Martin Hoefer - Academia.edu (original) (raw)

Papers by Martin Hoefer

In recent years several well-known approaches to visualize the topical structure of a document co... more In recent years several well-known approaches to visualize the topical structure of a document collection have been pro- posed. Most of them feature spectral analysis of a term-document matrix with influence values and dimensionality reduc- tion. We generalize this approach by arguing that there are many reasonable ways to project the term-document matrix into low-dimensional space in which different features

We study stable matching problems in networks where players are embedded in a social context, and... more We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. When the benefits from a match are the same for both players, we show that incorporating the well-being of other players into their matching decisions significantly decreases the price of stability, while the price of anarchy remains unaffected. Furthermore, a good stable matching achieving the price of stability bound always exists and can be reached in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different utilities from the match. For this more general case, we show that incorporating social context (i.e., "caring about your friends") can make an even larger difference, and greatly reduce the price of anarchy. We show a variety of existence results, and present upper and lower bounds on the prices of anarchy and stability for various matching utility structures. Finally, we extend most of our results to network contribution games, in which players can decide how much effort to contribute to each incident edge, instead of simply choosing a single node to match with.

Proceedings of the 28th Acm Symposium on Principles of Distributed Computing, Aug 10, 2009

Imitating successful behavior is a natural and frequently applied approach to trust in when facin... more Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents' strategy if the anticipated latency gain is sufficiently large. Our main focus is on convergence properties. Using a potential function argument, we show that our dynamics converge in a monotonic fashion to stable states. In such a state none of the players can improve its latency by imitating somebody else.

Corr, Jul 13, 2008

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting increase in social cost. Our model can be embedded in the framework of congestion games with player-specific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges. In addition to these results for uncoordinated dynamics, we consider a scenario in which a central altruistic institution can motivate agents to act altruistically. We provide constructive and hardness results for finding the minimum number of altruists to stabilize an optimal congestion profile and more general mechanisms to incentivize agents to adopt favorable behavior.

We present algorithms for implementing local spectrum redistribution in wireless networks using a... more We present algorithms for implementing local spectrum redistribution in wireless networks using a mechanism design approach. For example, in single-hop request scheduling, secondary users are modeled as rational agents that have private utility when getting assigned a channel for successful transmission. We present a rather simple algorithmic technique that allows to turn existing and future approximation algorithms and heuristics into truthful mechanisms for a large variety of networking problems. In contrast to previous work, our approach works for virtually all known interference models in the literature, including the physical model of interference based on SINR. It allows to address single-hop and multi-hop scheduling, routing, and even more general assignment and allocation problems. Our mechanisms are randomized and represent the first universally-truthful mechanisms for these problems with rigorous worst-case guarantees on the solution quality. In this way, our mechanisms can be used to obtain guaranteed solution quality even with risk-averse or risk-seeking bidders, for which existing approaches fail.

The main research in the area of image databases addresses the improvement of retrieval quality a... more The main research in the area of image databases addresses the improvement of retrieval quality and the speedup of the query processing. A number of image retrieval systems reached meanwhile a level, where these are used in real-world applications and thus create new demands. In particular dealing with a large, simultaneous number of users and queries requires concepts for resource management, which strongly consider the underlying architecture and the various approaches for image retrieval. This paper is our first step in this direction, as it provides a formal problem specification and prove that this problem is N P-hard.

Acm Transactions on Algorithms, Oct 28, 2014

ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest mod... more ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.

Acm Transactions on Economics and Computation, Dec 1, 2013

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our model can be embedded in the framework of congestion games with playerspecific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges.

