130 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
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
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
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