Stackelberg packing games

Stackelberg pricing games are pricing problems over a set of items. One player, the leader, sets prices for the items and the second player, the follower, buys a subset of items at minimal total cost subject to feasibility constraints. The constraints are determined by an optimization problem. For e...

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Published in:Theoretical computer science Vol. 943; pp. 16 - 35
Main Authors: Böhnlein, Toni, Schaudt, Oliver, Schauer, Joachim
Format: Journal Article
Language:English
Published: Elsevier B.V 17.01.2023
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ISSN:0304-3975
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Abstract Stackelberg pricing games are pricing problems over a set of items. One player, the leader, sets prices for the items and the second player, the follower, buys a subset of items at minimal total cost subject to feasibility constraints. The constraints are determined by an optimization problem. For example, the Stackelberg shortest path game is used to optimize the income from road tolls (cf. [21]). The items are edges in a network graph and the follower buys a subset of edges forming a path. The Stackelberg pricing games studied in the literature are formulated on top of covering problems. In this paper, we introduce pricing games based on packing problems. We are interested in the complexity of computing leader-optimal prices depending on different types of follower-constraints. We show that optimal prices can be computed in polynomial time if the follower-constraints are determined by the well-known interval scheduling problem. This problem is equivalent to the independent set problem on interval graphs. In case the follower-constraints are based on the independent set problem on perfect graphs or on the bipartite matching problem, we prove APX-hardness for the pricing problem. On a more general note, we prove Σ2p-completeness if the follower-constraints are given by a packing problem that is NP-complete, i.e., the leader's pricing problem is hard even if she has an NP-oracle at hand.
AbstractList Stackelberg pricing games are pricing problems over a set of items. One player, the leader, sets prices for the items and the second player, the follower, buys a subset of items at minimal total cost subject to feasibility constraints. The constraints are determined by an optimization problem. For example, the Stackelberg shortest path game is used to optimize the income from road tolls (cf. [21]). The items are edges in a network graph and the follower buys a subset of edges forming a path. The Stackelberg pricing games studied in the literature are formulated on top of covering problems. In this paper, we introduce pricing games based on packing problems. We are interested in the complexity of computing leader-optimal prices depending on different types of follower-constraints. We show that optimal prices can be computed in polynomial time if the follower-constraints are determined by the well-known interval scheduling problem. This problem is equivalent to the independent set problem on interval graphs. In case the follower-constraints are based on the independent set problem on perfect graphs or on the bipartite matching problem, we prove APX-hardness for the pricing problem. On a more general note, we prove Σ2p-completeness if the follower-constraints are given by a packing problem that is NP-complete, i.e., the leader's pricing problem is hard even if she has an NP-oracle at hand.
Author Böhnlein, Toni
Schauer, Joachim
Schaudt, Oliver
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  givenname: Joachim
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  fullname: Schauer, Joachim
  email: joachim.schauer@uni-graz.at
  organization: University of Graz, Graz, Austria
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Keywords Stackelberg pricing games
Graph algorithms
Approximation hardness
Algorithmic pricing
Language English
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Snippet Stackelberg pricing games are pricing problems over a set of items. One player, the leader, sets prices for the items and the second player, the follower, buys...
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StartPage 16
SubjectTerms Algorithmic pricing
Approximation hardness
Graph algorithms
Stackelberg pricing games
Title Stackelberg packing games
URI https://dx.doi.org/10.1016/j.tcs.2022.12.006
Volume 943
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