120 research outputs found
Multicast Network Design Game on a Ring
In this paper we study quality measures of different solution concepts for
the multicast network design game on a ring topology. We recall from the
literature a lower bound of 4/3 and prove a matching upper bound for the price
of stability, which is the ratio of the social costs of a best Nash equilibrium
and of a general optimum. Therefore, we answer an open question posed by
Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs
of a potential optimizer and of an optimum, provide a construction of a lower
bound, and give a computer-assisted argument that it reaches for any
precision. We then turn our attention to players arriving one by one and
playing myopically their best response. We provide matching lower and upper
bounds of 2 for the myopic sequential price of anarchy (achieved for a
worst-case order of the arrival of the players). We then initiate the study of
myopic sequential price of stability and for the multicast game on the ring we
construct a lower bound of 4/3, and provide an upper bound of 26/19. To the
end, we conjecture and argue that the right answer is 4/3.Comment: 12 pages, 4 figure
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 specifying a particular
social context, each player aims at optimizing a linear combination of the
payoffs of all the players in the game, where, for each player , the
multiplicative coefficient is given by the value . 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
On the Impact of Fair Best Response Dynamics
In this work we completely characterize how the frequency with which each
player participates in the game dynamics affects the possibility of reaching
efficient states, i.e., states with an approximation ratio within a constant
factor from the price of anarchy, within a polynomially bounded number of best
responses. We focus on the well known class of congestion games and we show
that, if each player is allowed to play at least once and at most times
any best responses, states with approximation ratio times the
price of anarchy are reached after best
responses, and that such a bound is essentially tight also after exponentially
many ones. One important consequence of our result is that the fairness among
players is a necessary and sufficient condition for guaranteeing a fast
convergence to efficient states. This answers the important question of the
maximum order of needed to fast obtain efficient states, left open by
[9,10] and [3], in which fast convergence for constant and very slow
convergence for have been shown, respectively. Finally, we show
that the structure of the game implicitly affects its performances. In
particular, we show that in the symmetric setting, in which all players share
the same set of strategies, the game always converges to an efficient state
after a polynomial number of best responses, regardless of the frequency each
player moves with
Improving Approximate Pure Nash Equilibria in Congestion Games
Congestion games constitute an important class of games to model resource
allocation by different users. As computing an exact or even an approximate
pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011)
present a polynomial-time algorithm that computes a ()-approximate pure Nash equilibria for games with linear cost
functions and further results for polynomial cost functions. We show that this
factor can be improved to and further improved results for
polynomial cost functions, by a seemingly simple modification to their
algorithm by allowing for the cost functions used during the best response
dynamics be different from the overall objective function. Interestingly, our
modification to the algorithm also extends to efficiently computing improved
approximate pure Nash equilibria in games with arbitrary non-decreasing
resource cost functions. Additionally, our analysis exhibits an interesting
method to optimally compute universal load dependent taxes and using linear
programming duality prove tight bounds on PoA under universal taxation, e.g,
2.012 for linear congestion games and further results for polynomial cost
functions. Although our approach yield weaker results than that in Bil\`{o} and
Vinci (2016), we remark that our cost functions are locally computable and in
contrast to Bil\`{o} and Vinci (2016) are independent of the actual instance of
the game
Sharing the cost of multicast transmissions in wireless networks
AbstractA crucial issue in non-cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network. Each station acts as a selfish agent that may misreport its utility (i.e., the maximum cost it is willing to incur to receive the service, in terms of power consumption) in order to maximize its individual welfare, defined as the difference between its true utility and its charged cost. A provider can discourage such deceptions by using a strategyproof cost sharing mechanism, that is a particular public algorithm that, by forcing the agents to truthfully reveal their utility, starting from the reported utilities, decides who gets the service (the receivers) and at what price. A mechanism is said budget balanced (BB) if the receivers pay exactly the (possibly minimum) cost of the transmission, and β-approximate budget balanced (β-BB) if the total cost charged to the receivers covers the overall cost and is at most β times the optimal one, while it is efficient if it maximizes the sum of the receivers’ utilities minus the total cost over all receivers’ sets. In this paper, we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks, in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or BB when the power assignments are induced by a fixed universal spanning tree, or (3ln(k+1))-BB (k is the number of receivers), otherwise. Then we consider the case in which the stations lay in a d-dimensional Euclidean space and the powers fall as 1/dα, and provide strategyproof mechanisms that are either 1-BB or efficient for α=1 or d=1. Finally, we show the existence of 2(3d-1)-BB strategyproof mechanisms in any d-dimensional space for every α⩾d. For the special case of d=2 such a result can be improved to achieve 12-BB mechanisms
Fairly Allocating Contiguous Blocks of Indivisible Items
In this paper, we study the classic problem of fairly allocating indivisible
items with the extra feature that the items lie on a line. Our goal is to find
a fair allocation that is contiguous, meaning that the bundle of each agent
forms a contiguous block on the line. While allocations satisfying the
classical fairness notions of proportionality, envy-freeness, and equitability
are not guaranteed to exist even without the contiguity requirement, we show
the existence of contiguous allocations satisfying approximate versions of
these notions that do not degrade as the number of agents or items increases.
