Automated Mechanism Design for Classification with Partial Verification

We study the problem of automated mechanism design with partial verification, where each type can (mis)report only a restricted set of types (rather than any other type), induced by the principal's limited verification power. We prove hardness results when the revelation principle does not necessarily hold, as well as when types have even minimally different preferences. In light of these hardness results, we focus on truthful mechanisms in the setting where all types share the same preference over outcomes, which is motivated by applications in, e.g., strategic classification. We present a number of algorithmic and structural results, including an efficient algorithm for finding optimal deterministic truthful mechanisms, which also implies a faster algorithm for finding optimal randomized truthful mechanisms via a characterization based on convexity. We then consider a more general setting, where the principal's cost is a function of the combination of outcomes assigned to each type. In particular, we focus on the case where the cost function is submodular, and give generalizations of essentially all our results in the classical setting where the cost function is additive. Our results provide a relatively complete picture for automated mechanism design with partial verification.Comment: AAAI'2

Partial Verification as a Substitute for Money

Recent work shows that we can use partial verification instead of money to implement truthful mechanisms. In this paper we develop tools to answer the following question. Given an allocation rule that can be made truthful with payments, what is the minimal verification needed to make it truthful without them? Our techniques leverage the geometric relationship between the type space and the set of possible allocations.Comment: Extended Version of 'Partial Verification as a Substitute for Money', AAAI 201

Probabilistic Verification in Mechanism Design

We introduce a model of probabilistic verification in a mechanism design setting. The principal verifies the agent's claims with statistical tests. The agent's probability of passing each test depends on his type. In our framework, the revelation principle holds. We characterize whether each type has an associated test that best screens out all the other types. In that case, the testing technology can be represented in a tractable reduced form. In a quasilinear environment, we solve for the revenue-maximizing mechanism by introducing a new expression for the virtual value that encodes the effect of testing

Bundling Equilibrium in Combinatorial auctions

This paper analyzes individually-rational ex post equilibrium in the VC (Vickrey-Clarke) combinatorial auctions. If $\Sigma$ is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in $\Sigma$. The $\Sigma$-VC combinatorial auctions (multi-good auctions) obtained in this way are known to be individually-rational truth-telling mechanisms. In contrast, this paper deals with non-restricted VC auctions, in which the buyers restrict themselves to bids on bundles in $\Sigma$, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in $\Sigma$, they are in an equilibrium. We fully characterize those $\Sigma$ that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in $\Sigma$ represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partition-based equilibrium, in which $\Sigma$ is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partition-based equilibrium

Imperfect state verification and financial contracting

An argument that in a costly state verification model of financial contracting, relaxing the assumption of perfect verification makes the measurement of information difficult.Contracts ; Information theory

Mechanisms with evidence: commitment and robustness

We show that in a class of I‐agent mechanism design problems with evidence, commitment is unnecessary, randomization has no value, and robust incentive compatibility has no cost. In particular, for each agent i, we construct a simple disclosure game between the principal and agent i where the equilibrium strategies of the agents in these disclosure games give their equilibrium strategies in the game corresponding to the mechanism but where the principal is not committed to his response. In this equilibrium, the principal obtains the same payoff as in the optimal mechanism with commitment. As an application, we show that certain costly verification models can be characterized using equilibrium analysis of an associated model of evidence.Accepted manuscrip

Computational Efficiency Requires Simple Taxation

We characterize the communication complexity of truthful mechanisms. Our departure point is the well known taxation principle. The taxation principle asserts that every truthful mechanism can be interpreted as follows: every player is presented with a menu that consists of a price for each bundle (the prices depend only on the valuations of the other players). Each player is allocated a bundle that maximizes his profit according to this menu. We define the taxation complexity of a truthful mechanism to be the logarithm of the maximum number of menus that may be presented to a player. Our main finding is that in general the taxation complexity essentially equals the communication complexity. The proof consists of two main steps. First, we prove that for rich enough domains the taxation complexity is at most the communication complexity. We then show that the taxation complexity is much smaller than the communication complexity only in "pathological" cases and provide a formal description of these extreme cases. Next, we study mechanisms that access the valuations via value queries only. In this setting we establish that the menu complexity -- a notion that was already studied in several different contexts -- characterizes the number of value queries that the mechanism makes in exactly the same way that the taxation complexity characterizes the communication complexity. Our approach yields several applications, including strengthening the solution concept with low communication overhead, fast computation of prices, and hardness of approximation by computationally efficient truthful mechanisms

Little Green Lies : Optimal environmental regulation with partially verifiable information

When the set of possible messages depends on the actual state of the world, optimal incentive schemes to control environmental problems may not always satisfy the revelation principle. As a result, in equilibrium some agents may send false messages, particularly when the information rents in the truth- telling scheme are high. I characterise optimal pollution regulation schemes and produce some numerical examples to show mechanisms which allow some dishonesty in equilibrium may frequently outperform truth-telling schemes.JEL Classification Codes: D82, Q58, H23http://www.grips.ac.jp/list/jp/facultyinfo/munro_alistair