Abstract: We consider algorithmic questions concerning the existence,
tractability and quality of atomic congestion games, among users that
are considered to participate in (static) selfish coalitions. We carefully
define a coalitional congestion model among atomic players.
Our findings in this model are quite interesting, in the sense that we
demonstrate many similarities with the non–cooperative case. For example,
there exist potentials proving the existence of Pure Nash Equilibria
(PNE) in the (even unrelated) parallel links setting; the Finite Improvement
Property collapses as soon as we depart from linear delays, but
there is an exact potential (and thus PNE) for the case of linear delays,
in the network setting; the Price of Anarchy on identical parallel
links demonstrates a quite surprising threshold behavior: it persists on
being asymptotically equal to that in the case of the non–cooperative
KP–model, unless we enforce a sublogarithmic number of coalitions.
We also show crucial differences, mainly concerning the hardness of algorithmic
problems that are solved efficiently in the non–cooperative case.
Although we demonstrate convergence to robust PNE, we also prove the
hardness of computing them. On the other hand, we can easily construct
a generalized fully mixed Nash Equilibrium. Finally, we propose a new
improvement policy that converges to PNE that are robust against (even
dynamically forming) coalitions of small size, in pseudo–polynomial time.
Keywords. Game Theory, Atomic Congestion Games, Coalitions, Convergence
to Equilibria, Price of Anarchy.

Abstract: We consider algorithmic questions concerning the existence,
tractability and quality of atomic congestion games, among users that
are considered to participate in (static) selfish coalitions. We carefully
define a coalitional congestion model among atomic players.
Our findings in this model are quite interesting, in the sense that we
demonstrate many similarities with the non–cooperative case. For example,
there exist potentials proving the existence of Pure Nash Equilibria
(PNE) in the (even unrelated) parallel links setting; the Finite Improvement
Property collapses as soon as we depart from linear delays, but
there is an exact potential (and thus PNE) for the case of linear delays,
in the network setting; the Price of Anarchy on identical parallel
links demonstrates a quite surprising threshold behavior: it persists on
being asymptotically equal to that in the case of the non–cooperative
KP–model, unless we enforce a sublogarithmic number of coalitions.
We also show crucial differences, mainly concerning the hardness of algorithmic
problems that are solved efficiently in the non–cooperative case.
Although we demonstrate convergence to robust PNE, we also prove the
hardness of computing them. On the other hand, we can easily construct
a generalized fully mixed Nash Equilibrium. Finally, we propose a new
improvement policy that converges to PNE that are robust against (even
dynamically forming) coalitions of small size, in pseudo–polynomial time.
Keywords. Game Theory, Atomic Congestion Games, Coalitions, Convergence
to Equilibria, Price of Anarchy.

Abstract: This chapter is an introduction to the basic concepts and advances of a new field, that of Computational (or Algorithmic) Game Theory. We study the computational complexity of Nash equilibria and review the related algorithms proposed in the literature. Then, given the apparent difficulty of computing exact Nash equilibria, we study the efficient computation of approximate notions of Nash equilibria. Next we deal with several computational issues related to the class of congestion games, which model the selfishbehavior of individuals when competing on the usage of a common set of resources. Finally, we study the price of anarchy (in the context of congestion games), which is defined as a measure of the performance degradation due to the the lack of coordination among the involved players.

Abstract: In large scale networks users often behave selfishly trying to minimize their routing cost. Modelling this as a noncooperative game, may yield a Nash equilibrium with unboundedly poor network performance. To measure this inefficacy, the Coordination Ratio or Price of Anarchy (PoA) was introduced. It equals the ratio of the cost induced by the worst Nash equilibrium, to the corresponding one induced by the overall optimum assignment of the jobs to the network. On improving the PoA of a given network, a series of papers model this selfishbehavior as a Stackelberg or Leader-Followers game.
We consider random tuples of machines, with either linear or M/M/1 latency functions, and PoA at least a tuning parameter c. We validate a variant (NLS) of the Largest Latency First (LLF) Leaderrsquos strategy on tuples with PoA ge c. NLS experimentally improves on LLF for systems with inherently high PoA, where the Leader is constrained to control low portion agr of jobs. This suggests even better performance for systems with arbitrary PoA. Also, we bounded experimentally the least Leaderrsquos portion agr0 needed to induce optimum cost. Unexpectedly, as parameter c increases the corresponding agr0 decreases, for M/M/1 latency functions. All these are implemented in an extensive Matlab toolbox.

