On the Shortest Path Game

Darmann, Andreas; Pferschy, Ulrich; Schauer, Joachim

doi:10.1016/j.dam.2015.08.003

Cited by 5 publications

(8 citation statements)

References 12 publications

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“…This situation was studied for other combinatorial optimization problems and two agents, e.g. in Darmann et al (2016). When dealing with k-agent scheduling, it would be interesting to identify polynomially solvable special cases, either by restricting the scheduling environment or the agents' strategies.…”

Section: Discussionmentioning

confidence: 99%

Competitive multi-agent scheduling with an iterative selection rule

2017

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In this work we address a class of deterministic scheduling problems in which k agents compete for the usage of a single machine. The agents have their own objective functions and submit their tasks in successive steps to an external coordination subject, who sequences them by selecting the shortest task in each step. We look at the problem in two different settings and consider different combinations of cost functions. In a centralized perspective, generalizing previous results for the case with k = 2 agents, we characterize the set of Pareto efficient solutions as for a classical multicriteria optimization problems. On one hand we determine the number of Pareto efficient solutions and on the other hand we study the computational complexity of the associated decision problem. Then, we consider the problem from a single agent perspective. In particular, we provide a worst-case analysis on the performance of two natural heuristic algorithms, SPT and WSPT, that suggest to an agent how to sequence its own tasks when its objective is makespan, sum of completion times, or sum of weighted completion times.

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Section: Discussionmentioning

confidence: 99%

Competitive multi-agent scheduling with an iterative selection rule

2017

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“…Thus, we can describe a rather precise boundary between polynomially solvable and hard graph classes. Note that the latter result is somewhat surprising given the fact that the related Shortest Path Game is easy to solve on cactus graphs (see Darmann et al [4]).…”

Section: Related Literature and Our Contributionmentioning

confidence: 99%

“…The game described above can be represented as a finite game in extensive form. All feasible decisions for the players can be represented in a game tree, where each node corresponds to the decision of a certain player in a vertex of the graph G. A similar representation was given in [4] for Shortest Path Game (see also Section 1.2).…”

Section: Game Theoretic Settingmentioning

confidence: 99%

“…Recently, Darmann et al [4] (see also Darmann et al [3]) considered the closely related Shortest Path Game where two players move together from a joint origin to a joint destination and take turns in selecting the next edge. The player choosing an edge has to pay its cost, and each of the players is aiming at minimizing its own total cost.…”

Section: Related Literature and Our Contributionmentioning

confidence: 99%

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The Shortest Connection Game

Darmann¹,

Pferschy²,

Schauer³

2015

Preprint

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We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently located at. In this way, each of the players forms a path that origins from its respective starting vertex. The game ends as soon as the two paths meet, i.e., a connection between the players is established. Each player has to carry the cost of its chosen edges and thus aims at minimizing its own total cost.In this work we analyze the computational complexity of Shortest Connection Game. On the negative side, Shortest Connection Game turns out to be computationally hard even on restricted graph classes such as bipartite, acyclic and cactus graphs. On the positive side, we can give a polynomial time algorithm for cactus graphs when the game is restricted to simple paths.

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“…On the other hand, f prop necessitates knowledge of A sf and B sf , which in general require exponential time to be computed. A recent paper by Darmann et al (2014b) studies the computational complexity of the related path game in general and on graphs with special structures.…”

Section: Formal Frameworkmentioning

confidence: 99%

Sharing the Cost of a Path

Darmann

Klamler

Pferschy

2015

Studies in Microeconomics

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In recent years, many authors have analyzed fair division aspects in problems containing network structures. Frequently, the connection of all vertices of the network, that is, a minimum cost spanning tree, and the sharing of its cost was considered. In this article, we study the fair division of costs of connecting two designated vertices by a path. Specifically, we will introduce two cost-sharing rules that provide a division of the costs of forming a shortest path. One of the cost-sharing rules will include aspects from non-cooperative extensive form games in the sense that selfish and individually rational behaviour without agreement between the agents in a sequential structure is taken into account for the determination of the cooperative solution. The other cost-sharing rule is based on an alternating structure along the shortest path. Axiomatic characterizations of the two cost-sharing rules are provided.

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On the Shortest Path Game

Cited by 5 publications

References 12 publications

Competitive multi-agent scheduling with an iterative selection rule

Competitive multi-agent scheduling with an iterative selection rule

The Shortest Connection Game

Sharing the Cost of a Path

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