Proceedings of the 13th Acm Conference on Electronic Commerce, Jun 4, 2012

We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n... more We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n communication requests need to be allocated to k available channels that are subject to interference and noise. We present the first truthful mechanisms for secondary spectrum auctions with symmetric or submodular valuations. Our approach to model interference uses an edge-weighted conflict graph, and our algorithms provide asymptotically almost optimal approximation bounds for conflict graphs with a small inductive independence number ρ ≪ n. This approach covers a large variety of interference models such as, e.g., the protocol model or the recently popular physical model of interference. For unweighted conflict graphs and symmetric valuations we use LP-rounding to obtain O(ρ)-approximate mechanisms; for weighted conflict graphs we get a factor of O(ρ · (log n + log k)). For submodular users we combine the convex rounding framework of with randomized meta-rounding to obtain O(ρ)-approximate mechanisms for matroid-rank-sum valuations; for weighted conflict graphs we can fully drop the dependence on k to get O(ρ · log n). We conclude with promising initial results for deterministically truthful mechanisms that allow approximation factors based on ρ.

Pdpta, 2005

This paper presents a novel concept for resource management in cluster-based image retrieval syst... more This paper presents a novel concept for resource management in cluster-based image retrieval systems. First, the paper describes image retrieval using static and dynamic feature extraction. The complexity of dynamic feature extraction requires the utilization of powerful parallel architectures and in order to provide the user with reasonable response times. Most existing methods for resource management in parallel image retrieval systems are based on sinlge query execution and do not take quality of service (QoS) aspects into account. This appears not to be practical in large-scale and commercial applications of image databases having a large number of users at any time. In order to allow an efficient utilization of the parallel system and to meet user-defined QoS demands associated with queries, we need to develop a new concept and a novel resource management architecture. Interesting aspects of the model include utility theory, flexible computations, QoS levels, and a hierarchical resource management architecture. Finally, an approach for algorithmic solution is described.

Theoretical Computer Science, 2011

... An intrinsic property of these games is that players allocate resources simultaneously and in... more ... An intrinsic property of these games is that players allocate resources simultaneously and instantly. ... Bhaskar et al. [9] further bound the price of anarchy for different social cost functions and show how to successfully apply Stackelberg strategies in this scenario. ...

Corr, May 28, 2008

In this paper we extend a popular non-cooperative network creation game (NCG) to allow for discon... more In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost \alpha, and the individual cost for a player represents a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the individual cost for a pair of disconnected players to a finite value \beta. Our analysis concentrates on existence, structure, and cost of disconnected Nash and strong equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected Nash (strong) equilibria can evolve. Components of these equilibria must be Nash (strong) equilibria of a smaller NCG. However, in contrast to the NCG, for almost all parameter values no tree is a stable component. Finally, we present a detailed characterization of the price of anarchy that reveals cases in which the price of anarchy is \Theta(n) and thus several orders of magnitude larger than in the NCG. Perhaps surprisingly, the strong price of anarchy increases to at most 4. This indicates that global communication and coordination can be extremely valuable to overcome socially inferior topologies in distributed selfish network design.

Acm Transactions on Internet Technology, Jul 28, 2010

We study combinatorial auctions for the secondary spectrum market. In this market, short-term lic... more We study combinatorial auctions for the secondary spectrum market. In this market, short-term licenses shall be given to wireless nodes for communication in their local neighborhood. In contrast to the primary market, channels can be assigned to multiple bidders, provided that the corresponding devices are well separated such that the interference is sufficiently low. Interference conflicts are described in terms of a conflict graph in which the nodes represent the bidders and the edges represent conflicts such that the feasible allocations for a channel correspond to the independent sets in the conflict graph. In this paper, we suggest a novel LP formulation for combinatorial auctions with conflict graph using a non-standard graph parameter, the so-called inductive independence number. Taking into account this parameter enables us to bypass the well-known lower bound of \Omega(n^{1-\epsilon}) on the approximability of independent set in general graphs with n nodes (bidders). We achieve significantly better approximation results by showing that interference constraints for wireless networks yield conflict graphs with bounded inductive independence number. Our framework covers various established models of wireless communication, e.g., the protocol or the physical model. For the protocol model, we achieve an O(\sqrt{k})-approximation, where k is the number of available channels. For the more realistic physical model, we achieve an O(\sqrt{k} \log^2 n) approximation based on edge-weighted conflict graphs. Combining our approach with the the LP-based framework of Lavi and Swamy, we obtain incentive compatible mechanisms for general bidders with arbitrary valuations on bundles of channels specified in terms of demand oracles.