Abstract: We study a problem of scheduling client requests to servers. Each client has a particular latency requirement at each server and may choose either to be assigned to some server in order to get serviced provided that her latency requirement is met, or not to participate in the assignment at all. From a global perspective, in order to optimize the performance of such a system, one would aim to maximize the number of clients that participate in the assignment. However, clients may behave selfishly in the sense that, each of them simply aims to participate in an assignment and get serviced by some server where her latency requirement is met with no regard to overall system performance. We model this selfishbehavior as a strategic game, show how to compute pure Nash equilibria efficiently, and assess the impact of selfishness on system performance. We also show that the problem of optimizing performance is computationally hard to solve, even in a coordinated way, and present efficient approximation and online algorithms.

Abstract: We study a problem of scheduling client requests to servers.
Each client has a particular latency requirement at each server and may
choose either to be assigned to some server in order to get serviced provided
that her latency requirement is met or not to participate in the
assignment at all. From a global perspective, in order to optimize the
performance of such a system, one would aim to maximize the number
of clients that participate in the assignment. However, clients may behave
selfishly in the sense that each of them simply aims to participate
in an assignment and get serviced by some server where her latency requirement
is met with no regard to the overall system performance. We
model this selfishbehavior as a strategic game, show how to compute
equilibria efficiently, and assess the impact of selfishness on system performance.
We also show that the problem of optimizing performance is
computationally hard to solve, even in a coordinated way, and present
efficient approximation and online algorithms.

Abstract: We present SeAl1, a novel data/resource and data-access management infrastructure designed for the purpose of addressing a key problem in P2P data sharing networks, namely the problem of wide-scale selfish peer behavior. Selfishbehavior has been manifested and well documented and it is widely accepted that unless this is dealt with, the scalability, efficiency, and the usefulness of P2P sharing networks will be diminished. SeAl essentially consists of a monitoring/accounting subsystem, an auditing/verification subsystem, and incentive mechanisms. The monitoring subsystem facilitates the classification of peers into selfish/altruistic. The auditing/verification layer provides a shield against perjurer/slandering and colluding peers that may try to cheat the monitoring subsystem. The incentives mechanisms efectively utilize these layers so to increase the computational/networking and data resources that are available to the community. Our extensive performance results show that SeAl performs its tasks swiftly, while the overhead introduced by our accounting and auditing mechanisms in terms of response time, network, and storage overheads are very small.

Abstract: We present SeAl, a novel data/resource and data-access management infrastructure designed for the purpose of addressing a key problem in P2P data sharing networks, namely the problem of wide-scale selfish peer behavior. Selfishbehavior has been manifested and well documented and it is widely accepted that unless this is dealt with, the scalability, efficiency, and the usefulness of P2P sharing networks will be diminished. SeAl essentially consists of a monitoring/accounting subsystem, an auditing/verification subsystem, and incentive mechanisms. The monitoring subsystem facilitates the classification of peers into selfish/altruistic. The auditing/verification layer provides a shield against perjurer/slandering and colluding peers that may try to cheat the monitoring subsystem. The incentives mechanisms effectively utilize these layers so to increase the computational/networking and data resources that are available to the community. Our extensive performance results show that SeAl performs its tasks swiftly, while the overhead introduced by our accounting and auditing mechanisms in terms of response time, network, and storage overheads are very small.

Abstract: We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non–cooperative and each wishes to follow strategies that minimize her own latency with no regard to the global optimum. Previous work has studied the impact of this selfishbehavior to system performance. In this paper, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfishbehavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.