138 research outputs found
Potentials in Social Environments
We develop and extend notions of potentials for normal-form games (Monderer and Shapley, 1996) to present a unified approach for the general class of social environments. The different potentials and corresponding social environments can be ordered in terms of their permissiveness. We classify different methods to construct potentials and we characterize potentials for specific examples such as matching problems, vote trading, multilateral trade, TU games, and various pillage games
Markov Games with Decoupled Dynamics: Price of Anarchy and Sample Complexity
This paper studies the finite-time horizon Markov games where the agents'
dynamics are decoupled but the rewards can possibly be coupled across agents.
The policy class is restricted to local policies where agents make decisions
using their local state. We first introduce the notion of smooth Markov games
which extends the smoothness argument for normal form games to our setting, and
leverage the smoothness property to bound the price of anarchy of the Markov
game. For a specific type of Markov game called the Markov potential game, we
also develop a distributed learning algorithm, multi-agent soft policy
iteration (MA-SPI), which provably converges to a Nash equilibrium. Sample
complexity of the algorithm is also provided. Lastly, our results are validated
using a dynamic covering game
The Cost of Informing Decision-Makers in Multi-Agent Maximum Coverage Problems with Random Resource Values
The emergent behavior of a distributed system is conditioned by the
information available to the local decision-makers. Therefore, one may expect
that providing decision-makers with more information will improve system
performance; in this work, we find that this is not necessarily the case. In
multi-agent maximum coverage problems, we find that even when agents'
objectives are aligned with the global welfare, informing agents about the
realization of the resource's random values can reduce equilibrium performance
by a factor of 1/2. This affirms an important aspect of designing distributed
systems: information need be shared carefully. We further this understanding by
providing lower and upper bounds on the ratio of system welfare when
information is (fully or partially) revealed and when it is not, termed the
value-of-informing. We then identify a trade-off that emerges when optimizing
the performance of the best-case and worst-case equilibrium.Comment: To appear: LCS
Differentially-private Distributed Algorithms for Aggregative Games with Guaranteed Convergence
The distributed computation of a Nash equilibrium in aggregative games is
gaining increased traction in recent years. Of particular interest is the
mediator-free scenario where individual players only access or observe the
decisions of their neighbors due to practical constraints. Given the
competitive rivalry among participating players, protecting the privacy of
individual players becomes imperative when sensitive information is involved.
We propose a fully distributed equilibrium-computation approach for aggregative
games that can achieve both rigorous differential privacy and guaranteed
computation accuracy of the Nash equilibrium. This is in sharp contrast to
existing differential-privacy solutions for aggregative games that have to
either sacrifice the accuracy of equilibrium computation to gain rigorous
privacy guarantees, or allow the cumulative privacy budget to grow unbounded,
hence losing privacy guarantees, as iteration proceeds. Our approach uses
independent noises across players, thus making it effective even when
adversaries have access to all shared messages as well as the underlying
algorithm structure. The encryption-free nature of the proposed approach, also
ensures efficiency in computation and communication. The approach is also
applicable in stochastic aggregative games, able to ensure both rigorous
differential privacy and guaranteed computation accuracy of the Nash
equilibrium when individual players only have stochastic estimates of their
pseudo-gradient mappings. Numerical comparisons with existing counterparts
confirm the effectiveness of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:2202.0111
Distribution games: a new class of games with application to user provided networks
User Provided Network (UPN) is a promising solution for sharing the limited network resources by utilizing user capabilities as a part of the communication infrastructure. In UPNs, it is an important problem to decide how to share the resources among multiple clients in decentralized manner. Motivated by this problem, we introduce a new class of games termed distribution games that can be used to distribute efficiently and fairly the bandwidth capacity among users. We show that every distribution game has at least one pure strategy Nash equilibrium (NE) and any best response dynamics always converges to such an equilibrium. We consider social welfare functions that are weighted sums of bandwidths allocated to clients. We present tight upper bounds for the price of anarchy and price of stability of these games provided that they satisfy some reasonable assumptions. We define two specific practical instances of distribution games that fit these assumptions. We conduct experiments on one of these instances and demonstrate that in most of the settings the social welfare obtained by the best response dynamics is very close to the optimum. Simulations show that this game also leads to a fair distribution of the bandwidth.Publisher's Versio
Mixed-integer programming representation for symmetrical partition function form games
In contexts involving multiple agents (players), determining how they can cooperate through the formation of coalitions and how they can share surplus benefits coming from the collaboration is crucial. This can provide decision-aid to players and analysis tools for policy makers regulating economic markets. Such settings belong to the field of cooperative game theory. A critical element in this area has been the size of the representation of these games: for each possible partition of players, the value of each coalition on it must be provided.
Symmetric partition function form games (SPFGs) belong to a class of cooperative games with two important characteristics. First, they account for externalities provoked by any group of players joining forces or splitting into subsets on the remaining coalitions of players. Second, they consider that players are indistinct, meaning that only the number of players in each coalition is relevant for the SPFG. Using mixed-integer programming, we present the first representation of SPFGs that is polynomial on the number of players in the game. We also characterize the family of SPFGs that we can represent. In particular, the representation is able to encode exactly all SPFGs with five players or less. Furthermore, we provide a compact representation approximating SPFGs when there are six players or more and the SPFG cannot be represented exactly. We also introduce a flexible framework that uses stability methods inspired from the literature to identify a stable social-welfare maximizing game outcome using our representation. We showcase the value of our compact (approximated) representation and approach to determine a stable partition and payoff allocation to a competitive market from the literature.Dans tout contexte impliquant plusieurs agents (joueurs), il est impératif de déterminer comment les agents coopéreront par la formation de coalitions et comment ils partageront les bénéfices supplémentaires issus de la collaboration. Ceci peut fournir une aide à la décision aux joueurs, ou encore des outils d'analyse pour les responsables en charge de réguler les marchés économiques. De telles situations relèvent de la théorie des jeux coopérative. Un élément crucial de ce domaine est la taille de la représentation de ces jeux : pour chaque partition de joueurs possible, la valeur de chaque coalition qu'on y retrouve doit être donnée.
