Competitive Online Multicommodity Routing

Harks, Tobias; Stefan, Heinz G.; Pfetsch, Marc E.

doi:10.1007/s00224-009-9187-5

Cited by 15 publications

References 24 publications

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The Online Best Reply Algorithm for Resource Allocation Problems

Klimm¹,

Schmand

Tönnis

2019

Algorithmic Game Theory

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We study online resource allocation problems with a diseconomy of scale. In these problems, there are certain requests, each demanding a set of resources, that arrive in an online manner. The cost of each resource is semi-convex and grows superlinearly in the total load on the resource. An irrevocable allocation decision has to be made directly after the arrival of each request with the goal to minimize the total cost on the resources. We focus on two simple greedy online policies that provide very fast and easy approximation algorithms.The first policy is to minimize the individual cost of the current online request with respect to all previous requests that have been allocated before. The second policy is to minimize the marginal total cost over all requests that have arrived up to this point. In the literature, these type of algorithms is also considered as one-round walks in congestion games starting from the empty state.We consider the weighted and unweighted version of the problem. In the weighted variant, and for cost functions that are polynomials with maximal degree d and positive coefficients, we proof a tight competitive ratio of d √ 2 − 1 −(d+1) for the marginal total cost policy. This interestingly exactly matches the approximation factor for the corresponding multiple-round walk algorithm. Our work indicates that one-round walks that start in an empty starting state are exactly as efficient as multiple-round walks. We also show that this does not carry over to the unweighted version of the problem. For unweighted instances, we provide lower bounds for both policies that are significantly larger than the corresponding multiple-round walks. We complement our results with an upper and lower bound on the solution quality of the personal cost policy for weighted and unweighted instances.

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The Online Best Reply Algorithm for Resource Allocation Problems

Klimm¹,

Schmand

Tönnis

2019

Algorithmic Game Theory

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Routing Games over Time with FIFO Policy

Ismaili

2017

Web and Internet Economics

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We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a first-in-first-out queue and may wait: an edge is associated with a capacity, which defines how many agents-pertime-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.(a) Static routing games were a crucial testbed for the Price of Anarchy, a concept that bounds a game's loss of efficiency due to selfish behaviors.

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The quality of equilibria for set packing and throughput scheduling games

Jong

Uetz

2019

Int J Game Theory

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We introduce set packing games as an abstraction of situations in which n selfish players select subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this class of games. Assuming that players are able to approximately play equilibrium strategies, we show that the total quality of the resulting equilibrium solutions is only moderately suboptimal. Our results are tight bounds on the price of anarchy for three equilibrium concepts, namely Nash equilibria, subgame perfect equilibria, and an equilibrium concept that we refer to as k-collusion Nash equilibrium.

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Competitive Online Multicommodity Routing

Cited by 15 publications

References 24 publications

The Online Best Reply Algorithm for Resource Allocation Problems

The Online Best Reply Algorithm for Resource Allocation Problems

Routing Games over Time with FIFO Policy

The quality of equilibria for set packing and throughput scheduling games

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