Results 1  10
of
15
Pure Nash equilibria in playerspecific and weighted congestion games
 In Proc. of the 2nd Int. Workshop on Internet and Network Economics (WINE
, 2006
"... Additionally, our analysis of playerspecific matroid congestion games yields a polynomial time algorithm for computing pure equilibria. We also address questions related to the convergence time of such games. For playerspecific matroid congestion games, in which the best response dynamics may cycl ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
Additionally, our analysis of playerspecific matroid congestion games yields a polynomial time algorithm for computing pure equilibria. We also address questions related to the convergence time of such games. For playerspecific matroid congestion games, in which the best response dynamics may cycle, we show that from every state there exists a short sequences of better responses to an equilibrium. For weighted matroid congestion games, we present a superpolynomial lower bound on the convergence time of the best response dynamics showing that players do not even converge in pseudopolynomial time.
Congestion games with playerspecific constants
 In Proceedings of the 32nd International Symposium on Mathematical Foundations of Computer Science
, 2007
"... Abstract. We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (nondecreasing) delay function together with a playerspecific constant. For each particular resource, the resourcespecific delay fun ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
Abstract. We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (nondecreasing) delay function together with a playerspecific constant. For each particular resource, the resourcespecific delay function and the playerspecific constant (for that resource) are composed by means of a group operation (such as addition or multiplication) into a playerspecific latency function. We assume that the underlying group is a totally ordered abelian group. In this way, we obtain the class of (weighted) congestion games with playerspecific constants; we observe that this class is contained in the new intuitive class of dominance (weighted) congestion games. Wefocusonpure Nash equilibria for congestion games with playerspecific constants; for these equilibria, we study questions of existence, computational complexity and convergence via improvement or bestreply steps of players. Our findings are as follows: – Games on parallel links: Every unweighted congestion game has an ordinal potential; hence,ithastheFinite Improvement Property and a pure Nash equilibrium. There is a weighted congestion game with 3 players on 3 parallel links that does not have
Malicious Bayesian Congestion Games
 6th Workshop on Approximation and Online Algorithms (WAOA
, 2008
"... Abstract. In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types. Either the player is a rational player seeking to minimize her own delay, or – with a certain probabilit ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Abstract. In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types. Either the player is a rational player seeking to minimize her own delay, or – with a certain probability – the player is malicious in which case her only goal is to disturb the other players as much as possible. We show that such games do in general not possess a Bayesian Nash equilibrium in pure strategies (i.e. a pure Bayesian Nash equilibrium). Moreover, given a game, we show that it is NPcomplete to decide whether it admits a pure Bayesian Nash equilibrium. This result even holds when resource latency functions are linear, each player is malicious with the same probability, and all strategy sets consist of singleton sets of resources. For a slightly more restricted class of malicious Bayesian congestion games, we provide easy checkable properties that are necessary and sufficient for the existence of a pure Bayesian Nash equilibrium. In the second part of the paper we study the impact of the malicious types on the overall performance of the system (i.e. the social cost). To measure this impact, we use the Price of Malice. We provide (tight) bounds on the Price of Malice for an interesting class of malicious Bayesian congestion games. Moreover, we show that for certain congestion games the advent of malicious types can also be beneficial to the system in the sense that the social cost of the worst case equilibrium decreases. We provide a tight bound on the maximum factor by which this happens. 1
Computing equilibria: A computational complexity perspective
, 2009
"... Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications for computation, games, and behavior. We assume
On the complexity of pure Nash equilibria in playerspecific network congestion games
 In WINE ’07
"... Abstract. Network congestion games with playerspecific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NPcomplete to decide whether such games possess pure Nash equilibria. ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract. Network congestion games with playerspecific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NPcomplete to decide whether such games possess pure Nash equilibria. This negative result still holds in the case of games with two players only. In contrast, we show that one can decide in polynomial time whether an equilibrium exists if the number of resources is constant. In addition, we introduce a family of playerspecific network congestion games which are guaranteed to possess equilibria. In these games players have identical delay functions, however, each player may only use a certain subset of the edges. For this class of games we prove that finding a pure Nash equilibrium is PLScomplete even in the case of three players. Again, in the case of a constant number of edges an equilibrium can be computed in polynomial time. We conclude that the number of resources has a bigger impact on the computation complexity of certain problems related to network congestion games than the number of players. 1
On the complexity of Nash equilibria of ActionGraph Games
 In SODA: Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2009
"... In light of much recent interest in finding a model of multiplayer multiaction games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the computational complexity of Nash equilibria in the recently proposed model of actiongraph games (A ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