Several algorithms have been proposed to compute partitions of networks into communities that sco... more Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.

Lecture Notes in Computer Science, 2009

In this paper we consider altruism, a phenomenon widely observed in nature and practical applicat... more In this paper we consider altruism, a phenomenon widely observed in nature and practical applications, in the prominent model of selfish load balancing with coordination mechanisms. Our model of altruistic behavior follows recent work by assuming that agent incentives are a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our results show that even in very simple cases a variety of standard coordination mechanisms are not robust against altruistic behavior, as pure Nash equilibria are absent or better response dynamics cycle. In contrast, we show that a recently introduced Time-Sharing policy yields a potential game even for partially altruistic agents. In addition, for this policy a Nash equilibrium can be computed in polynomial time. In this way our work provides new insights on the robustness of coordination mechanisms. On a more fundamental level, our results highlight the limitations of stability and convergence when altruistic agents are introduced into games with weighted and lexicographical potential functions.

Lecture Notes in Computer Science, 2012

A prevalent assumption in game theory is that all players act in a purely selfish manner, but thi... more A prevalent assumption in game theory is that all players act in a purely selfish manner, but this assumption has been repeatedly questioned by economists and social scientists. In this paper, we study a model that allows to incorporate the social context of players into their decision making. We consider the impact of other-regarding preferences in potential games, one of the most popular and central classes of games in algorithmic game theory. Our results concern the existence of pure Nash equilibria and potential functions in games with social context. The main finding is a tight characterization of the class of potential games that admit exact potential functions for any social context. In addition, we prove complexity results on deciding existence of pure Nash equilibria in numerous popular classes of potential games, such as different classes of load balancing, congestion, cost and market sharing games.

Lecture Notes in Computer Science, 2009

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our model can be embedded in the framework of congestion games with playerspecific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges.

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, 2011

ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest mod... more ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.

In recent years several well-known approaches to visualize the topical structure of a document co... more In recent years several well-known approaches to visualize the topical structure of a document collection have been pro- posed. Most of them feature spectral analysis of a term-document matrix with influence values and dimensionality reduc- tion. We generalize this approach by arguing that there are many reasonable ways to project the term-document matrix into low-dimensional space in which different features

We study stable matching problems in networks where players are embedded in a social context, and... more We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. When the benefits from a match are the same for both players, we show that incorporating the well-being of other players into their matching decisions significantly decreases the price of stability, while the price of anarchy remains unaffected. Furthermore, a good stable matching achieving the price of stability bound always exists and can be reached in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different utilities from the match. For this more general case, we show that incorporating social context (i.e., "caring about your friends") can make an even larger difference, and greatly reduce the price of anarchy. We show a variety of existence results, and present upper and lower bounds on the prices of anarchy and stability for various matching utility structures. Finally, we extend most of our results to network contribution games, in which players can decide how much effort to contribute to each incident edge, instead of simply choosing a single node to match with.

Proceedings of the 28th Acm Symposium on Principles of Distributed Computing, Aug 10, 2009

Imitating successful behavior is a natural and frequently applied approach to trust in when facin... more Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents' strategy if the anticipated latency gain is sufficiently large. Our main focus is on convergence properties. Using a potential function argument, we show that our dynamics converge in a monotonic fashion to stable states. In such a state none of the players can improve its latency by imitating somebody else.

Corr, Jul 13, 2008

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting increase in social cost. Our model can be embedded in the framework of congestion games with player-specific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges. In addition to these results for uncoordinated dynamics, we consider a scenario in which a central altruistic institution can motivate agents to act altruistically. We provide constructive and hardness results for finding the minimum number of altruists to stabilize an optimal congestion profile and more general mechanisms to incentivize agents to adopt favorable behavior.

