Stackelberg Max Closure with Multiple Followers

Mathematics of Operations Research, vol. 47, pp. 3010–3024

Abstract

In a Stackelberg max closure game, we are given a digraph whose vertices correspond to projects from which firms can choose and whose arcs represent precedence constraints. Some projects are under the control of a leader who sets prices in the first stage of the game, while in the second stage, the firms choose a feasible subset of projects of maximum value. For a single follower, the leader’s problem of finding revenue-maximizing prices can be solved in strongly polynomial time. In this paper, we focus on the setting with multiple followers and distinguish two situations. In the case in which only one copy of each project is available (limited supply), we show that the two-follower problem is solvable in strongly polynomial time, whereas the problem with three or more followers is NP-hard. In the case of unlimited supply, that is, when sufficient copies of each project are available, we show that the two-follower problem is already APX-hard. As a side result, we prove that Stackelberg min vertex cover on bipartite graphs with a single follower is APX-hard.

Authors 3

1. Karsten Jungnitsch Aachen School of Business and Economics

   RWTH Aachen University

   Affiliation as printed

   School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany;

2. Britta Peis Aachen School of Business and Economics

   RWTH Aachen University

   Affiliation as printed

   School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany;

3. Marc Schröder

   Maastricht University · Institute for Operations Research and the Management Sciences

   Affiliation as printed

   School of Business and Economics, Maastricht University, 6211 LK Maastricht, Netherlands

   Institute for Operations Research and the Management Sciences (INFORMS) INFORMS is located in Maryland, USA