Efficient Interdependent Value Combinatorial Auctions with Single Minded Bidders

We study the problem of designing efficient auctions where bidders have interdependent values; i.e., values that depend on the signals of other agents. We consider a contingent bid model in which agents can explicitly condition the value of their bids on the bids submitted by others. In particular, we adopt a linear contingent bidding model for single minded combinatorial auctions (CAs), in which submitted bids are linear combinations of bids received from others. We extend the existing state of the art, by identifying constraints on the interesting bundles and contingency weights reported by the agents which allow the efficient second priced, fixed point bids auction to be implemented in single minded CAs. Moreover, for domains in which the required single crossing condition fails (which characterizes when efficient, IC auctions are possible), we design a two-stage mechanism in which a subset of agents (''experts") are allocated first, using their reports to allocate the remaining items to the other agents.Engineering and Applied Science

Instantiating the contingent bids model of truthful interdependent value auctions

(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Ito, Takayuki, and David C. Parkes. 2006. Instantiating the contingent bids model of truthful interdependent value auctions. I

On the Inefficiency of the Uniform Price Auction

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general. The uniform pricing rule is, however, widely popular by its appeal to the natural anticipation, that identical items should be identically priced. In this work we study equilibria of the Uniform Price Auction for bidders with (symmetric) submodular valuation functions, over the number of units that they win. We investigate pure Nash equilibria of the auction in undominated strategies; we produce a characterization of these equilibria that allows us to prove that a fraction 1-1/e of the optimum social welfare is always recovered in undominated pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we study the auction under the incomplete information setting and prove a bound of 4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor corrections on the previous version

Computing Bayes Nash Equilibrium Strategies in Auction Games via Simultaneous Online Dual Averaging

Auctions are modeled as Bayesian games with continuous type and action spaces. Computing equilibria in auction games is computationally hard in general and no exact solution theory is known. We introduce algorithms computing distributional strategies on a discretized version of the game via online convex optimization. One advantage of distributional strategies is that we do not have to make any assumptions on the shape of the bid function. Besides, the expected utility of agents is linear in the strategies. It follows that if our regularized optimization algorithms converge to a pure strategy, then they converge to an approximate equilibrium of the discretized game with high precision. Importantly, we show that the equilibrium of the discretized game approximates an equilibrium in the continuous game. In a wide variety of auction games, we provide empirical evidence that the method approximates the analytical (pure) Bayes Nash equilibrium closely. This speed and precision is remarkable, because in many finite games learning dynamics do not converge or are even chaotic. In standard models where agents are symmetric, we find equilibrium in seconds. The method allows for interdependent valuations and different types of utility functions and provides a foundation for broadly applicable equilibrium solvers that can push the boundaries of equilibrium analysis in auction markets and beyond