We also study the efficiency loss of contiguous allocations due to fairness
constraints.Comment: Appears in the 10th International Symposium on Algorithmic Game
Theory (SAGT), 201
Coalition Resilient Outcomes in Max k-Cut Games
We investigate strong Nash equilibria in the \emph{max -cut game}, where
we are given an undirected edge-weighted graph together with a set of colors. Nodes represent players and edges capture their mutual
interests. The strategy set of each player consists of the colors. When
players select a color they induce a -coloring or simply a coloring. Given a
coloring, the \emph{utility} (or \emph{payoff}) of a player is the sum of
the weights of the edges incident to , such that the color chosen
by is different from the one chosen by . Such games form some of the
basic payoff structures in game theory, model lots of real-world scenarios with
selfish agents and extend or are related to several fundamental classes of
games.
Very little is known about the existence of strong equilibria in max -cut
games. In this paper we make some steps forward in the comprehension of it. We
first show that improving deviations performed by minimal coalitions can cycle,
and thus answering negatively the open problem proposed in
\cite{DBLP:conf/tamc/GourvesM10}. Next, we turn our attention to unweighted
graphs. We first show that any optimal coloring is a 5-SE in this case. Then,
we introduce -local strong equilibria, namely colorings that are resilient
to deviations by coalitions such that the maximum distance between every pair
of nodes in the coalition is at most . We prove that -local strong
equilibria always exist. Finally, we show the existence of strong Nash
equilibria in several interesting specific scenarios.Comment: A preliminary version of this paper will appear in the proceedings of
the 45th International Conference on Current Trends in Theory and Practice of
Computer Science (SOFSEM'19
Augmenting graphs to minimize the diameter
We study the problem of augmenting a weighted graph by inserting edges of
bounded total cost while minimizing the diameter of the augmented graph. Our
main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure
Network Creation Games: Think Global - Act Local
We investigate a non-cooperative game-theoretic model for the formation of
communication networks by selfish agents. Each agent aims for a central
position at minimum cost for creating edges. In particular, the general model
(Fabrikant et al., PODC'03) became popular for studying the structure of the
Internet or social networks. Despite its significance, locality in this game
was first studied only recently (Bil\`o et al., SPAA'14), where a worst case
locality model was presented, which came with a high efficiency loss in terms
of quality of equilibria. Our main contribution is a new and more optimistic
view on locality: agents are limited in their knowledge and actions to their
local view ranges, but can probe different strategies and finally choose the
best. We study the influence of our locality notion on the hardness of
computing best responses, convergence to equilibria, and quality of equilibria.
Moreover, we compare the strength of local versus non-local strategy-changes.
Our results address the gap between the original model and the worst case
locality variant. On the bright side, our efficiency results are in line with
observations from the original model, yet we have a non-constant lower bound on
the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication
in the proceedings of the 40th International Conference on Mathematical
Foundations on Computer Scienc
Nash Social Welfare in Selfish and Online Load Balancing
In load balancing problems there is a set of clients, each wishing to select
a resource from a set of permissible ones, in order to execute a certain task.
Each resource has a latency function, which depends on its workload, and a
client's cost is the completion time of her chosen resource. Two fundamental
variants of load balancing problems are {\em selfish load balancing} (aka. {\em
load balancing games}), where clients are non-cooperative selfish players aimed
at minimizing their own cost solely, and {\em online load balancing}, where
clients appear online and have to be irrevocably assigned to a resource without
any knowledge about future requests. We revisit both selfish and online load
balancing under the objective of minimizing the {\em Nash Social Welfare},
i.e., the geometric mean of the clients' costs. To the best of our knowledge,
despite being a celebrated welfare estimator in many social contexts, the Nash
Social Welfare has not been considered so far as a benchmarking quality measure
in load balancing problems. We provide tight bounds on the price of anarchy of
pure Nash equilibria and on the competitive ratio of the greedy algorithm under
very general latency functions, including polynomial ones. For this particular
class, we also prove that the greedy strategy is optimal as it matches the
performance of any possible online algorithm
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