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Networkformation games with regular objectives
 In Proc. 17th FoSSaCS, LNCS 8412
, 2014
"... Abstract. Classical networkformation games are played on a directed graph. Players have reachability objectives, and each player has to select a path satisfying his objective. Edges are associated with costs, and when several players use the same edge, they evenly share its cost. The theoretical a ..."
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Abstract. Classical networkformation games are played on a directed graph. Players have reachability objectives, and each player has to select a path satisfying his objective. Edges are associated with costs, and when several players use the same edge, they evenly share its cost. The theoretical and practical aspects of networkformation games have been extensively studied and are well understood. We introduce and study networkformation games with regular objectives. In our setting, the edges are labeled by alphabet letters and the objective of each player is a regular language over the alphabet of labels, given by means of an automaton or a temporallogic formula. Thus, beyond reachability properties, a player may restrict attention to paths that satisfy certain properties, referring, for example, to the providers of the traversed edges, the actions associated with them, their quality of service, security, etc. Unlike the case of networkformation games with reachability objectives, here the paths selected by the players need not be simple, thus a player may traverse some transitions several times. Edge costs are shared by the players with the share being proportional to the number of times the transition is traversed. We study the existence of a pure Nash equilibrium (NE), convergence of bestresponsedynamics, the complexity of finding the social optimum, and the inefficiency of a NE compared to a socialoptimum solution. We examine several classes of networks (for example, networks with uniform edge costs, or alphabet of size 1) and several classes of regular objectives. We show that many properties of classical networkformation games are no longer valid in our game. In particular, a pure NE might not exist and the Price of Stability equals the number of players (as opposed to logarithmic in the number of players in the classic setting, where a pure NE always exists). In light of these results, we also present special cases for which the resulting game is more stable. 1
1On the Sequential Price of Anarchy of Isolation Games
"... In competitive location games [2] players aim at choosing suitable locations or points in given metric spaces so as to maximize their utility or revenue. Depending on different parameters such as the underlying metric space, the number of players, the adopted solution concept, the customers ’ behav ..."
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In competitive location games [2] players aim at choosing suitable locations or points in given metric spaces so as to maximize their utility or revenue. Depending on different parameters such as the underlying metric space, the number of players, the adopted solution concept, the customers ’ behavior and so on, several scenarios arise. In this work we consider isolation games [6], a class of competitive location games in which the utility of a player is defined as a function of her distances from the other ones in an underlying edgeweighted graph. For example, one can define the utility of a player as being equal to the distance from the nearest one (nearestneighbor isolation game), or to the sum of the distances from all the other players (totaldistance isolation game). Isolation games find a natural application in data clustering and geometric sampling. Moreover, as pointed out in [6], they can be used to obtain a good approximation of the strategy a player should compute in another competitive location game, called Voronoi game, which is among the most studied competitive location games. Here, the utility of a player is given by the total number of all points that are closer to her than to any other player (Voronoi area), where points which are equidistant to several players are evenly split up among them. As another interesting field of application for isolation games,
The Sequential Price Of Anarchy for Atomic Congestion Games
"... Abstract. In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, we consider games where players choose their actions sequentially. The ..."
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Abstract. In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos Model and Notation We consider atomic congestion games with affine cost functions. The input of an instance I ∈ I consists of a finite set of resources R, a finite set of players N = {1, . . . , n}, and for each player i ∈ N a collection A i of possible actions A i ⊆ R. We say a resource r ∈ R is chosen by player i if r ∈ A i , where A i is the action chosen by player i. By A = (A i ) i∈N we denote a possible outcome, that is, a complete profile of actions chosen by all players i ∈ N . Each resource r ∈ R has a constant activation cost d r ≥ 0 and a variable cost or weight w r ≥ 0 that expresses the fact that the resource gets more congested the more players choose it. The total cost of resource r ∈ R, for outcome A, is then f r (A) = d r +w r ·n r (A), where n r (A) denotes the number of players choosing resource r in A. Given outcome A, the total cost of all resources chosen by player i is cost i (A) = r∈Ai f r (A). Players aim to minimize their costs. The total cost over all players of an outcome A is denoted by cost(A) = i∈N cost i (A). Note that this class of problems includes as a special case the celebrated network routing games as studied e.g. in Research supported by CTIT (www.ctit.nl) and 3TU.AMI (www.3tu.nl), project "Mechanisms for Decentralized Service Systems".
1 SmartAssoc: Decentralized Access Point Selection Algorithm to Improve Throughput (Supplementary File)
"... In this supplementary file, we examine the network performance in terms of competitive ratio and convergence if selfish strategy is applied, and provide detailed proofs of theorems stated in the main manuscript. 1 SELFISH USER STRATEGY One natural alternative to solving the association problem, with ..."
