274 research outputs found
Penalty-regulated dynamics and robust learning procedures in games
Starting from a heuristic learning scheme for N-person games, we derive a new
class of continuous-time learning dynamics consisting of a replicator-like
drift adjusted by a penalty term that renders the boundary of the game's
strategy space repelling. These penalty-regulated dynamics are equivalent to
players keeping an exponentially discounted aggregate of their on-going payoffs
and then using a smooth best response to pick an action based on these
performance scores. Owing to this inherent duality, the proposed dynamics
satisfy a variant of the folk theorem of evolutionary game theory and they
converge to (arbitrarily precise) approximations of Nash equilibria in
potential games. Motivated by applications to traffic engineering, we exploit
this duality further to design a discrete-time, payoff-based learning algorithm
which retains these convergence properties and only requires players to observe
their in-game payoffs: moreover, the algorithm remains robust in the presence
of stochastic perturbations and observation errors, and it does not require any
synchronization between players.Comment: 33 pages, 3 figure
A Hierarchical Game with Strategy Evolution for Mobile Sponsored Content and Service Markets
In sponsored content and service markets, the content and service providers
are able to subsidize their target mobile users through directly paying the
mobile network operator, to lower the price of the data/service access charged
by the network operator to the mobile users. The sponsoring mechanism leads to
a surge in mobile data and service demand, which in return compensates for the
sponsoring cost and benefits the content/service providers. In this paper, we
study the interactions among the three parties in the market, namely, the
mobile users, the content/service providers and the network operator, as a
two-level game with multiple Stackelberg (i.e., leader) players. Our study is
featured by the consideration of global network effects owning to consumers'
grouping. Since the mobile users may have bounded rationality, we model the
service-selection process among them as an evolutionary-population follower
sub-game. Meanwhile, we model the pricing-then-sponsoring process between the
content/service providers and the network operator as a non-cooperative
equilibrium searching problem. By investigating the structure of the proposed
game, we reveal a few important properties regarding the equilibrium existence,
and propose a distributed, projection-based algorithm for iterative equilibrium
searching. Simulation results validate the convergence of the proposed
algorithm, and demonstrate how sponsoring helps improve both the providers'
profits and the users' experience
Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty
Motivated by the massive deployment of power-hungry data centers for service
provisioning, we examine the problem of routing in optical networks with the
aim of minimizing traffic-driven power consumption. To tackle this issue,
routing must take into account energy efficiency as well as capacity
considerations; moreover, in rapidly-varying network environments, this must be
accomplished in a real-time, distributed manner that remains robust in the
presence of random disturbances and noise. In view of this, we derive a pricing
scheme whose Nash equilibria coincide with the network's socially optimum
states, and we propose a distributed learning method based on the Boltzmann
distribution of statistical mechanics. Using tools from stochastic calculus, we
show that the resulting Boltzmann routing scheme exhibits remarkable
convergence properties under uncertainty: specifically, the long-term average
of the network's power consumption converges within of its
minimum value in time which is at most ,
irrespective of the fluctuations' magnitude; additionally, if the network
admits a strict, non-mixing optimum state, the algorithm converges to it -
again, no matter the noise level. Our analysis is supplemented by extensive
numerical simulations which show that Boltzmann routing can lead to a
significant decrease in power consumption over basic, shortest-path routing
schemes in realistic network conditions.Comment: 24 pages, 4 figure
Random walks with asymmetric time delays
We studied simple random-walk models with asymmetric time delays. Stochastic
simulations were performed for hyperbolic-tangent fitness functions and to
obtain analytical results we approximated them by step functions. A novel
behavior has been observed. Namely, the mean position of a walker depends on
time delays. This is a joint effect of both stochasticity and time delays
present in the system. We also observed that by shifting appropriately fitness
functions we may reverse the effect of time delays - the mean position of the
walker changes the sign
Survival of dominated strategies under evolutionary dynamics
We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. We also show that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics. Numerical analysis reveals that dominated strategies can persist at nontrivial frequencies even when the level of domination is not small.Evolutionary game theory, evolutionary game dynamics, nonconvergnece, dominated strategies
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