Information in Mechanism Design

We survey the recent literature on the role of information for mechanism design. We specifically consider the role of endogeneity of and robustness to private information in mechanism design. We view information acquisition of and robustness to private information as two distinct but related aspects of information management important in many design settings. We review the existing literature and point out directions for additional future work.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

The impact of the irrelevant – Temporary buy-options and bidding behavior in online auctions

In a laboratory experiment, we investigate the impact of temporary buy-options on efficiency, revenues, and bidding behavior in online proxy-auctions when bidders have independent private valuations. We show that the introduction of a buy-option reduces efficiency and at the same time fails to enhance revenues. In particular, we observe that the former presence of a temporary buy-option lowers final prices in an auction (even though the option is no longer available once an auction has started). If bidders have imprecise information about their private value, auction prices are increasing in the price of the buy-option which suggests anchoring as an explanation. Surprisingly, the former presence of a temporary buy-option also tends to reduce final auction prices if bidders are perfectly informed about their private value. In fact, we demonstrate that bidders are reluctant to bid above the option price regardless of the precision of their private information and the price of the option.microeconomics ;

THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important notion of fairness is envy-freeness: No player wishes to switch the portion of the cake received with another player's portion. Despite intense efforts in the past, it is still an open question whether there is a \emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number of players, and even for four players. We introduce the notion of degree of guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting protocol can approximate the ideal of envy-freeness while keeping the protocol finite bounded (trading being disregarded). We propose a new finite bounded proportional protocol for any number n \geq 3 of players, and show that this protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best DGEF among known finite bounded cake-cutting protocols for an arbitrary number of players. We will make the case that improving the DGEF even further is a tough challenge, and determine, for comparison, the DGEF of selected known finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure

Information in Mechanism Design

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payoff and strategic information for the design and the efficiency of the mechanism. We specifically consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

Learn While You Earn: Two Approaches to Learning Auction Parameters in Take-it-or-leave-it Auctions

Much of the research in auction theory assumes that the auctioneer knows the distribution of participants ’ valuations with complete certainty. However, this is unrealistic. Thus, we analyse cases in which the auctioneer is uncertain about the valuation distributions; specifically, we consider a repeated auction setting in which the auctioneer can learn these distributions. Using take-it-or-leave-it auctions (Sandholm and Gilpin, 2006) as an exemplar auction format, we consider two auction design criteria. Firstly, an auctioneer could maximise expected revenue each time the auction is held. Secondly, an auctioneer could maximise the information gained in earlier auctions (as measured by the Kullback-Liebler divergence between its posterior and prior) to develop good estimates of the unknowns, which are later exploited to improve the revenue earned in the long-run. Simulation results comparing the two criteria indicate that setting offers to maximise revenue does not significantly detract from learning performance, but optimising offers for information gain substantially reduces expected revenue while not producing significantly better parameter estimates

Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Environmental Innovation, War of Attrition and Investment Grants

The paper analyses the timing of spontaneous environmental innovation when second-mover advantages, arising from the expectation of declining investment costs, increase the option value of waiting created by investment irreversibility and uncertainty about private payoffs. We then focus on the design of public subsidies aimed at bridging the gap between the spontaneous time of technological change and the socially desirable one. Under network externalities and incomplete information about firms’ switching costs, auctioning investment grants appears to be a cost-effective way of accelerating pollution abatement, in that it allows targeting grants instead of subsidizing the entire industry indiscriminatelyEnvironmental innovation, Investment irreversibility, Network externalities, Investment grants, Second-price auction.