2,422 research outputs found
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
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
Games and Mechanism Design in Machine Scheduling – An Introduction
In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;
Scheduling Games with Machine-Dependent Priority Lists
We consider a scheduling game in which jobs try to minimize their completion
time by choosing a machine to be processed on. Each machine uses an individual
priority list to decide on the order according to which the jobs on the machine
are processed. We characterize four classes of instances in which a pure Nash
equilibrium (NE) is guaranteed to exist, and show, by means of an example, that
none of these characterizations can be relaxed. We then bound the performance
of Nash equilibria for each of these classes with respect to the makespan of
the schedule and the sum of completion times. We also analyze the computational
complexity of several problems arising in this model. For instance, we prove
that it is NP-hard to decide whether a NE exists, and that even for instances
with identical machines, for which a NE is guaranteed to exist, it is NP-hard
to approximate the best NE within a factor of for all
. In addition, we study a generalized model in which players'
strategies are subsets of resources, each having its own priority list over the
players. We show that in this general model, even unweighted symmetric games
may not have a pure NE, and we bound the price of anarchy with respect to the
total players' costs.Comment: 19 pages, 2 figure
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