Item Bidding Research Articles

Best-response dynamics in combinatorial auctions with item bidding

In a combinatorial auction with item bidding, agents participate in multiple single-item second-price auctions at once. As some items might be substitutes, agents need to strategize in order to maximize their utilities. A number of results indicate that high social welfare can be achieved this way, giving bounds on the welfare at equilibrium. Recently, however, criticism has been raised that equilibria of this game are hard to compute and therefore unlikely to be attained.In this paper, we take a different perspective by studying simple best-response dynamics. Often these dynamics may take exponentially long before they converge or they may not converge at all. However, as we show, convergence is not even necessary for good welfare guarantees. Given that agents' bid updates are aggressive enough but not too aggressive, the game will reach and remain in states of high welfare after each agent has updated his bid at least once.

Nash Equilibria in Combinatorial Auctions with Item Bidding and Subadditive Symmetric Valuations

Nash Equilibria in Combinatorial Auctions with Item Bidding and Subadditive Symmetric Valuations

Network Capacity Enhancement in HetNets Using Incentivized Offloading Mechanism

This paper investigates distributed algorithms for joint power allocation and user association in heterogeneous networks. We propose auction-based algorithms for offloading macrocell users ( MUs ) from the macrocell base station to privately owned small-cell access points (SCAs). We first propose a simultaneous multiple-round ascending auction (SMRA) for allocating MUs to SCAs. Taking into account the overheads incurred by SCAs during valuation in the SMRA, further improvements are proposed using techniques known as sub-optimal altered SMRA, the combinatorial auction with item bidding (CAIB), and its variations; the sequential CAIB and the repetitive CAIB. The proof for existence of the Walrasian equilibrium is demonstrated through establishing that the valuation function used by the SCAs is a gross substitute. Finally, we show that truthful bidding is individual rational for all of our proposed algorithms.

Item bidding for combinatorial public projects

We analyze a simple mechanism for the Combinatorial Public Project Problem (Cppp). The problem asks to select k out of m available items, so as to maximize the social welfare for autonomous agents with combinatorial preferences (valuation functions) over subsets of items. The Cppp constitutes an abstract model for decision making by autonomous agents and has been shown to present severe computational hardness, in the design of tractable truthful approximation mechanisms. We study a non-truthful mechanism that is, however, practically relevant to multi-agent environments, by virtue of its natural simplicity. The mechanism employs an item bidding interface, where every agent issues a separate bid for the inclusion of each distinct item in the outcome; the k items with the highest sums of bids are then chosen. As for the payment scheme, the agents are charged according to a direct adaptation of the VCG payment rule. For fairly expressive classes of the agents' valuation functions, we establish existence of socially optimal pure Nash equilibria, as well as strong equilibria, that are resilient to coordinated deviations of subsets of agents. Particularly with respect to pure Nash equilibria, we prove convergence of an iterative procedure. Subsequently, we derive worst-case bounds on the approximation of the optimum social welfare achieved in (strong) equilibrium by the mechanism. We show that the mechanism's performance improves with the number of agents that can coordinate their bids, and reaches half of the optimum welfare at strong equilibrium. Finally, we derive bounds on the mechanism's performance in Bayes–Nash equilibrium, under an incomplete information setting.

Nash Equilibria in Combinatorial Auctions with Item Bidding by Two Bidders

Nash Equilibria in Combinatorial Auctions with Item Bidding by Two Bidders

Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions

We study the price of anarchy (PoA) of simultaneous first-price auctions (FPAs) for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian price of anarchy (BPoA) of these auctions are e /( e − 1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases even for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of e /( e − 1) for FPAs with fractionally subadditive valuations that reveals the worst-case price distribution, which is used as a building block for the matching lower bound construction. We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including FPAs and all-pay auctions) where the winner is always the highest bidder and each bidder’s payment depends only on his own bid. Finally, we apply our techniques to discriminatory price multiunit auctions. We complement the results of de Keijzer et al. [2013] for the case of subadditive valuations by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e /( e − 1) using our nonsmooth approach.

Item Bidding for Combinatorial Public Projects

We present and analyze a mechanism for the Combinatorial Public Project Problem (CPPP). The problem asks to select k out of m available items, so as to maximize the social welfare for autonomous agents with combinatorial preferences (valuation functions) over subsets of items. The CPPP constitutes an abstract model for decision making by autonomous agents and has been shown to present severe computational hardness, in the design of truthful approximation mechanisms. We study a non-truthful mechanism that is, however, practically relevant to multi-agent environments, by virtue of its natural simplicity. It employs an Item Bidding interface, wherein every agent issues a separate bid for the inclusion of each distinct item in the outcome; the k items with the highest sums of bids are chosen and agents are charged according to a VCG-based payment rule. For fairly expressive classes of the agents' valuation functions, we establish existence of socially optimal pure Nash and strong equilibria, that are resilient to coordinated deviations of subsets of agents. Subsequently we derive tight worst-case bounds on the approximation of the optimum social welfare achieved in equilibrium. We show that the mechanism's performance improves with the number of agents that can coordinate, and reaches half of the optimum welfare at strong equilibrium.