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On Stackelberg Pricing with Computationally Bounded Consumers

  • Patrick Briest
  • Martin Hoefer
  • Luciano Gualà
  • Carmine Ventre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5929)

Abstract

In a Stackelberg pricing game a leader aims to set prices on a subset of a given collection of items, such as to maximize her revenue from a follower purchasing a feasible subset of the items. We focus on the case of computationally bounded followers who cannot optimize exactly over the range of all feasible subsets, but apply some publicly known algorithm to determine the set of items to purchase. This corresponds to general multi-dimensional pricing assuming that consumers cannot optimize over the full domain of their valuation functions but still aim to act rationally to the best of their ability.

We consider two versions of this novel type of Stackelberg pricing games. Assuming that items are weighted objects and the follower seeks to purchase a min-cost selection of objects of some minimum weight (the Min-Knapsack problem) and uses a simple greedy 2-approximate algorithm, we show how an extension of the known single-price algorithm can be used to derive a polynomial-time (2 + ε)-approximation algorithm for the leader’s revenue maximization problem based on so-called near-uniform price assignments. We also prove the problem to be strongly NP-hard.

Considering the case that items are subsets of some ground set which the follower seeks to cover (the Set-Cover problem) via a standard primal-dual approach, we prove that near-uniform price assignments fail to yield a good approximation guarantee. However, in the special case of elements with frequency 2 (the Vertex-Cover problem) it turns out that exact revenue maximization can be done in polynomial-time. This stands in sharp contrast to the fact that revenue maximization becomes APX-hard already for elements with frequency 3.

Keywords

Greedy Algorithm Vertex Cover Price Problem Congestion Game Approximation Guarantee 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Patrick Briest
    • 1
  • Martin Hoefer
    • 2
  • Luciano Gualà
    • 3
  • Carmine Ventre
    • 4
  1. 1.Department of Computer ScienceUniversity of PaderbornGermany
  2. 2.Lehrstuhl Informatik IRWTH Aachen UniversityGermany
  3. 3.Dipartimento di MatematicaUniversitá di Roma “Tor Vergata”Italy
  4. 4.Department of Computer ScienceUniversity of LiverpoolUK

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