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In this supplementary file, we examine the network performance in terms of competitive ratio and convergence if selfish strategy is applied, and provide detailed proofs of theorems stated in the main manuscript. 1 SELFISH USER STRATEGY One natural alternative to solving the association problem, with respect to our goal, is to let the clients behave myopically by applying in decentralized AP selection the bestreply policy. Explicitly, it means that every user keeps moving to associate with the AP that could offer it the best throughput until no user can gain higher throughput by unilaterally deviating from its current decision (Nash Equilibrium). To simplify the analysis for selfish users, we make two assumptions in this section. In the next section, we will use a more realistic assumptions. First, we assume that the interference between the communications of two APs is not considered, i.e., the nearby APs operate on orthogonal channels. Second, the association procedure of a user is considered as an atomic operation, so only one user performs the association at a time. The time at which a user makes a decision to change APs is marked as a decision step. However, we do not require users to follow a certain decision order, which means in each decision step the user who is picking a new AP could be any one.
Load Rebalancing Games in Dynamic Systems with Migration Costs
, 2013
"... We consider the following dynamic load balancing game: Given an initial assignment of jobs to identical parallel machines, the system is modified; specifically, some machines are added or removed. Each job’s cost is the load on the machine it is assigned to; thus, when machines are added, jobs have ..."
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We consider the following dynamic load balancing game: Given an initial assignment of jobs to identical parallel machines, the system is modified; specifically, some machines are added or removed. Each job’s cost is the load on the machine it is assigned to; thus, when machines are added, jobs have an incentive to migrate to the new unloaded machines. When machines are removed, the jobs assigned to them must be reassigned. Consequently, other jobs might also benefit from migrations. In our jobextension penalty model, for a given extension parameter δ ≥ 0, if the machine on which a job is assigned to in the modified schedule is different from its initial machine, then the job’s processing time is extended by δ. We provide answers to the basic questions arising in this model. Namely, the existence and calculation of a Nash Equilibrium and a Strong Nash Equilibrium, and their inefficiency compared to an optimal schedule. Our results show that the existence of jobmigration penalties might lead to poor stable schedules; however, if the modification is a result of a sequence of improvement steps or, better, if the sequence of improvement steps can be supervised in some way (by forcing the jobs to play in a specific order) then any stable modified schedule approximates well an optimal one. Our work adds two realistic considerations to the study of job scheduling games: the analysis of the common situation in which systems are upgraded or suffer from failures, and the practical fact according to which job migrations are associated with a cost. 1
Equilibrium in Combinatorial Public Projects
"... Abstract. We study simple item bidding mechanisms for the combinatorial public project problem and explore their eciency guarantees in various wellknown solution concepts. We rst study sequential mechanisms where each agent, in sequence, reports her bid for every item in a prede ned order on the ..."
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Abstract. We study simple item bidding mechanisms for the combinatorial public project problem and explore their eciency guarantees in various wellknown solution concepts. We rst study sequential mechanisms where each agent, in sequence, reports her bid for every item in a prede ned order on the agents determined by the mechanism. We show that if agents ' valuations are unitdemand any subgame perfect equilibrium of a sequential mechanism achieves the optimal social welfare. For the simultaneous bidding equivalent of the above auction we show that for any class of bidder valuations, all Strong Nash Equilibria achieve at least a O(logn) factor of the optimal social welfare. For Pure Nash Equilibria we show that the worstcase loss in eciency is proportional to the number of agents. For public projects in which only one item is selected we show constructively that there always exists a Pure Nash Equilibrium that guarantees at least 1 2 (1 1 n) of the optimum. We also show eciency bounds for Correlated Equilibria and BayesNash Equilibria, via the recent smooth mechanism framework [26]. 1
Sequential Scheduling on Identical Machines
, 2014
"... We study a sequential version of the wellknown KPmodel: Each of n agents has a job that needs to be processed on any of m machines. Agents sequentially select a machine for processing their jobs. The goal of each agent is to minimize the finish time of his machine. We study the corresponding seque ..."
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We study a sequential version of the wellknown KPmodel: Each of n agents has a job that needs to be processed on any of m machines. Agents sequentially select a machine for processing their jobs. The goal of each agent is to minimize the finish time of his machine. We study the corresponding sequential price of anarchy for m identical machines under arbitrary and LPT orders, and suggest insights into the case of two unrelated machines. Keywords: sequential price of anarchy, machine scheduling, congestion games, load balancing, subgameperfect equilibrium, makespan minimization. 1