Mallesh M. Pai

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 jump-started 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.

Optimal Dynamic Auctions and Simple Index Rules

A monopolist seller has multiple units of an indivisible good to sell over a discrete, finite time horizon. Buyers with unit demand arrive over time and each buyer privately knows her arrival time, her value for a unit, and her deadline. We study whether the sellers optimal allocation rule is a simple index rule. Each buyer is assigned an index and the allocation rule is calculated by a dynamic knapsack algorithm using those indices. “Simple” indicates that the index of a buyer depends only on “local” information, i.e., the distribution information for that time period. If buyer deadlines are public, such simple index rules are optimal if the standard increasing hazard rate condition on the distribution of valuations holds, and, given two buyers with the same deadline, the later-arriving one has a lower hazard rate implying stochastically higher valuations. When buyer deadlines are private, this condition is neither sufficient nor necessary. If the rule we identify is not feasible, then the optimal allocation rule is not a simple index rule and cannot be calculated by backward induction.

Social Learning with Costly Search

We study a sequential social learning model where agents privately acquire information by costly search. Search costs of agents are private to them, and are independently and identically distributed. We show that asymptotic learning occurs if and only if search costs are not bounded away from zero. We explicitly characterize the speed of learning for the case of two actions, and show that the probability of late moving agents taking the suboptimal action vanishes at a linear rate. Social welfare converges to the social optimum as the discount rate converges to one if and only if search costs are not bounded away from zero.

Coarse decision making and overfitting

We study decision makers who willingly forgo decision rules that vary finely with available information, even though these decision rules are technologically feasible. We model this behavior as a consequence of using classical, frequentist methods to draw robust inferences from data. Coarse decision making then arises to mitigate the problem of over-fitting the data. The resulting behavior tends to be biased towards simplicity: decision makers choose models that are statistically simple, in a sense we make precise. In contrast to existing approaches, the key determinant of the level of coarsening is the amount of data available to the decision maker. The decision maker may choose a coarser decision rule as the stakes increase.

Fairness Incentives for Myopic Agents

We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualifie ones [8]. We investigate whether it is possible to design inexpensive subsidy or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost o(T) (for the classic setting with k arms, ~{O}(\sqrtk3T), and for the d-dimensional linear contextual setting ~{O}(d\sqrtk3T)). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the k groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes.

The Strange Case of Privacy in Equilibrium Models

We study how privacy technologies affect user and advertiser behavior in a simple economic model of targeted advertising. In our model, a consumer first decides whether or not to buy a good, and then an advertiser chooses an advertisement to show the consumer. The consumers value for the good is correlated with her type, which determines which ad the advertiser would prefer to show to her---and hence, the advertiser would like to use information about the consumers purchase decision to target the ad that he shows. In our model, the advertiser is given only a differentially private signal about the consumers behavior---which can range from no signal at all to a perfect signal, as we vary the differential privacy parameter. This allows us to study equilibrium behavior as a function of the level of privacy provided to the consumer. We show that this behavior can be highly counter-intuitive, and that the effect of adding privacy in equilibrium can be completely different from what we would expect if we ignored equilibrium incentives. Specifically, we show that increasing the level of privacy can actually increase the amount of information about the consumers type contained in the signal the advertiser receives, lead to decreased utility for the consumer, and increased profit for the advertiser, and that generally these quantities can be non-monotonic and even discontinuous in the privacy level of the signal.

An Antifolk Theorem for Large Repeated Games

In this article, we study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems showing that when the signals observed by the players satisfy a condition known as (ε, γ)-differential privacy, the folk theorem has little bite: for values of ε and γ sufficiently small, for a fixed discount factor, any equilibrium of the repeated game involves players playing approximate equilibria of the stage game in every period. Next we argue that in large games (n player games in which unilateral deviations by single players have only a small impact on the utility of other players), many monitoring settings naturally lead to signals that satisfy (ε, γ)-differential privacy for ε and γ tending to zero as the number of players n grows large. We conclude that in such settings, the set of equilibria of the repeated game collapses to the set of equilibria of the stage game. Our results nest and generalize previous results of Green [1980] and Sabourian [1990], suggesting that differential privacy is a natural measure of the “largeness” of a game. Further, techniques from the literature on differential privacy allow us to prove quantitative bounds, where the existing literature focuses on limiting results.

Evaluating Strategic Forecasters

Motivated by the question of how one should evaluate professional election forecasters, we study a novel dynamic mechanism design problem without transfers. A principal who wishes to hire only high-quality forecasters is faced with an agent of unknown quality. The agent privately observes signals about a publicly observable future event, and may strategically misrepresent information to inflate the principal’s perception of his quality. We show that the optimal deterministic mechanism is simple and easy to implement in practice: it evaluates a single, optimally timed prediction. We study the generality of this result and its robustness to randomization and noncommitment.