Smoothness for Simultaneous Composition of Mechanisms with Admission

We study social welfare of learning outcomes in mechanisms with admission. In our repeated game there are $n$ bidders and $m$ mechanisms, and in each round each mechanism is available for each bidder only with a certain probability. Our scenario is an elementary case of simple mechanism design with incomplete information, where availabilities are bidder types. It captures natural applications in online markets with limited supply and can be used to model access of unreliable channels in wireless networks. If mechanisms satisfy a smoothness guarantee, existing results show that learning outcomes recover a significant fraction of the optimal social welfare. These approaches, however, have serious drawbacks in terms of plausibility and computational complexity. Also, the guarantees apply only when availabilities are stochastically independent among bidders. In contrast, we propose an alternative approach where each bidder uses a single no-regret learning algorithm and applies it in all rounds. This results in what we call availability-oblivious coarse correlated equilibria. It exponentially decreases the learning burden, simplifies implementation (e.g., as a method for channel access in wireless devices), and thereby addresses some of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian settings. Our main results are general composition theorems for smooth mechanisms when valuation functions of bidders are lattice-submodular. They rely on an interesting connection to the notion of correlation gap of submodular functions over product lattices.Comment: Full version of WINE 2016 pape

Measuring the Efficiency of an FCC Spectrum Auction

FCC spectrum auctions sell licenses to provide mobile phone service in designated geographic territories. We propose a method to structurally estimate the deterministic component of bidder valuations and apply it to the 1995–1996 C-block auction. We base our estimation of bidder values on a pairwise stability condition, which implies that two bidders cannot exchange licenses in a way that increases total surplus. Pairwise stability holds in many theoretical models of simultaneous ascending auctions, including some models of intimidatory collusion and demand reduction. Pairwise stability is also approximately satisfied in data that we examine from economic experiments. The lack of post-auction resale also suggests pairwise stability. Using our estimates of deterministic valuations, we measure the allocative efficiency of the C-block outcome.

Mechanism Design via Correlation Gap

For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al.\ (SODA10) quantifies how much we {}"lose" in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al.\ for several environments. In particular, we show that it gives an $e/(e-1)$-approximation for matroid environments, gives asymptotically a $1/(1-1/\sqrt{2\pi k})$-approximation for the important sub-case of $k$-unit auctions, and gives a $(p+1)$-approximation for environments with $p$-independent set system constraints

Does Laboratory Trading Mirror Behavior in Real World Markets? Fair Bargaining and Competitive Bidding on EBay

We conducted a controlled field experiment on eBay and examined to what extent both social and competitive laboratory behavior is robust to institutionally complex real world markets with experienced traders, who selected themselves into these markets. EBay’s natural trading system provides bridges between lab and field environment that can be exploited to explore differences in behavior in the two environments. We find that many sellers do not make use of their commitment power as predicted by standard theories of both selfish and social behavior. However, a concern for equity strongly affects outcomes and reputation building in bilateral bargaining, while buyer competition effectively masks this concern and robustly yields equilibrium outcomes. The dichotomy of behaviors mirrors observations in laboratory research. Furthermore, we find that behavioral patterns in the field experiment mirror fully naturally occurring trading patterns in the market.eBay, auctions, behavioral economics, trust, market design

Optimal two-object auctions with synergies.

We design the revenue-maximizing auction for two goods when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the goods inefficiently with respect to an environ-ment with no synergies. In particular, if the synergy is large then it may occur that a buyer’s valuations for the goods weakly dominate the valuations of another buyer and the latter one receives the bundle. We link this fact, which contrasts with the results for a setting without synergies, to "non-regular" one-good models.Multiple-unit Auctions; Multi-dimensional Screening; Bundling