Strategy-Proof Facility Location for Concave Cost Functions

We consider k-Facility Location games, where n strategic agents report their locations on the real line, and a mechanism maps them to k facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the identity cost function, we are interested in mechanisms without payments that are (group) strategyproof for any given cost function, and achieve a good approximation ratio for the social cost and/or the maximum cost of the agents. We present a randomized mechanism, called Equal Cost, which is group strategyproof and achieves a bounded approximation ratio for all k and n, for any given concave cost function. The approximation ratio is at most 2 for Max Cost and at most n for Social Cost. To the best of our knowledge, this is the first mechanism with a bounded approximation ratio for instances with k > 2 facilities and any number of agents. Our result implies an interesting separation between deterministic mechanisms, whose approximation ratio for Max Cost jumps from 2 to unbounded when k increases from 2 to 3, and randomized mechanisms, whose approximation ratio remains at most 2 for all k. On the negative side, we exclude the possibility of a mechanism with the properties of Equal Cost for strictly convex cost functions. We also present a randomized mechanism, called Pick the Loser, which applies to instances with k facilities and n = k+1 agents, and for any given concave cost function, is strongly group strategyproof and achieves an approximation ratio of 2 for Social Cost

The mixed strategy equilibrium of the three-firm location game with discrete location choices

In the paper, we derive a symmetric MSE for the three-firm location game on the discrete strategy space. Rather than being uniformly distributed, the MSE for the game has a multimodal distribution. Our theory is more convincing to predict equilibria of three-firm location games in the real world or controlled experiments, where players face finitely many choices.mixed strategy equilibrium, multimodal distribution, discrete strategy space

An optimal internet location strategy for markets with different tax rates

The traditional view that a high sales tax rate reduces trade by driving a wedge between the purchase and sale price may not apply to internet commerce for two reasons. The first reason is that the sales tax paid by buyers purchasing via the internet is determined by the tax rate in the region of the buyer. The second reason is that a high sales tax may lower the before-tax price if sellers absorb part of the tax. Taken together, this implies that internet distributors may profitably target customers in regions with low tax rates by locating their selling addresses in high tax regions. Consequently the optimal marketing strategy for a global internet distributor may include siting selling locations in regions with high tax rates in order to target customers in regions with low tax rates. An empirical analysis of the European car market suggests that this is more than a remote theoretical possibility by demonstrating that the before-tax prices recommended by manufacturers for new cars are lower in high tax countries

Nonautonomous control of stable and unstable manifolds in two-dimensional flows

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are to be moved to a user-specified time-varying location which is near the steady location. We determine the nonautonomous perturbation to the vector field required to achieve this control, and give a theoretical bound for the error in the manifolds resulting from applying this control. The efficacy of the control strategy is illustrated via a numerical example

TIP spatial index: efficient access to digital libraries in a context-aware mobile system

We present a framework for efficient, uniform, location-based access to digital library collections that are external to a context-aware mobile information system. Using a tourist Information system, we utilize a spatial index to manage the context of location. We show how access to resources from within and outside of the tourist information system can be carried out in a seamless manner. We show how the spatial index can be navigated to continually provide information to the user. An empirical evaluation of the navigation strategy versus traditional spatial searching shows that navigation is efficient and outperforms traditional spatial search. In conclusion, our work provides a strategy for context-aware mobile systems to co-operate with digital libraries in a seamless and efficient manner

Do we buy more or less when we want to learn? The knowledge strategies and structural forms of US cross-border acquisitions

Cross-border acquisitions may be a primary mode for accessing novel knowledge and the building up of knowledge capabilities. However, the successful exploration of novel business and/or location knowledge may require specific structural forms for the incorporation and internal transfer to occur. In this paper we examine the relationship between the knowledge strategy and the structural form of the acquisition, specifically the degree of equity acquired. Our analyses of 439 US cross-border acquisitions revealed a curvilinear effect of location-related knowledge exploration but a linear effect of business-related knowledge exploration on the structural form of cross-border acquisition. We conclude that the knowledge strategy, and perhaps the type of knowledge being sought, is related in complex manners to the structural form adopted.cross-border acquisitions, knowledge strategy, equity ownership, structural forms, learning