Coalitional games on graphs: core structure, substitutes and frugality

We study mechanisms that can be modelled as coalitional games with transferable utilities, and apply ideas from mechanism design and game theory to problems arising in a network design setting. We establish an equivalence between the game-theoretic notion of agents being substitutes and the notion of frugality of a mechanism. We characterize the core of the network design game and relate it to outcomes in a sealed bid auction with VCG payments. We show that in a game, agents are substitutes if and only if the core of the forms a complete lattice. We look at two representative games – Minimum Spanning Tree and Shortest Path – in this light.

• Type: Conference
• Year: 2003
• Where: SIGECOM
• Authors: Rahul Garg, Vijay Kumar, Atri Rudra, Akshat Verma
• Keywords: Game-theoretic Notion, Network Design, Sealed Bid Auction, SIGECOM 2003