Delegation equilibrium payoffs in integer-splitting games

Sorin, Sylvain; Wan, Cheng

doi:10.1051/ro/2013026

Cited by 3 publications

(4 citation statements)

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“…If a firm can ex-ante commit itself to delegating the production choice to several smaller franchises, this is equivalent to a commitment to a higher level of production. A rather similar intuition also exists in congestion games: Sorin and Wan (2013) show that a player may benefit from "delegating" itself and not internalizing the congestion externality.…”

Section: Related Literaturementioning

confidence: 74%

Strategic decentralization and the provision of global public goods

Foucart

Wan

2018

Journal of Environmental Economics and Management

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We study strategic decentralization in the provision of a global public good. A federation, with the aim of maximizing the aggregate utility of its members, may find it advantageous to decentralize the decision-making, so that its members act autonomously to maximize their own utility. If utility is fully transferable within a federation, the larger a federation is or the more sensitive it is to the public good, the more it has incentives to remain centralized. If an overall increase in the sensitivity to the public good induces some federation(s) to decentralize, it may lead to a decrease in the aggregate provision. With non-transferable utility within a federation, those members that are smaller or less sensitive to the public good are more likely to prefer decentralization. Some members within a federation becoming more sensitive to the public good may thus lead to a lower aggregate provision, because the increased heterogeneity of the federation makes it more inclined to decentralize.

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Section: Related Literaturementioning

confidence: 74%

Strategic decentralization and the provision of global public goods

Foucart

Wan

2018

Journal of Environmental Economics and Management

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“…Decentralization games in which all the atomic players decentralize simultaneously are worth examining. Another potential extension follows Sorin and Wan 2013 [30], where a deputy can also decentralize, and his deputies as well, and so on. In their case, a player has a finite integer weight and can only have deputies of integer weight.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…One should not deduce from Theorem 3.2 that the study of unilateral decentralization is useless because, once being the first mover, an atomic player need only do what her optimal deputies would have done. As pointed out in Sorin and Wan 2013 [30], in a congestion game, a player's choice has an influence on other players' costs not via her identity (i.e. anonymously) but via the weight of her stock attributing to each particular choice.…”

Section: Unilateral Decentralization and Stackelberg Gamementioning

confidence: 99%

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Strategic decentralization in binary choice composite congestion games

Wan¹

2016

European Journal of Operational Research

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This paper studies strategic decentralization in binary choice composite network congestion games. A player decentralizes if she lets some autonomous agents to decide respectively how to send different parts of her stock from the origin to the destination. This paper shows that, with convex, strictly increasing and differentiable arc cost functions, an atomic splittable player always has an optimal unilateral decentralization strategy. Besides, unilateral decentralization gives her the same advantage as being the leader in a Stackelberg congestion game. Finally, unilateral decentralization of an atomic player has a negative impact on the social cost and on the costs of the other players at the equilibrium of the congestion game.Although the above results are obtained in the specific setting of binary choice games, the goal of this paper is to introduce the notion of strategic decentralization into composite congestion games, to point out its significance, and to initiate a systematic study of its properties.The paper is organized as follows. Section 2 presents the model, defines decentralization, and shows the special role of single-atomic decentralization strategies. Section 3 proves the existence of an optimal unilateral decentralization strategy, and shows that unilateral decen-tralization gives an atomic player the same advantage as being the leader in a Stackelberg congestion game. Section 4 focuses on the impact of unilateral decentralization on the social cost and the other players' cost. Section 5 concludes. The proofs and auxiliary results are regrouped in Section 6. Related literatureThe "inverse" concept of decentralization -coalition formation or collusion between playershas been extensively studied. Hayrapetyan et al. 2006 [13] first define the price of collusion (PoC) of a parallel network to be the ratio between the worst equilibrium social cost after the nonatomic players form disjoint coalitions and the worst equilibrium social cost without coalitions. Bhaskar et al. 2010 [4] extended this study to series-parallel networks. (A seriesparallel network can be constructed by merging in series or in parallel several graphs of parallel arcs.) This index is closely related to another important notion: the price of anarchy (PoA), which is introduced by Koutsoupias and Papadimitriou 1999 [17] (and [22]) as the ratio between the worst equilibrium social cost and the minimal social cost in nonatomic games. Cominetti et al. 2009 [9] derives the first bounds on the PoA with atomic players. For a specific network structure, one can deduce the PoC by the PoA with atomic players and the PoA with nonatomic players. Further results on the bound of the PoA with atomic players are obtained in Harks 2011 [12], Roughgarden and Schoppmann 2011 [28] and Bhaskar et al. 2010 [4]. Roughgarden and Tardos 2002 [29] and Correa et al. 2008 [10] provide fundamental results on the bound of the PoA with nonatomic players. PoA in nonatomic games with asymmetric costs or elastic demands are studied in [23] and [8], among others.

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