Strategic decentralization in binary choice composite congestion games

Abstract

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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