In light of much recent interest in finding a model of multiplayer multiaction games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the computational complexity of Nash equilibria in the recently proposed model of actiongraph games (AGGs). AGGs, introduced by Bhat and LeytonBrown, are succinct representations of games that encapsulate both local dependencies as in graphical games, and partial indifference to other agents ’ identities as in anonymous games, which occur in many natural settings such as financial markets. This is achieved by specifying a graph on the set of actions, so that the payoff of an agent for selecting a strategy depends only on the number of agents playing each of the neighboring strategies in the action graph. We present a simple Fully Polynomial Time Approximation Scheme for computing mixed Nash equilibria of AGGs with constant degree, constant treewidth and a constant number of agent types (but an arbitrary number of strategies), and extend this algorithm to a broader set of instances. However, the main results of this paper are negative, showing that when either of the latter conditions are relaxed the problem becomes intractable. In particular, we show that even if the action graph is a tree but the number of agenttypes is unconstrained, it is NP– complete to decide the existence of a purestrategy Nash equilibrium and PPAD–complete to compute a mixed Nash equilibrium (even an approximate one). Similarly for AGGs with a constant number of agent types but unconstrained treewidth. These hardness results suggest that, in some sense, our FPTAS is as strong a positive result as one can expect. In the broader context of trying to pin down the boundary where the equilibria of multiplayer games can be computed efficiently, these results complement recent hardness results for graphical games and algorithmic results for anonymous games.
Weighted boolean formula games
 In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE
, 2007
"... We introduce a new class of succinct games, called weighted boolean formula games. Here, each player has a set of boolean formulas he wants to get satisfied. The boolean formulas of all players involve a ground set of boolean variables, and every player controls some of these variables. The payoff o ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We introduce a new class of succinct games, called weighted boolean formula games. Here, each player has a set of boolean formulas he wants to get satisfied. The boolean formulas of all players involve a ground set of boolean variables, and every player controls some of these variables. The payoff of a player is the weighted sum of the values of his boolean formulas. For these games, we consider pure Nash equilibria [42] and their wellstudied refinement of payoffdominant equilibria [30], where every player is no worseoff than in any other pure Nash equilibrium. We study both structural and complexity properties for both decision and search problems with respect to the two concepts: • We consider a subclass of weighted boolean formula games, called mutual weighted boolean formula games, which make a natural mutuality assumption on the payoffs of distinct players. We present a very simple exact potential for mutual weighted boolean formula games. We also prove that each weighted, linearaffine (network) congestion game with playerspecific constants is polynomial, sound NashHarsanyiSelten homomorphic to a mutual weighted boolean formula game. In a general way, we prove that each weighted, linearaffine (network)
Network topology and equilibrium existence in weighted network congestion games
, 2009
"... Abstract. Every finite noncooperative game can be presented as a weighted network congestion game, and also as a network congestion game with playerspecific costs. In the first presentation, different players may contribute differently to congestion, and in the second, they are differently (negativ ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. Every finite noncooperative game can be presented as a weighted network congestion game, and also as a network congestion game with playerspecific costs. In the first presentation, different players may contribute differently to congestion, and in the second, they are differently (negatively) affected by it. This paper shows that the topology of the underlying (undirected twoterminal) network provides information about the existence of purestrategy Nash equilibrium in the game. For some networks, but not for others, every corresponding game has at least one such equilibrium. For the weighted presentation, a complete characterization of the networks with this property is given. The necessary and sufficient condition is that the (undirected) network does not have four routes with the property that no two of them transverse any edge in the opposite directions, or it consists of several such networks connected in series. The corresponding problem for playerspecific costs remains open. Keywords: Congestion games, network topology, existence of equilibrium. 1
The Complexity of Welfare Maximization in Congestion Games
, 2008
"... We investigate issues of complexity related to welfare maximization in congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general c ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We investigate issues of complexity related to welfare maximization in congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and the properties of its associated cost functions. Many of these problem variants turn out to be NPhard, and some are hard to approximate to within any finite factor, unless P = NP. We also identify several versions of the problem that are solvable in polynomial time. 1
The Complexity of Congestion Games
"... We investigate issues of complexity related to congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we ..."
Abstract
 Add to MetaCart
We investigate issues of complexity related to congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and the properties of its associated cost functions. Many of these problem variants are NPhard, and some are hard to approximate. We also identify several versions of the problem that are solvable in polynomial time. 1