110 research outputs found
Unilateral Altruism in Network Routing Games with Atomic Players
We study a routing game in which one of the players unilaterally acts
altruistically by taking into consideration the latency cost of other players
as well as his own. By not playing selfishly, a player can not only improve the
other players' equilibrium utility but also improve his own equilibrium
utility. To quantify the effect, we define a metric called the Value of
Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the
altruistic user to the equilibrium utility he would have received in Nash
equilibrium if he were selfish. We show by example that the VoU, in a game with
nonlinear latency functions and atomic players, can be arbitrarily large. Since
the Nash equilibrium social welfare of this example is arbitrarily far from
social optimum, this example also has a Price of Anarchy (PoA) that is
unbounded. The example is driven by there being a small number of players since
the same example with non-atomic players yields a Nash equilibrium that is
fully efficient
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
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.
Price of Anarchy in Bernoulli Congestion Games with Affine Costs
We consider an atomic congestion game in which each player participates in
the game with an exogenous and known probability , independently
of everybody else, or stays out and incurs no cost. We first prove that the
resulting game is potential. Then, we compute the parameterized price of
anarchy to characterize the impact of demand uncertainty on the efficiency of
selfish behavior. It turns out that the price of anarchy as a function of the
maximum participation probability is a nondecreasing
function. The worst case is attained when players have the same participation
probabilities . For the case of affine costs, we provide an
analytic expression for the parameterized price of anarchy as a function of
. This function is continuous on , is equal to for , and increases towards when . Our work can be interpreted as
providing a continuous transition between the price of anarchy of nonatomic and
atomic games, which are the extremes of the price of anarchy function we
characterize. We show that these bounds are tight and are attained on routing
games -- as opposed to general congestion games -- with purely linear costs
(i.e., with no constant terms).Comment: 29 pages, 6 figure
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
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Robust Methods for Influencing Strategic Behavior
Today's world contains many examples of engineered systems that are tightly coupled with their users and customers. In these settings, the strategic and economic behavior of users and customers can have a significant impact on the performance of the overall system, and it may be desirable for an engineer to devise appropriate methods of incentivizing human behavior to improve system performance. This work seeks to understand the fundamental tradeoffs involved in designing behavior-influencing mechanisms for complex interconnected sociotechnical systems. We study several examples and pose them as problems of game design: a planner chooses appropriate ways to select or modify the utility functions of individual agents in order to promote desired behavior. In social systems these modifications take the form of monetary or other incentives, whereas in multiagent engineered systems the modifications may be algorithmic. Here, we ask questions of sensitivity and robustness: for example, if the quality of information available to the planner changes, how can we quantify the impact of this change on the planner's ability to influence behavior? We propose a simple overarching framework for studying this, and then apply it to three distinct domains: incentives for network routing, distributed control design for multiagent engineered systems, and impersonation attacks in networked systems. We ask the following questions:- What features of a behavior-influencing mechanism directly confer robustness?We show weaknesses of several existing methodologies which use pricing for congestion control in transportation networks. In response to these issues, we propose a universal taxation mechanism which can incentivize optimal routing in transportation networks, requiring no information about network structure or user sensitivities, provided that it can charge sufficiently large prices. This suggests that large prices have more robustness than small ones. We also directly compare flow-varying tolls to fixed tolls, and show that a great deal of robustness can be gained by using a flow-varying approach.- How much information does a planner need to be confident that an incentive mechanism will not inadvertently induce pathological behavior?We show that for simple enough transportation networks (symmetric parallel networks are sufficient), a planner can provably avoid perverse incentives by applying a generalized marginal-cost taxation approach. On the other hand, we show that on general networks, perverse incentives are always a risk unless the incentive mechanism is given some information about network structure.- How can robust games be designed for multiagent coordination?We investigate a setting of multiagent coordination in which autonomous agents may suffer from unplanned communication loss events; the planner's task is to program agents with a policy (analogous to an incentive mechanism) for updating their utility functions in response to such events. We show that even when the nominal game is well-behaved and the communication loss is between weakly-coupled agents, there exists no utility update policy which can prevent arbitrarily-poor states from emerging. We also investigate a setting in which an adversary attempts to influence a distributed system in a robust way; here, by understanding susceptibility to adversarial influence, we hope to inform the design of more robust network systems
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