288 research outputs found
On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
In \emph{bandwidth allocation games} (BAGs), the strategy of a player
consists of various demands on different resources. The player's utility is at
most the sum of these demands, provided they are fully satisfied. Every
resource has a limited capacity and if it is exceeded by the total demand, it
has to be split between the players. Since these games generally do not have
pure Nash equilibria, we consider approximate pure Nash equilibria, in which no
player can improve her utility by more than some fixed factor through
unilateral strategy changes. There is a threshold (where
is a parameter that limits the demand of each player on a specific
resource) such that -approximate pure Nash equilibria always exist for
, but not for . We give both
upper and lower bounds on this threshold and show that the
corresponding decision problem is -hard. We also show that the
-approximate price of anarchy for BAGs is . For a restricted
version of the game, where demands of players only differ slightly from each
other (e.g. symmetric games), we show that approximate Nash equilibria can be
reached (and thus also be computed) in polynomial time using the best-response
dynamic. Finally, we show that a broader class of utility-maximization games
(which includes BAGs) converges quickly towards states whose social welfare is
close to the optimum
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
We introduce a class of finite strategic games with the property that every
deviation of a coalition of players that is profitable to each of its members
strictly decreases the lexicographical order of a certain function defined on
the set of strategy profiles. We call this property the Lexicographical
Improvement Property (LIP) and show that it implies the existence of a
generalized strong ordinal potential function. We use this characterization to
derive existence, efficiency and fairness properties of strong Nash equilibria.
We then study a class of games that generalizes congestion games with
bottleneck objectives that we call bottleneck congestion games. We show that
these games possess the LIP and thus the above mentioned properties. For
bottleneck congestion games in networks, we identify cases in which the
potential function associated with the LIP leads to polynomial time algorithms
computing a strong Nash equilibrium. Finally, we investigate the LIP for
infinite games. We show that the LIP does not imply the existence of a
generalized strong ordinal potential, thus, the existence of SNE does not
follow. Assuming that the function associated with the LIP is continuous,
however, we prove existence of SNE. As a consequence, we prove that bottleneck
congestion games with infinite strategy spaces and continuous cost functions
possess a strong Nash equilibrium
Tight Inefficiency Bounds for Perception-Parameterized Affine Congestion Games
Congestion games constitute an important class of non-cooperative games which
was introduced by Rosenthal in 1973. In recent years, several extensions of
these games were proposed to incorporate aspects that are not captured by the
standard model. Examples of such extensions include the incorporation of risk
sensitive players, the modeling of altruistic player behavior and the
imposition of taxes on the resources. These extensions were studied intensively
with the goal to obtain a precise understanding of the inefficiency of
equilibria of these games. In this paper, we introduce a new model of
congestion games that captures these extensions (and additional ones) in a
unifying way. The key idea here is to parameterize both the perceived cost of
each player and the social cost function of the system designer. Intuitively,
each player perceives the load induced by the other players by an extent of
{\rho}, while the system designer estimates that each player perceives the load
of all others by an extent of {\sigma}. The above mentioned extensions reduce
to special cases of our model by choosing the parameters {\rho} and {\sigma}
accordingly. As in most related works, we concentrate on congestion games with
affine latency functions here. Despite the fact that we deal with a more
general class of congestion games, we manage to derive tight bounds on the
price of anarchy and the price of stability for a large range of pa- rameters.
Our bounds provide a complete picture of the inefficiency of equilibria for
these perception-parameterized congestion games. As a result, we obtain tight
bounds on the price of anarchy and the price of stability for the above
mentioned extensions. Our results also reveal how one should "design" the cost
functions of the players in order to reduce the price of anar- chy
The Price of Anarchy for Selfish Ring Routing is Two
We analyze the network congestion game with atomic players, asymmetric
strategies, and the maximum latency among all players as social cost. This
important social cost function is much less understood than the average
latency. We show that the price of anarchy is at most two, when the network is
a ring and the link latencies are linear. Our bound is tight. This is the first
sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page
Budget-restricted utility games with ordered strategic decisions
We introduce the concept of budget games. Players choose a set of tasks and
each task has a certain demand on every resource in the game. Each resource has
a budget. If the budget is not enough to satisfy the sum of all demands, it has
to be shared between the tasks. We study strategic budget games, where the
budget is shared proportionally. We also consider a variant in which the order
of the strategic decisions influences the distribution of the budgets. The
complexity of the optimal solution as well as existence, complexity and quality
of equilibria are analyzed. Finally, we show that the time an ordered budget
game needs to convergence towards an equilibrium may be exponential
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