6,019 research outputs found
Measuring the interactions among variables of functions over the unit hypercube
By considering a least squares approximation of a given square integrable
function by a multilinear polynomial of a specified
degree, we define an index which measures the overall interaction among
variables of . This definition extends the concept of Banzhaf interaction
index introduced in cooperative game theory. Our approach is partly inspired
from multilinear regression analysis, where interactions among the independent
variables are taken into consideration. We show that this interaction index has
appealing properties which naturally generalize the properties of the Banzhaf
interaction index. In particular, we interpret this index as an expected value
of the difference quotients of or, under certain natural conditions on ,
as an expected value of the derivatives of . These interpretations show a
strong analogy between the introduced interaction index and the overall
importance index defined by Grabisch and Labreuche [7]. Finally, we discuss a
few applications of the interaction index
Least Square Approximations and Conic Values of Cooperative Games
URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2015.47 - ISSN : 1955-611XThe problem of least square approximation for set functions by set functions satisfying specified linear equality or inequality constraints is considered. The problem has important applications in the field of pseudo-Boolean functions, decision making and in cooperative game theory, where approximation by additive set functions yields so-called least square values. In fact, it is seem that every linear value for cooperative games arises from least square approximation. We provide a general approach and problem overview. In particular, we derive explicit formulas for solutions under mild constraints, which include and extend previous results in the literature.On considĂšre le problĂšme de l'approximation au sens des moindres carrĂ©s des fonctions d'ensemble par des fonctions d'ensemble satisfaisant des contraintes linĂ©aires d'Ă©galitĂ© ou d'inĂ©galitĂ©. Le problĂšme a des applications importantes dans le domaine des fonctions pseudo-BoolĂ©ennes, la dĂ©cision et la thĂ©orie des jeux coopĂ©ratifs, oĂč l'approximation par des jeux additifs mĂšne Ă la notion de valeur aux moindres carrĂ©s. En fait, on voit que toute valeur linĂ©aire pour les jeux coopĂ©ratifs vient d'un problĂšme d'approximation par les moindres carrĂ©s. Nous proposons une approche gĂ©nĂ©rale du problĂšme. En particulier, nous obtenons des formules explicites pour les solutions sous des hypothĂšses faibles, qui incluent et Ă©tendent des rĂ©sultats prĂ©cĂ©dents de la littĂ©rature
Evolutionary prisoner's dilemma games with optional participation
Competition among cooperators, defectors, and loners is studied in an
evolutionary prisoner's dilemma game with optional participation. Loners are
risk averse i.e. unwilling to participate and rather rely on small but fixed
earnings. This results in a rock-scissors-paper type cyclic dominance of the
three strategies. The players are located either on square lattices or random
regular graphs with the same connectivity. Occasionally, every player
reassesses its strategy by sampling the payoffs in its neighborhood. The loner
strategy efficiently prevents successful spreading of selfish, defective
behavior and avoids deadlocks in states of mutual defection. On square
lattices, Monte Carlo simulations reveal self-organizing patterns driven by the
cyclic dominance, whereas on random regular graphs different types of
oscillatory behavior are observed: the temptation to defect determines whether
damped, periodic or increasing oscillations occur. These results are compared
to predictions by pair approximation. Although pair approximation is incapable
of distinguishing the two scenarios because of the equal connectivity, the
average frequencies as well as the oscillations on random regular graphs are
well reproduced.Comment: 6 pages, 7 figure
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Non-atomic Games for Multi-User Systems
In this contribution, the performance of a multi-user system is analyzed in
the context of frequency selective fading channels. Using game theoretic tools,
a useful framework is provided in order to determine the optimal power
allocation when users know only their own channel (while perfect channel state
information is assumed at the base station). We consider the realistic case of
frequency selective channels for uplink CDMA. This scenario illustrates the
case of decentralized schemes, where limited information on the network is
available at the terminal. Various receivers are considered, namely the Matched
filter, the MMSE filter and the optimum filter. The goal of this paper is to
derive simple expressions for the non-cooperative Nash equilibrium as the
number of mobiles becomes large and the spreading length increases. To that end
two asymptotic methodologies are combined. The first is asymptotic random
matrix theory which allows us to obtain explicit expressions of the impact of
all other mobiles on any given tagged mobile. The second is the theory of
non-atomic games which computes good approximations of the Nash equilibrium as
the number of mobiles grows.Comment: 17 pages, 4 figures, submitted to IEEE JSAC Special Issue on ``Game
Theory in Communication Systems'
Non-neutrality of economic policy: An application of the Tinbergen-Theilâs approach to a strategic context
Issues of policy effectiveness and neutrality are widespread in the economic literature. They have been increasingly raised in specific contexts within the class of LQ (linear-quadratic) policy games in the last 20 years, notably with reference to monetary policy. The more general conditions ensuring nonneutrality in a strategic environment remain however to be inquired. We fill this gap by applying the classical theory of economic policy to a strategic context. This is also useful to highlight some existence conditions for policy game solutions. We restrict ourselves to the common LQ-games in a static perfect information framework, but our simple logic can be extended to other more general situations.LQ-policy games, policy ineffectiveness, controllability.
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