The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Draft Auctions

We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium over sequential item auctions where predetermined items are auctioned at each time step. Specifically, we show that for any subadditive valuation the social welfare at equilibrium is an $O(\log^2(m))$-approximation to the optimal social welfare, where $m$ is the number of items. We also provide tighter approximation results for several subclasses. Our welfare guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes, via the smooth-mechanism framework. Of independent interest, our techniques show that in a combinatorial auction setting, efficiency guarantees of a mechanism via smoothness for a very restricted class of cardinality valuations, extend with a small degradation, to subadditive valuations, the largest complement-free class of valuations. Variants of draft auctions have been used in practice and have been experimentally shown to outperform other auctions. Our results provide a theoretical justification

A dominant strategy, double clock auction with estimation-based tatonnement

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility and individual rationality. We introduce a double clock auction for a homogeneous good market with multidimensional private information and multiunit traders that is deficit‐free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tâtonnement process that adjusts the clock prices based on the estimates

Descending Price Optimally Coordinates Search

Investigating potential purchases is often a substantial investment under uncertainty. Standard market designs, such as simultaneous or English auctions, compound this with uncertainty about the price a bidder will have to pay in order to win. As a result they tend to confuse the process of search both by leading to wasteful information acquisition on goods that have already found a good purchaser and by discouraging needed investigations of objects, potentially eliminating all gains from trade. In contrast, we show that the Dutch auction preserves all of its properties from a standard setting without information costs because it guarantees, at the time of information acquisition, a price at which the good can be purchased. Calibrations to start-up acquisition and timber auctions suggest that in practice the social losses through poor search coordination in standard formats are an order of magnitude or two larger than the (negligible) inefficiencies arising from ex-ante bidder asymmetries.Comment: JEL Classification: D44, D47, D82, D83. 117 pages, of which 74 are appendi

A dominant strategy, double clock auction with estimation-based tâtonnement

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility. We introduce a double clock auction for a homogeneous good market with multi-dimensional private information and multi-unit traders that is deficit-free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tatonnement process that adjusts the clock prices based on the estimates

Auctions as Coordination Devices

This paper develops an economic argument relating auctions to high market prices. At the core of the argument is the claim that market competition and bidding in an auction should be analyzed as part of one game, where the pricing strategies in the market subgame depend on the bidding strategies during the auction. I show that when there are two licenses for sale the only equilibrium in the overall game that is consistent with the logic of forward induction is the one where firms bid an amount (almost) equal to the profits of the cooperative market outcome and follow a cooperative pricing strategy in the market game resulting in high prices. With three or more licenses the auction format determines whether the forward induction argument works.Auctions, Market prices, Coordination

A Free Exchange e-Marketplace for Digital Services

The digital era is witnessing a remarkable evolution of digital services. While the prospects are countless, the e-marketplaces of digital services are encountering inherent game-theoretic and computational challenges that restrict the rational choices of bidders. Our work examines the limited bidding scope and the inefficiencies of present exchange e-marketplaces. To meet challenges, a free exchange e-marketplace is proposed that follows the free market economy. The free exchange model includes a new bidding language and a double auction mechanism. The rule-based bidding language enables the flexible expression of preferences and strategic conduct. The bidding message holds the attribute-valuations and bidding rules of the selected services. The free exchange deliberates on attributes and logical bidding rules for automatic deduction and formation of elicited services and bids that result in a more rapid self-managed multiple exchange trades. The double auction uses forward and reverse generalized second price auctions for the symmetric matching of multiple digital services of identical attributes and different quality levels. The proposed double auction uses tractable heuristics that secure exchange profitability, improve truthful bidding and deliver stable social efficiency. While the strongest properties of symmetric exchanges are unfeasible game-theoretically, the free exchange converges rapidly to the social efficiency, Nash truthful stability, and weak budget balance by multiple quality-levels cross-matching, constant learning and informs at repetitive thick trades. The empirical findings validate the soundness and viability of the free exchange