Bounding the Inefficiency of Altruism Through Social Contribution Games

We introduce a new class of games, called social contribution games (SCGs), where each player's individual cost is equal to the cost he induces on society because of his presence. Our results reveal that SCGs constitute useful abstractions of altruistic games when it comes to the analysis of the robust price of anarchy. We first show that SCGs are altruism-independently smooth, i.e., the robust price of anarchy of these games remains the same under arbitrary altruistic extensions. We then devise a general reduction technique that enables us to reduce the problem of establishing smoothness for an altruistic extension of a base game to a corresponding SCG. Our reduction applies whenever the base game relates to a canonical SCG by satisfying a simple social contribution boundedness property. As it turns out, several well-known games satisfy this property and are thus amenable to our reduction technique. Examples include min-sum scheduling games, congestion games, second price auctions and valid utility games. Using our technique, we derive mostly tight bounds on the robust price of anarchy of their altruistic extensions. For the majority of the mentioned game classes, the results extend to the more differentiated friendship setting. As we show, our reduction technique covers this model if the base game satisfies three additional natural properties

On Linear Congestion Games with Altruistic Social Context

We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a framework, given a real matrix $\Gamma=(\gamma_{ij})$ specifying a particular social context, each player $i$ aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player $j$, the multiplicative coefficient is given by the value $\gamma_{ij}$. We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature

Social Context and Cost-Sharing in Congestion Games

Congestion games are one of the most prominent classes of games in non- cooperative game theory as they model a large collection of important applications in networks, such as selfish routing in traffic or telecommunications. For this reason, congestion games have been a driving force in recent research and my thesis lies on two major extensions of this class of games. The first extension considers congestion games embedded in a social network where players are not necessarily selfish and might care about others. We call this class social context congestion games and study how the social interactions among players affect it. In particular, we study existence of approximate pure Nash equilibria and our main result is the following. For any given set of cost functions, we provide a threshold value such that: for the class of social context congestion games with cost functions within the given set, sequences of improvement steps of players, are guaranteed to converge to an approximate pure Nash equilibrium if and only if the improvement step factor is larger than this threshold value. The second topic considers weighted congestion games under a fair cost sharing system which depends on the weight of each player, the (weighted) Shapley values. This class considers weighted congestion games where (weighted) Shapley values are used as an alternative (to proportional shares) for distributing the total cost of each resource among its users. We study the efficiency of this class of games in terms of the price of anarchy and the price of stability. Regard- ing the price of anarchy, we show general tight bounds, which apply to general equilibrium concepts. For the price of stability, we prove an upper bound for the special case of Shapley values. This bound holds for general sets of cost functions and is tight in special cases of interest, such as bounded degree polynomials. Also for bounded degree polynomials, we show that a slight deviation from the Shapley value has a huge impact on the price of stability. In fact, the price of stability becomes as bad as the price of anarchy. For this model, we also study computation of equilibria. We propose an algorithm to compute approximate pure Nash equilibria which executes a polynomial number of strategy updates. Due to the complex nature of Shapley values, computing a single strategy update is hard, however, applying sampling techniques allow us to achieve polynomial running time. We generalise the previous model allowing each player to control multiple flows. For this generalised model, we study existence and efficiency of equilibria. We exhibit a separation from the original model (each player controls only one flow) by proving that Shapley values are the only cost-sharing method that guarantees pure Nash equilibria existence in the generalised model. Also, we prove that the price of anarchy and price of stability become no larger than in the original model

Complexité des dynamiques de jeux

La th eorie de la complexit e permet de classi er les problemes en fonction de leur di cult e. Le cadre classique dans lequel elle s applique est celui d un algorithme centralis e qui dispose de toutes les informations. Avec l essor des r eseaux et des architectures d ecentralis ees, l algo- rithmique distribu ee a et e etudi ee. Dans un grand nombre de problemes, en optimisation et en economie, les d ecisions et les calculs sont e ectu es par des agents ind ependants qui suivent des objectifs di erents dont la r ealisation d epend des d ecisions des autres agents. La th eorie des jeux est un cadre naturel pour analyser les solutions de tels problemes. Elle propose des concepts de stabilit e, le plus classique etant l equilibre de Nash.Une maniere naturelle de calculer de telles solutions est de faire r eagir les agents ; si un agent voit quelles sont les d ecisions des autres joueurs ou plus g en eralement un etat du jeu , il peut d ecider de changer sa d ecision pour atteindre son objectif faisant ainsi evoluer l etat du jeu. On dit que ces algorithmes sont des dynamiques .On sait que certaines dynamiques convergent vers un concept de solution. On s int eresse a la vitesse de convergence des dynamiques. Certains concepts de solutions sont m eme complets pour certaines classes de complexit e ce qui rend peu vraisemblable l existence de dynamiques simples qui convergent rapidement vers ces solutions. On a utilis e alors trois approches pour obtenir une convergence rapide : am eliorer la dynamique (en utilisant par exemple des bits al eatoires), restreindre la structure du probleme, et rechercher une solution approch ee.Sur les jeux de congestion, on a etendu les r esultats de convergence rapide vers un equilibre de Nash approch e aux jeux n egatifs. Cependant, on a montr e que sur les jeux sans contrainte de signe, calculer un equilibre de Nash approch e est PLS-complet. Sur les jeux d appariement, on a etudi e la vitesse de dynamiques concurrentes lorsque les joueurs ont une information partielle param etr ee par un r eseau social. En particulier, on a am elior e des dynamiques naturelles a n qu elles atteignent un equilibre enO(log(n)) tours (avec n le nombre de joueurs).Complexity theory allows to classify problems by their algorithmic hardness. The classical framework in which it applies is the one of a centralized algorithm that knows every informa- tion. With the development of networks and decentralized architectures, distributed dynamics was studied. In many problems, in optimization or economy, actions and computations are made by independant agents that don t share the same objective whose realization depends on the actions of other agents. Game theory is a natural framework to study solutions of this kind of problem. It provides solution concepts such as the Nash equilibrium.A natural way to compute these solutions is to make the agents react ; if an agent sees the actions of the other player, or more generally the state of the game, he can decide to change his decision to reach his objective and updates the state of the game. We call dynamics this kind of algorithms.We know some dynamics converges to a stable solution. We are interested by the speed of convergence of these dynamics. Some solution concepts are even complete for some complexity classes which make unrealistic the existence of fast converging dynamics. We used three ways to obtain a fast convergence : improving dynamics (using random bits), nding simple subcases, and nding an approximate solution.We extent fast convergence results to an approximate Nash equilibria in negative congestion games. However, we proved that nding an approximate Nash equilibrium in a congestion games without sign restriction is PLS-complete. On matching game, we studied the speed of concurrent dynamics when players have partial information that depends on a social network. Especially, we improved natural dynamics for them to reach an equilibrium inO(log(n)) rounds (with n is the number of players).PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF