Geometric spanner games

Abstract

Consider a scenario in which several agents are located in the Euclidean space, and the agents want to create a network in which everyone has fast access to all or some other agents. Geometric t-spanners are examples of such a network providing fast connections between the nodes of the network for some fixed value t, i.e. the length of the shortest path between any two nodes in the network is at most t times their Euclidean distance. Geometric t-spanners have been extensively studied in the area of computational geometry where they are created by a central authority. In this paper, we investigate a situation in which selfish agents want to create such a network in the absence of a central authority. To this end, we introduce two different non-cooperative games: the t-spanner game and the sink t-spanner game, where it is vital for the agents to have a fast connection to all other agents or to a special node, respectively. We study the existence of the Nash equilibrium in both games and present some structural properties of the resulting networks in the Nash equilibrium.