556 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
CSMA Local Area Networking under Dynamic Altruism
In this paper, we consider medium access control of local area networks
(LANs) under limited-information conditions as befits a distributed system.
Rather than assuming "by rule" conformance to a protocol designed to regulate
packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game
framework and build a dynamic altruism term into the net utility. The effects
of altruism are analyzed at Nash equilibrium for both the ALOHA and CSMA
frameworks in the quasistationary (fictitious play) regime. We consider either
power or throughput based costs of networking, and the cases of identical or
heterogeneous (independent) users/players. In a numerical study we consider
diverse players, and we see that the effects of altruism for similar players
can be beneficial in the presence of significant congestion, but excessive
altruism may lead to underuse of the channel when demand is low
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
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
Path deviations outperform approximate stability in heterogeneous congestion games
We consider non-atomic network congestion games with heterogeneous players
where the latencies of the paths are subject to some bounded deviations. This
model encompasses several well-studied extensions of the classical Wardrop
model which incorporate, for example, risk-aversion, altruism or travel time
delays. Our main goal is to analyze the worst-case deterioration in social cost
of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an
original Nash flow. We show that for homogeneous players perturbed Nash flows
coincide with approximate Nash flows and derive tight bounds on their
inefficiency. In contrast, we show that for heterogeneous populations this
equivalence does not hold. We derive tight bounds on the inefficiency of both
perturbed and approximate Nash flows for arbitrary player sensitivity
distributions. Intuitively, our results suggest that the negative impact of
path deviations (e.g., caused by risk-averse behavior or latency perturbations)
is less severe than approximate stability (e.g., caused by limited
responsiveness or bounded rationality). We also obtain a tight bound on the
inefficiency of perturbed Nash flows for matroid congestion games and
homogeneous populations if the path deviations can be decomposed into edge
deviations. In particular, this provides a tight bound on the Price of
Risk-Aversion for matroid congestion games
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
Weighted Congestion Games With Separable Preferences
Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the implications of separability for the existence of pure-strategy Nash equilibrium and the prospects of spontaneous convergence to equilibrium. It is shown that these properties may or may not be guaranteed, depending on the exact nature of player heterogeneity.congestion games, separable preferences, pure equilibrium, finite improvement property, potential.
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