559 research outputs found
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
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
Nash Social Welfare in Selfish and Online Load Balancing (Short Paper)
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 selfish load balancing (aka. load balancing games), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and 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 problems under the objective of minimizing the 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
Resource allocation games of various social objectives
In this paper, we study resource allocation games of two different cost components for individual game players and various social costs. The total cost of each individual player consists of the congestion cost, which is the same for all players sharing the same resource, and resource activation cost, which is proportional to the individual usage of the resource. The social costs we consider are, respectively, the total of costs of all players and the maximum congestion cost plus total resource activation cost.
Using the social costs we assess the quality of Nash equilibria in terms of the price of anarchy (PoA) and the price of stability (PoS). For each problem, we identify one or two problem parameters and provide parametric bounds on the PoA and PoS. We show that they are unbounded in general if the parameter involved are not restricted
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