknown mechanism that preserves differential privacy. Our work is aimed at better understanding the behavior of agents in settings where their privacy concerns are explicitly given. We consider a toy setting where agent A, in an attempt to discover the secret type of agent B, offers B a gift that one type of B agent likes and the other type dislikes. As opposed to previous works, B’s incentive to keep her type a secret isn’t the result of “hardwiring ” B’s utility function to consider privacy, but rather takes the form of a payment between B and A. We investigate three different types of payment functions and analyze B’s behavior in each of the resulting games. As we show, under some payments, B’s behavior is very different than the behavior of agents with hardwired privacy concerns and might even be deterministic. Under a different payment we show that B’s BNE strategy does fall into the framework of Randomized Response. 1