We present algorithms for implementing local spectrum redistribution in wireless networks using a... more We present algorithms for implementing local spectrum redistribution in wireless networks using a mechanism design approach. For example, in single-hop request scheduling, secondary users are modeled as rational agents that have private utility when getting assigned a channel for successful transmission. We present a rather simple algorithmic technique that allows to turn existing and future approximation algorithms and heuristics into truthful mechanisms for a large variety of networking problems. In contrast to previous work, our approach works for virtually all known interference models in the literature, including the physical model of interference based on SINR. It allows to address single-hop and multi-hop scheduling, routing, and even more general assignment and allocation problems. Our mechanisms are randomized and represent the first universally-truthful mechanisms for these problems with rigorous worst-case guarantees on the solution quality. In this way, our mechanisms can be used to obtain guaranteed solution quality even with risk-averse or risk-seeking bidders, for which existing approaches fail.

The main research in the area of image databases addresses the improvement of retrieval quality a... more The main research in the area of image databases addresses the improvement of retrieval quality and the speedup of the query processing. A number of image retrieval systems reached meanwhile a level, where these are used in real-world applications and thus create new demands. In particular dealing with a large, simultaneous number of users and queries requires concepts for resource management, which strongly consider the underlying architecture and the various approaches for image retrieval. This paper is our first step in this direction, as it provides a formal problem specification and prove that this problem is N P-hard.

Acm Transactions on Algorithms, Oct 28, 2014

ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest mod... more ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.

Acm Transactions on Economics and Computation, Dec 1, 2013

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our model can be embedded in the framework of congestion games with playerspecific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges.

Proceedings of the 13th Acm Conference on Electronic Commerce, Jun 4, 2012

We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n... more We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n communication requests need to be allocated to k available channels that are subject to interference and noise. We present the first truthful mechanisms for secondary spectrum auctions with symmetric or submodular valuations. Our approach to model interference uses an edge-weighted conflict graph, and our algorithms provide asymptotically almost optimal approximation bounds for conflict graphs with a small inductive independence number ρ ≪ n. This approach covers a large variety of interference models such as, e.g., the protocol model or the recently popular physical model of interference. For unweighted conflict graphs and symmetric valuations we use LP-rounding to obtain O(ρ)-approximate mechanisms; for weighted conflict graphs we get a factor of O(ρ · (log n + log k)). For submodular users we combine the convex rounding framework of with randomized meta-rounding to obtain O(ρ)-approximate mechanisms for matroid-rank-sum valuations; for weighted conflict graphs we can fully drop the dependence on k to get O(ρ · log n). We conclude with promising initial results for deterministically truthful mechanisms that allow approximation factors based on ρ.

Pdpta, 2005

This paper presents a novel concept for resource management in cluster-based image retrieval syst... more This paper presents a novel concept for resource management in cluster-based image retrieval systems. First, the paper describes image retrieval using static and dynamic feature extraction. The complexity of dynamic feature extraction requires the utilization of powerful parallel architectures and in order to provide the user with reasonable response times. Most existing methods for resource management in parallel image retrieval systems are based on sinlge query execution and do not take quality of service (QoS) aspects into account. This appears not to be practical in large-scale and commercial applications of image databases having a large number of users at any time. In order to allow an efficient utilization of the parallel system and to meet user-defined QoS demands associated with queries, we need to develop a new concept and a novel resource management architecture. Interesting aspects of the model include utility theory, flexible computations, QoS levels, and a hierarchical resource management architecture. Finally, an approach for algorithmic solution is described.

Theoretical Computer Science, 2011

... An intrinsic property of these games is that players allocate resources simultaneously and in... more ... An intrinsic property of these games is that players allocate resources simultaneously and instantly. ... Bhaskar et al. [9] further bound the price of anarchy for different social cost functions and show how to successfully apply Stackelberg strategies in this scenario. ...

