3,596 research outputs found
The Price of Stability in Selfish Scheduling Games
10.3233/WIA-2009-0171Web Intelligence and Agent Systems74321-33
The Price of Stability in Selfish Scheduling Games
Singapore Management Universit
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
Efficiency analysis of load balancing games with and without activation costs
In this paper, we study two models of resource allocation games: the classical load-balancing game and its new variant involving resource activation costs. The resources we consider are identical and the social costs of the games are utilitarian, which are the average of all individual players' costs.
Using the social costs we assess the quality of pure Nash equilibria in terms of the price of anarchy (PoA) and the price of stability (PoS). For each game problem, we identify suitable problem parameters and provide a parametric bound on the PoA and the PoS. In the case of the load-balancing game, the parametric bounds we provide are sharp and asymptotically tight
Enforcing efficient equilibria in network design games via subsidies
The efficient design of networks has been an important engineering task that
involves challenging combinatorial optimization problems. Typically, a network
designer has to select among several alternatives which links to establish so
that the resulting network satisfies a given set of connectivity requirements
and the cost of establishing the network links is as low as possible. The
Minimum Spanning Tree problem, which is well-understood, is a nice example.
In this paper, we consider the natural scenario in which the connectivity
requirements are posed by selfish users who have agreed to share the cost of
the network to be established according to a well-defined rule. The design
proposed by the network designer should now be consistent not only with the
connectivity requirements but also with the selfishness of the users.
Essentially, the users are players in a so-called network design game and the
network designer has to propose a design that is an equilibrium for this game.
As it is usually the case when selfishness comes into play, such equilibria may
be suboptimal. In this paper, we consider the following question: can the
network designer enforce particular designs as equilibria or guarantee that
efficient designs are consistent with users' selfishness by appropriately
subsidizing some of the network links? In an attempt to understand this
question, we formulate corresponding optimization problems and present positive
and negative results.Comment: 30 pages, 7 figure
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
Selfishness Level of Strategic Games
We introduce a new measure of the discrepancy in strategic games between the
social welfare in a Nash equilibrium and in a social optimum, that we call
selfishness level. It is the smallest fraction of the social welfare that needs
to be offered to each player to achieve that a social optimum is realized in a
pure Nash equilibrium. The selfishness level is unrelated to the price of
stability and the price of anarchy and is invariant under positive linear
transformations of the payoff functions. Also, it naturally applies to other
solution concepts and other forms of games.
We study the selfishness level of several well-known strategic games. This
allows us to quantify the implicit tension within a game between players'
individual interests and the impact of their decisions on the society as a
whole. Our analyses reveal that the selfishness level often provides a deeper
understanding of the characteristics of the underlying game that influence the
players' willingness to cooperate.
In particular, the selfishness level of finite ordinal potential games is
finite, while that of weakly acyclic games can be infinite. We derive explicit
bounds on the selfishness level of fair cost sharing games and linear
congestion games, which depend on specific parameters of the underlying game
but are independent of the number of players. Further, we show that the
selfishness level of the -players Prisoner's Dilemma is ,
where and are the benefit and cost for cooperation, respectively, that
of the -players public goods game is , where is
the public good multiplier, and that of the Traveler's Dilemma game is
, where is the bonus. Finally, the selfishness level of
Cournot competition (an example of an infinite ordinal potential game, Tragedy
of the Commons, and Bertrand competition is infinite.Comment: 34 page
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