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Register a new userFairness in Combinatorial Auctions
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Added by
Shrisha Rao
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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The market economy deals with many interacting agents such as buyers and sellers who are autonomous intelligent agents pursuing their own interests. One such multi-agent system (MAS) that plays an important role in auctions is the combinatorial auctioning system (CAS). We use this framework to define our concept of fairness in terms of what we call as basic fairness and extended fairness. The assumptions of quasilinear preferences and dominant strategies are taken into consideration while explaining fairness. We give an algorithm to ensure fairness in a CAS using a Generalized Vickrey Auction (GVA). We use an algorithm of Sandholm to achieve optimality. Basic and extended fairness are then analyzed according to the dominant strategy solution concept.
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One of the Multi-Agent Systems that is widely used by various government agencies, buyers and sellers in a market economy, in such a manner so as to attain optimized resource allocation, is the Combinatorial Auctioning System (CAS). We study another important aspect of resource allocations in CAS, namely fairness. We present two important notions of fairness in CAS, extended fairness and basic fairness. We give an algorithm that works by incorporating a metric to ensure fairness in a CAS that uses the Vickrey-Clark-Groves (VCG) mechanism, and uses an algorithm of Sandholm to achieve optimality. Mathematical formulations are given to represent measures of extended fairness and basic fairness.
We study combinatorial auctions with bidders that exhibit endowment effect. In most of the previous work on cognitive biases in algorithmic game theory (e.g., [Kleinberg and Oren, EC14] and its follow-ups) the focus was on analyzing the implications and mitigating their negative consequences. In contrast, in this paper we show how in some cases cognitive biases can be harnessed to obtain better outcomes. Specifically, we study Walrasian equilibria in combinatorial markets. It is well known that Walrasian equilibria exist only in limited settings, e.g., when all valuations are gross substitutes, but fails to exist in more general settings, e.g., when the valuations are submodular. We consider combinatorial settings in which bidders exhibit the endowment effect, that is, their value for items increases with ownership. Our main result shows that when the valuations are submodular, even a mild degree of endowment effect is sufficient to guarantee the existence of Walrasian equilibria. In fact, we show that in contrast to Walrasian equilibria with standard utility maximizing bidders -- in which the equilibrium allocation must be efficient -- when bidders exhibit endowment effect any local optimum can be an equilibrium allocation. Our techniques reveal interesting connections between the LP relaxation of combinatorial auctions and local maxima. We also provide lower bounds on the intensity of the endowment effect that the bidders must have in order to guarantee the existence of a Walrasian equilibrium in various settings.
Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocation, require us to consider two-sided combinatorial auctions in which buyers have preferences on subsets of items, and sellers may offer multiple heterogeneous items. No efficient mechanism was known so far for such two-sided combinatorial markets. This work provides the first IR, IC and SBB mechanisms that provides an O(1)-approximation to the optimal social welfare for two-sided markets. An initial construction yields such a mechanism, but exposes a conceptual problem in the traditional SBB notion. This leads us to define the stronger notion of direct trade strong budget balance (DSBB). We then proceed to design mechanisms that are IR, IC, DSBB, and again provide an O(1)-approximation to the optimal social welfare. Our mechanisms work for any number of buyers with XOS valuations - a class in between submodular and subadditive functions - and any number of sellers. We provide a mechanism that is dominant strategy incentive compatible (DSIC) if the sellers each have one item for sale, and one that is bayesian incentive compatible (BIC) if sellers hold multiple items and have additive valuations over them. Finally, we present a DSIC mechanism for the case that the valuation functions of all buyers and sellers are additive.
We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of $O(log^2 m)$ [STOC06], where $m$ is the number of items. This was subsequently improved to $O(log mlog log m)$ [Dobzinski, APPROX07] and then to $O(log m)$ [Krysta and Vocking, ICALP12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of $O(sqrt {log m})$. Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a. fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.
In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of $2$ for every order of the items. We show that if the valuations are vertex cover functions and the order is random then the expected approximation ratio imrpoves to $frac 7 4$.
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