Corr, May 28, 2008

In this paper we extend a popular non-cooperative network creation game (NCG) to allow for discon... more In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost \alpha, and the individual cost for a player represents a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the individual cost for a pair of disconnected players to a finite value \beta. Our analysis concentrates on existence, structure, and cost of disconnected Nash and strong equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected Nash (strong) equilibria can evolve. Components of these equilibria must be Nash (strong) equilibria of a smaller NCG. However, in contrast to the NCG, for almost all parameter values no tree is a stable component. Finally, we present a detailed characterization of the price of anarchy that reveals cases in which the price of anarchy is \Theta(n) and thus several orders of magnitude larger than in the NCG. Perhaps surprisingly, the strong price of anarchy increases to at most 4. This indicates that global communication and coordination can be extremely valuable to overcome socially inferior topologies in distributed selfish network design.

Acm Transactions on Internet Technology, Jul 28, 2010

We study combinatorial auctions for the secondary spectrum market. In this market, short-term lic... more We study combinatorial auctions for the secondary spectrum market. In this market, short-term licenses shall be given to wireless nodes for communication in their local neighborhood. In contrast to the primary market, channels can be assigned to multiple bidders, provided that the corresponding devices are well separated such that the interference is sufficiently low. Interference conflicts are described in terms of a conflict graph in which the nodes represent the bidders and the edges represent conflicts such that the feasible allocations for a channel correspond to the independent sets in the conflict graph. In this paper, we suggest a novel LP formulation for combinatorial auctions with conflict graph using a non-standard graph parameter, the so-called inductive independence number. Taking into account this parameter enables us to bypass the well-known lower bound of \Omega(n^{1-\epsilon}) on the approximability of independent set in general graphs with n nodes (bidders). We achieve significantly better approximation results by showing that interference constraints for wireless networks yield conflict graphs with bounded inductive independence number. Our framework covers various established models of wireless communication, e.g., the protocol or the physical model. For the protocol model, we achieve an O(\sqrt{k})-approximation, where k is the number of available channels. For the more realistic physical model, we achieve an O(\sqrt{k} \log^2 n) approximation based on edge-weighted conflict graphs. Combining our approach with the the LP-based framework of Lavi and Swamy, we obtain incentive compatible mechanisms for general bidders with arbitrary valuations on bundles of channels specified in terms of demand oracles.

Several algorithms have been proposed to compute partitions of networks into communities that sco... more Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.

Lecture Notes in Computer Science, 2009

In this paper we consider altruism, a phenomenon widely observed in nature and practical applicat... more In this paper we consider altruism, a phenomenon widely observed in nature and practical applications, in the prominent model of selfish load balancing with coordination mechanisms. Our model of altruistic behavior follows recent work by assuming that agent incentives are a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our results show that even in very simple cases a variety of standard coordination mechanisms are not robust against altruistic behavior, as pure Nash equilibria are absent or better response dynamics cycle. In contrast, we show that a recently introduced Time-Sharing policy yields a potential game even for partially altruistic agents. In addition, for this policy a Nash equilibrium can be computed in polynomial time. In this way our work provides new insights on the robustness of coordination mechanisms. On a more fundamental level, our results highlight the limitations of stability and convergence when altruistic agents are introduced into games with weighted and lexicographical potential functions.

Lecture Notes in Computer Science, 2012

A prevalent assumption in game theory is that all players act in a purely selfish manner, but thi... more A prevalent assumption in game theory is that all players act in a purely selfish manner, but this assumption has been repeatedly questioned by economists and social scientists. In this paper, we study a model that allows to incorporate the social context of players into their decision making. We consider the impact of other-regarding preferences in potential games, one of the most popular and central classes of games in algorithmic game theory. Our results concern the existence of pure Nash equilibria and potential functions in games with social context. The main finding is a tight characterization of the class of potential games that admit exact potential functions for any social context. In addition, we prove complexity results on deciding existence of pure Nash equilibria in numerous popular classes of potential games, such as different classes of load balancing, congestion, cost and market sharing games.

Lecture Notes in Computer Science, 2009

This paper studies the effects of introducing altruistic agents into atomic congestion games. Alt... more This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our model can be embedded in the framework of congestion games with playerspecific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges.

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, 2011

ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest mod... more ABSTRACT We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.