Celebrity games

We introduce Celebrity games, a new model of network creation games. In this model players have weights (W being the sum of all the player's weights) and there is a critical distance ß as well as a link cost a. The cost incurred by a player depends on the cost of establishing links to other players and on the sum of the weights of those players that remain farther than the critical distance. Intuitively, the aim of any player is to be relatively close (at a distance less than ß ) from the rest of players, mainly of those having high weights. The main features of celebrity games are that: computing the best response of a player is NP-hard if ß>1 and polynomial time solvable otherwise; they always have a pure Nash equilibrium; the family of celebrity games having a connected Nash equilibrium is characterized (the so called star celebrity games) and bounds on the diameter of the resulting equilibrium graphs are given; a special case of star celebrity games shares its set of Nash equilibrium profiles with the MaxBD games with uniform bounded distance ß introduced in Bilò et al. [6]. Moreover, we analyze the Price of Anarchy (PoA) and of Stability (PoS) of celebrity games and give several bounds. These are that: for non-star celebrity games PoA=PoS=max{1,W/a}; for star celebrity games PoS=1 and PoA=O(min{n/ß,Wa}) but if the Nash Equilibrium is a tree then the PoA is O(1); finally, when ß=1 the PoA is at most 2. The upper bounds on the PoA are complemented with some lower bounds for ß=2.Peer ReviewedPostprint (author's final draft

Stars and celebrities: A network creation game

CoRRCelebrity games, a new model of network creation games is introduced. The specific features of this model are that players have different celebrity weights and that a critical distance is taken into consideration. The aim of any player is to be close (at distance less than critical) to the others, mainly to those with high celebrity weights. The cost of each player depends on the cost of establishing direct links to other players and on the sum of the weights of those players at a distance greater than the critical distance. We show that celebrity games always have pure Nash equilibria and we characterize the family of subgames having connected Nash equilibria, the so called star celebrity games. Exact bounds for the PoA of non star celebrity games and a bound of O(n/ß+ß) for star celebrity games are provided. The upper bound on the PoA can be tightened when restricted to particular classes of Nash equilibria graphs. We show that the upper bound is O(n/ß) in the case of 2-edge-connected graphs and 2 in the case of trees.Preprin

Celebrity games and critical distance

En aquest projecte estudiem el comportament dinàmic del Sum Celebrity i Max Celebrity Games definits per Alvarez et al. 2016 i Àlvarez & Messegué 2016, respectivament. Aquests treballs analitzen les propietats estructurals dels equilibris de Nash junt amb la relació entre el cost social i el cost social òptim (Preu de l'anarquia i Preu de l'estabilitat) d'acord amb els paràmetres que defineixen aquests jocs: alfa o cost de l'enllaç, beta o distància crítica i els pesos de cadascun dels jugadors. En aquest projecte analitzem les diferents dinàmiques dels models del Sum i Max Celebrity Games i la seva convergència a configuracions d'equilibri en funció de la distància crítica. Una dinàmica consisteix en una seqüència de moviments on la política de selecció del jugador i el tipus d'estratègia egoista que el jugador corresponent aplica, pot afectar la convergència. El punt de partida és que en ambdós models calcular la Best Response per a un jugador és computable en temps polinòmic per ß = 1, però NP-hard per ß > 1. A causa d'aquesta diferència en el comportament, els dos casos han estat analitzats per separat. Per ß = 1 hem obtingut que per a tots dos models el problema de calcular un equilibri de Nash és temps polinòmic. A més, en el cas del Max hem demostrat l'existència de cicles en una dinàmica en la qual s'aplica el Best Response, en contraposició amb el Sum on no són possibles. Atès que el problema de calcular la Best Response per a tots dos models quan ß > 1 és NP-hard, hem proposat un model greedy en què les possibles estratègies d'un jugador estan restringides. Tot i que està demostrat l'existència de cicles, no hem trobat experimentalment una instància cíclica per als jocs Sum i Max Greedy Celebrity Games.In this project we study the dynamic behavior of Sum Celebrity and Max Celebrity Games defined in Àlvarez et al. 2016 and Àlvarez & Messegué 2016, respectively. These works analyze the structural properties of the Nash equilibrium graphs and the relationship between the social cost and the optimal social cost (Price of the Anarchy and Price of Stability) according to the parameters that define these games: alpha or cost of each link, beta or critical distance and weights of each of the players. In this project we analyze different dynamics of the Sum and Max Celebrity Games models and their convergence to equilibrium configurations as a function of the critical distance. A dynamics consists of a sequence of movements where both the policy to select the player and the kind of selfish strategy that the corresponding player applies, can affect convergence. The starting point is that in both models the Best Response strategy of a player is computable in polynomial time for ß = 1, but NP-hard for ß > 1. Due to this difference in behavior, both cases have been analyzed separately. For ß = 1 we have obtained that for both models the problem of computing a Nash equilibrium is polynomial time. Furthermore, in the case of Max we have proven the existence of cycles in a Best Response dynamics, in contrast to the Sum where they are not possible. Since the problem of computing a Best Response for both models when ß > 1 is NP-hard, we have proposed a greedy model in which the possible strategies of a player are restricted. Although the existence of cycles is proven, we have not found experimentally a cyclic instance for the Sum and Max Greedy Celebrity Games

Selfish Network Creation with Non-Uniform Edge Cost

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.Comment: To appear at SAGT'1

On the Tree Conjecture for the Network Creation Game

Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.[PODC\u2703] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of alpha per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all alpha and that for alpha >= n all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bounds for both conjectures. In particular we show that for alpha > 4n-13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees

Field of Dreams: Is the Movie Site\u27s Commercialization a Dream Plan With Significant Benefits or a Nightmare Script With Crippling Effects?

This Comment will detail the field’s powerful attraction, discuss and analyze the applicable zoning laws and governing case law associated with comparable property disputes in relation to the present facts, praise the use of tax rebates to help subsidize the project, and assert that the public sector could have established even further requirements for the private business to meet before receiving such substantial public funds