4,856 research outputs found
On Zero-Sum Two Person Perfect Information Stochastic Games
A zero-sum two person Perfect Information Stochastic game (PISG) under
limiting average payoff has a value and both the maximiser and the minimiser
have optimal pure stationary strategies. Firstly we form the matrix of
undiscounted payoffs corresponding to each pair of pure stationary strategies
(for each initial state) of the two players and prove that this matrix has a
pure saddle point. Then by using the results by Derman [1] we prove the
existence of optimal pure stationary strategy pair of the players. A crude but
finite step algorithm is given to compute such an optimal pure stationary
strategy pair of the players.Comment: arXiv admin note: text overlap with arXiv:2201.0017
On Zero-Sum Two Person Perfect Information Semi-Markov Games
A zero-sum two-person Perfect Information Semi-Markov game (PISMG) under
limiting ratio average payoff has a value and both the maximiser and the
minimiser have optimal pure semi-stationary strategies. We arrive at the result
by first fixing an arbitrary initial state and forming the matrix of
undiscounted payoffs corresponding to each pair of pure stationary strategies
of the two players and proving that this matrix has a pure saddle point
Holographic Construction of Excited CFT States
We present a systematic construction of bulk solutions that are dual to CFT
excited states. The bulk solution is constructed perturbatively in bulk fields.
The linearised solution is universal and depends only on the conformal
dimension of the primary operator that is associated with the state via the
operator-state correspondence, while higher order terms depend on detailed
properties of the operator, such as its OPE with itself and generally involve
many bulk fields. We illustrate the discussion with the holographic
construction of the universal part of the solution for states of two
dimensional CFTs, either on or on . We compute the
1-point function both in the CFT and in the bulk, finding exact agreement. We
comment on the relation with other reconstruction approaches.Comment: 26 pages, 4 figures, v2: comments adde
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