Internet Mathematics

Complexity of Pure Nash Equilibria in Player-Specific Network Congestion Games

Heiner Ackermann and Alexander Skopalik

Full-text: Open access

Abstract

Network congestion games with player-specific delay functions do not possess pure Nash equilibria in general. We therefore address the computational complexity of the corresponding decision problem and prove that it is $NP$-complete to decide whether a pure Nash equilibrium exists. This result is true for games with directed edges as well as for networks with undirected edges, and still holds for games with two players only. In contrast to games with networks of arbitrary size, we present a polynomial-time algorithm deciding whether there exists a Nash equilibrium in games with networks of constant size.

Additionally, we introduce a family of player-specific network congestion games that are guaranteed to possess equilibria. In these games players have identical delay functions. However, each player may use only a certain subset of the edges. For this class of games we prove that finding a pure Nash equilibrium is $PLS$-complete. Again, this result is true for networks with directed edges as well as for networks with undirected edges, and still holds for games with three players only. In games with networks of constant size, however, we prove that pure Nash equilibria can be computed in polynomial time.

Article information

Source
Internet Math., Volume 5, Number 4 (2008), 323-342.

Dates
First available in Project Euclid: 1 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.im/1265033168

Mathematical Reviews number (MathSciNet)
MR2604965

Zentralblatt MATH identifier
1194.91055

Citation

Ackermann, Heiner; Skopalik, Alexander. Complexity of Pure Nash Equilibria in Player-Specific Network Congestion Games. Internet Math. 5 (2008), no. 4, 323--342. https://projecteuclid.org/euclid.im/1265033168


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