90,677 research outputs found
On values of repeated games with signals
We study the existence of different notions of value in two-person zero-sum
repeated games where the state evolves and players receive signals. We provide
some examples showing that the limsup value (and the uniform value) may not
exist in general. Then we show the existence of the value for any Borel payoff
function if the players observe a public signal including the actions played.
We also prove two other positive results without assumptions on the signaling
structure: the existence of the value in any game and the existence of
the uniform value in recursive games with nonnegative payoffs.Comment: Published at http://dx.doi.org/10.1214/14-AAP1095 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games
We prove a Tauberian theorem for nonexpansive operators, and apply it to the
model of zero-sum stochastic game. Under mild assumptions, we prove that the
value of the lambda-discounted game v_{lambda} converges uniformly when lambda
goes to 0 if and only if the value of the n-stage game v_n converges uniformly
when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and
Sorin (1992) to the two-player zero-sum case. We also provide the first example
of a stochastic game with public signals on the state and perfect observation
of actions, with finite state space, signal sets and action sets, in which for
some initial state k_1 known by both players, (v_{lambda}(k_1)) and (v_n(k_1))
converge to distinct limits
Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture ""
We study two-player zero-sum recursive games with a countable state space and
finite action spaces at each state. When the family of -stage values
is totally bounded for the uniform norm, we prove the
existence of the uniform value. Together with a result in Rosenberg and Vieille
(2000), we obtain a uniform Tauberian theorem for recursive games:
converges uniformly if and only if converges uniformly.
We apply our main result to finite recursive games with signals (where
players observe only signals on the state and on past actions). When the
maximizer is more informed than the minimizer, we prove the Mertens conjecture
. Finally, we deduce
the existence of the uniform value in finite recursive game with symmetric
information.Comment: 32 page
Near-Optimal Deviation-Proof Medium Access Control Designs in Wireless Networks
Distributed medium access control (MAC) protocols are essential for the
proliferation of low cost, decentralized wireless local area networks (WLANs).
Most MAC protocols are designed with the presumption that nodes comply with
prescribed rules. However, selfish nodes have natural motives to manipulate
protocols in order to improve their own performance. This often degrades the
performance of other nodes as well as that of the overall system. In this work,
we propose a class of protocols that limit the performance gain which nodes can
obtain through selfish manipulation while incurring only a small efficiency
loss. The proposed protocols are based on the idea of a review strategy, with
which nodes collect signals about the actions of other nodes over a period of
time, use a statistical test to infer whether or not other nodes are following
the prescribed protocol, and trigger a punishment if a departure from the
protocol is perceived. We consider the cases of private and public signals and
provide analytical and numerical results to demonstrate the properties of the
proposed protocols.Comment: 14 double-column pages, submitted to ACM/IEEE Trans Networkin
The value of Repeated Games with an informed controller
We consider the general model of zero-sum repeated games (or stochastic games
with signals), and assume that one of the players is fully informed and
controls the transitions of the state variable. We prove the existence of the
uniform value, generalizing several results of the literature. A preliminary
existence result is obtained for a certain class of stochastic games played
with pure strategies
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