Les jeux symétriques à fonction de partition (SPFG) appartiennent à une classe de jeux coopératifs possédant deux caractéristiques principales. Premièrement, ils sont sensibles aux externalités, provoquées par n'importe quel groupe de joueurs qui s'allient ou défont leurs alliances, qui sont ressenties par les autres coalitions de joueurs. Deuxièmement, ils considèrent que les joueurs sont indistincts, et donc que seul le nombre de joueurs dans chaque coalition est à retenir pour représenter un SPFG. Par l'utilisation d'outils de programmation mixte en nombres entiers, nous présentons la première représentation de SPFG qui est polynomiale en nombre de joueurs dans le jeu. De surcroît, nous caractérisons la famille des SPFG qu'il est possible de représenter, qui inclut notamment tous les SPFG de cinq joueurs ou moins. De plus, elle dispose d'une approximation compacte pour le cas où, dans un jeu à six joueurs ou plus, le SPFG ne peut pas être représenté de façon exacte. Également, nous introduisons un cadre flexible qui utilise des méthodes visant la stabilité inspirées par la littérature pour identifier, à l'aide de notre représentation, une issue stable qui maximise le bien-être social des joueurs. Nous démontrons la valeur de notre représentation (approximée) compacte et de notre approche pour sélectionner une partition stable et une allocation des profits dans une application de marché compétitif provenant de la littérature
Les jeux de congestion dans les réseaux sous l’angle de la vérification
Congestion games are a well-studied areaof research, and Network congestion games (NCG) model the problem of congestion in flow networks. The most common problem is to study, broadly speaking, how well or how bad a model of NCG is in terms of total cost for all players when each player plays selfishly. We view network congestion games from a formal methods standpoint, in which we are interested in problems like given an instance (network and number of players fixed) of a chosen model of NCG and given a specification, does there exist an optimal profile satisfying the specification? We define a model of network congestion games with two peculiarities: first, the players bear congestion effect on their cost for an edge only if they use that edge with other players simultaneously; second, players can choose their path dynamically, at each step of their route, which differs from the classical setting where players choose their path at the beginning. We show that in this model Nash Equilibria always exist by showing convergence of best-response dynamics. Then we study three decision problems on Social optima, Nash Equilibria and Subgame perfect Equilibria, each of which asks whether, given an instance of our model and a bound, there is a corresponding strategy profile with bounded social cost. In the second part of the thesis, we study parameterized network congestion games, where the number of players is left as a parameter. Our main problem here is to compute Nash Equilibria for instances with many players, from instances with fewer players, instead of computing them from scratch. Here, we started solving the problem for the classical model of NCG, without the above mentioned two pecularities, and with the arena restricted to series-parallel graph. We obtained some preliminary results on this problem, and formulated a conjecture about how to efficiently compute all Nash equilibria for any number of players.Les jeux de congestion sont un domaine de recherche bien étudié ; dans ce domaine, les jeux de congestion dans les réseaux permettent de représenter la congestion des réseaux de distribution, et d’étudier à quel point un modèle de réseau est bon ou mauvais en termes de coût total lorsque chaque joueur joue de façon égoïste, cherchant uniquement à optimiser son propre coût ; Nous considérons ces jeux de congestion du point de vue des méthodes formelles, cherchant à vérifier par exemple que, dans un réseaux fixé, il existe un profil de stratégies optimal qui satisfasse une propriété donnée. Nous définissons un modèle de jeux de congestion avec deux particularités : d’une part, le calcul du coût d’une transition dépend du nombre de joueurs utilisant simultanément une arête ; d’autre part, les joueurs choisissent leur chemin de façon dynamique en fonction des choix des autres joueurs. Nous montrons que dans ce modèle les équilibres de Nash existent toujours en montrant la convergence de la dynamique de meilleure réponse. Nous étudions ensuite le problème de vérification mentionné ci-dessus, résolvant le problème de l’existence d’un équilibre social, d’un équilibre de Nash ou d’un équilibre parfait en sous-jeux ayant un côut borné. Dans une deuxième partie, nous étudions les jeux de congestion paramétrés, dans lesquels le nombre de joueurs est un paramètre. Nous nous intéressons à l’évolution des équilibres de Nash en fonction du nombre de joueurs : notre objectif est de calculer efficacement l’ensemble des équilibres de Nash pour un nombre arbitrairement grand de joueurs, à partir des équilibres de Nash pour de petits nombres de joueurs. Nos premiers résultats portent sur les réseaux série-parall‘ele, sans les particularités ci-dessus. Nous conjecturons que ces résultats s’étendent à l’ensemble des graphes, ce qui donnerait lieu à un calcul efficace de tous les équilibres de Nash, quel que soit le nombre de joueurs
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