Customer and Cost Sharing in a Jackson Network

Timmer, Judith B.; Scheinhardt, Willem R.W.

doi:10.1142/s0219198918500020

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…In security, queueing theory is used to model stochastic elements in interdiction games [13,27]. A cooperative game on a network of single server queues is introduced in [24,25], where each server in this network is considered to be a player. In [24] the players are allowed to cooperate by redistributing their service rates over the nodes in order to minimize the long-run expected queue length, whereas in [25] the players cooperate by redistributing the arrival rates of the customers.…”

Section: Introductionmentioning

confidence: 99%

Non-cooperative queueing games on a network of single server queues

2021

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This paper introduces non-cooperative games on a network of single server queues with fixed routes. A player has a set of routes available and has to decide which route(s) to use for its customers. Each player’s goal is to minimize the expected sojourn time of its customers. We consider two cases: a continuous strategy space, where each player is allowed to divide its customers over multiple routes, and a discrete strategy space, where each player selects a single route for all its customers. For the continuous strategy space, we show that a unique pure-strategy Nash equilibrium exists that can be found using a best-response algorithm. For the discrete strategy space, we show that the game has a Nash equilibrium in mixed strategies, but need not have a pure-strategy Nash equilibrium. We show the existence of pure-strategy Nash equilibria for four subclasses: (i) N-player games with equal arrival rates for the players, (ii) 2-player games with identical service rates for all nodes, (iii) 2-player games on a $$2\times 2$$ 2 × 2 -grid, and (iv) 2-player games on an $$A\times B$$ A × B -grid with small differences in the service rates.

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Section: Introductionmentioning

confidence: 99%

Non-cooperative queueing games on a network of single server queues

2021

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“…The theoretical game techniques have been quite successfully used in computer science [13][14][15][16] and other engineering disciplines [17,18]. 6 The literature on network formation is vast.…”

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confidence: 99%

Formation of Stable and Efficient Social Storage Cloud

Mane

Krishnamurthy

Ahuja

2019

Games

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In this paper, we study the formation of endogenous social storage cloud in a dynamic setting, where rational agents build their data backup connections strategically. We propose a degree-distance-based utility model, which is a combination of benefit and cost functions. The benefit function of an agent captures the expected benefit that the agent obtains by placing its data on others’ storage devices, given the prevailing data loss rate in the network. The cost function of an agent captures the cost that the agent incurs to maintain links in the network. With this utility function, we analyze what network is likely to evolve when agents themselves decide with whom they want to form links and with whom they do not. Further, we analyze which networks are pairwise stable and efficient. We show that for the proposed utility function, there always exists a pairwise stable network, which is also efficient. We show that all pairwise stable networks are efficient, and hence, the price of anarchy is the best that is possible. We also study the effect of link addition and deletion between a pair of agents on their, and others’, closeness and storage availability.

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“…In this chapter, we discuss a game on a Jackson network. The cooperative variant of Jackson games is introduced by Timmer and Scheinhardt in [121,122]. This game is played on a network of M/M/1 queues and each server in this network is considered as a player.…”

Section: Introductionmentioning

confidence: 99%

“…In [121], the authors analyze the game where the players are allowed to cooperate by redistributing their service rates over the nodes in order to minimize the lung run expected queue length. In [122], a similar game is considered where the players cooperate by redistributing the arrival rates of the customers. We introduce the non-cooperative variant of this sgame and analyze for several cases the existence of a Nash equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Games for the optimal deployment of security forces

Laan

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CHAPTER 1 is already known. Therefore, the game value for Stackelberg equilibria can be different from the game values for Nash equilibria. However, in this thesis, we mainly consider zero-sum games (in which the gain for one player equals the loss for the other player) and for these games, the game value and agent's strategy coincide [133]. In the following example, we give a basic security game to explain the different game elements. Example 1.1 (Basic security game). Consider a patrolling game on a part of the North Sea which can be divided into two areas A and B. Since this is a protected area, it is not allowed to fish in A and B. However, in both areas, there is a lot of fish available, so these are popular places for fishermen (intruder) to fish illegally. To prevent illegal fishing in both areas, the coast guard (agent) has one patrolling ship available. This ship is able to patrol and protect one area from illegal fishing each day. At the beginning of a day, the intruder chooses one area to fish. When the intruder fishes successfully, i.e., without being caught by the agent, he obtains a gain. Assume that fishing in B is better than in A: the gain of successfully fishing in area A equals 3 and for area B, the fisherman's gain equals 5. The gain for the intruder equals the loss for the agent if he is patrolling the area where the intruder is not fishing. However, when the agent is patrolling the area where the intruder is fishing, the intruder is caught and the gain for the agent equals 1 (which is also the loss for the intruder). The game above can be described in a matrix displaying the actions and payoffs for all players. In this game, the matrix is given by:

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Customer and Cost Sharing in a Jackson Network

Cited by 5 publications

References 9 publications

Non-cooperative queueing games on a network of single server queues

Non-cooperative queueing games on a network of single server queues

Formation of Stable and Efficient Social Storage Cloud

Games for the optimal deployment of security forces

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