Locality-based network creation games

Abstract

Network creation games have been extensively studied, both from economists and computer scientists, due to their versatility in modeling individual-based community formation processes, which in turn are the theoretical counterpart of several economics, social, and computational applications on the Internet. In their several variants, these games model the tension of a player between her two antagonistic goals: to be as close as possible to the other players, and to activate a cheapest possible set of links. However, the generally adopted assumption is that players have a common and complete information about the ongoing network, which is quite unrealistic in practice. In this paper, we consider a more compelling scenario in which players have only limited information about the network they are embedded in. More precisely, we explore the game-theoretic and computational implications of assuming that players have a complete knowledge of the network structure only up to a given radius k, which is one of the most qualified local-knowledge models used in distributed computing. To this respect, we define a suitable equilibrium concept, and we provide a comprehensive set of upper and lower bounds to the price of anarchy for the entire range of values of k, and for the two classic variants of the game, namely those in which a player's cost -besides the activation cost of the owned links -depends on the maximum/sum of all the distances to the other nodes in the network, respectively. These bounds are finally assessed through an extensive set of experiments.

Coalition Resilient Outcomes in Max k-Cut Games

“…Finally, they show that the dynamics, where at each step a coalition can deviate so that all of its members strictly improve their utility by changing strategy, can cycle. The main consequence of this latter fact is that no strong potential function 4 can exist for the game, and hence the existence of an SE cannot be proved by simply exhibiting it. It is worth noticing that strong potential functions are one of the main tools used to prove the existence of an SE.…”

“…Concerning local coalitions, a notion of equilibrium close in spirit to our LSE has been studied in the context of network design games in [19]. Moreover, locality aspects have been also considered when restricting the strategy space in single-player deviations (see for example [4,10]).…”

An Improved Bound for the Tree Conjecture in Network Creation Games

“…We remark that numerous extensions and variations of the network creation game have also been studied; we refer the interested reader to [2,4,5,7,8,9].…”

Network Creation Games: Think Global – Act Local

“…Yet, due to the size and dynamics of those networks, this assumption is hard to justify. Only recently, Bilò et al [6] introduced the first variant of the popular (and mathematically beautiful) model by Fabrikant et al [11] that explicitly incorporates a locality constraint. In this model, the selfish agents are nodes in a network which can buy arbitrary incident edges.…”

“…To the best of our knowledge, the only models in the realm of NCGs that consider locality constraints are [6] and [7]. As discussed above, both model the local knowledge in a very pessimistic way.…”