1,216 research outputs found
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
A cognitive hierarchy theory of one-shot games: Some preliminary results
Strategic thinking, best-response, and mutual consistency (equilibrium) are three
key modelling principles in noncooperative game theory. This paper relaxes mutual
consistency to predict how players are likely to behave in in one-shot games before they
can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model
to predict behavior in one-shot games, and initial conditions in repeated games. The CH
approach assumes that players use k steps of reasoning with frequency f (k). Zero-step
players randomize. Players using k (≥ 1) steps best respond given partially rational
expectations about what players doing 0 through k - 1 steps actually choose. A simple
axiom which expresses the intuition that steps of thinking are increasingly constrained by
working memory, implies that f (k) has a Poisson distribution (characterized by a mean
number of thinking steps Ď„ ). The CH model converges to dominance-solvable equilibria
when Ď„ is large, predicts monotonic entry in binary entry games for Ď„ < 1:25, and predicts
effects of group size which are not predicted by Nash equilibrium. Best-fitting values of
Ď„ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental
samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable
p-beauty contests. The CH model also has economic value because subjects would have
raised their earnings substantially if they had best-responded to model forecasts instead
of making the choices they did
Rewarding cooperation in social dilemmas
One of the most direct human mechanisms of promoting cooperation is rewarding it. We study
the effect of sharing a reward among cooperators in the most stringent form of social dilemma.
Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the
shared reward despite the possibility of being exploited by defectors; on the other hand, if too
many players do that, cooperators will obtain a poor reward and defectors will outperform them.
By appropriately tuning the amount to be shared we can cast a vast variety of scenarios,
including traditional ones in the study of cooperation as well as more complex situations where
unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer
game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a
general class of public good games where competition among individuals with the same strategy
exists
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Distributed Learning Policies for Power Allocation in Multiple Access Channels
We analyze the problem of distributed power allocation for orthogonal
multiple access channels by considering a continuous non-cooperative game whose
strategy space represents the users' distribution of transmission power over
the network's channels. When the channels are static, we find that this game
admits an exact potential function and this allows us to show that it has a
unique equilibrium almost surely. Furthermore, using the game's potential
property, we derive a modified version of the replicator dynamics of
evolutionary game theory which applies to this continuous game, and we show
that if the network's users employ a distributed learning scheme based on these
dynamics, then they converge to equilibrium exponentially quickly. On the other
hand, a major challenge occurs if the channels do not remain static but
fluctuate stochastically over time, following a stationary ergodic process. In
that case, the associated ergodic game still admits a unique equilibrium, but
the learning analysis becomes much more complicated because the replicator
dynamics are no longer deterministic. Nonetheless, by employing results from
the theory of stochastic approximation, we show that users still converge to
the game's unique equilibrium.
Our analysis hinges on a game-theoretical result which is of independent
interest: in finite player games which admit a (possibly nonlinear) convex
potential function, the replicator dynamics (suitably modified to account for
nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of
order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more
material and figures for the case of stochastically fluctuating channels.
This version will appear in the IEEE Journal on Selected Areas in
Communication, Special Issue on Game Theory in Wireless Communication
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