Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Approximate Revenue Maximization with Multiple Items

Maximizing the revenue from selling _more than one_ good (or item) to a single buyer is a notoriously difficult problem, in stark contrast to the one-good case. For two goods, we show that simple "one-dimensional" mechanisms, such as selling the goods separately, _guarantee_ at least 73% of the optimal revenue when the valuations of the two goods are independent and identically distributed, and at least $50\%$ when they are independent. For the case of $k>2$ independent goods, we show that selling them separately guarantees at least a $c/\log^2 k$ fraction of the optimal revenue; and, for independent and identically distributed goods, we show that selling them as one bundle guarantees at least a $c/\log k$ fraction of the optimal revenue. Additional results compare the revenues from the two simple mechanisms of selling the goods separately and bundled, identify situations where bundling is optimal, and extend the analysis to multiple buyers.Comment: Presented in ACM EC conference, 201

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study.

Stability and Distributed Power Control in MANETs with Outages and Retransmissions

In the current work the effects of hop-by-hop packet loss and retransmissions via ARQ protocols are investigated within a Mobile Ad-hoc NET-work (MANET). Errors occur due to outages and a success probability function is related to each link, which can be controlled by power and rate allocation. We first derive the expression for the network's capacity region, where the success function plays a critical role. Properties of the latter as well as the related maximum goodput function are presented and proved. A Network Utility Maximization problem (NUM) with stability constraints is further formulated which decomposes into (a) the input rate control problem and (b) the scheduling problem. Under certain assumptions problem (b) is relaxed to a weighted sum maximization problem with number of summants equal to the number of nodes. This further allows the formulation of a non-cooperative game where each node decides independently over its transmitting power through a chosen link. Use of supermodular game theory suggests a price based algorithm that converges to a power allocation satisfying the necessary optimality conditions of (b). Implementation issues are considered so that minimum information exchange between interfering nodes is required. Simulations illustrate that the suggested algorithm brings near optimal results.Comment: 25 pages, 6 figures, 1 table, submitted to the IEEE Trans. on Communication