Fair Tree Connection Games with Topology-Dependent Edge Cost

How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al. (FOCS'04) and selfish spanning tree games by Gourv\`es and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.Comment: Accepted at FSTTCS 2020, full versio

Geometric network design with selfish agents

A simple non-cooperative network creation game has been introduced in [2]. In this paper we study a geometric version of this game, assuming Euclidean metric edge costs on the plane. The price of anarchy in such geometric games with k players is still Θ(k). Hence, we consider the task of minimizing players incentives to deviate from a payment scheme, purchasing the minimum cost network, which was introduced in [2]. In contrast to general games, in small geometric games (2 players and 2 terminals per player), a Nash equilibrium purchasing the optimum network exists. This can be translated into a (1 + ɛ)-approximate Nash equilibrium purchasing the optimum network using some more practical assumptions, for any ɛ> 0. For more players, however, there are games with 2 terminals per player, such that any Nash equilibrium purchasing the optimum solution is at least � 4 3 − ɛ�-approximate. On the algorithmic side, we show that playing small games with best-response strategies yields low-cost Nash equilibria. The distinguishing feature of our paper is the fact that we needed to develop new techniques to deal with the geometric setting, which are fundamentally different from the techniques used in [2] for general games.