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On Markov games
Author(s) -
Wal J. van der,
Wessels J.
Publication year - 1976
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1976.tb00266.x
Subject(s) - markov chain , markov decision process , markov model , mathematical proof , markov property , markov kernel , mathematics , markov process , markov perfect equilibrium , mathematical economics , variable order markov model , computer science , markov renewal process , mathematical optimization , nash equilibrium , statistics , geometry
In the paper it is demonstrated, how a dynamic programming approach may be useful for the analysis of Markov games or stochastic games. Markov games with finitely many stages are dealt with extensively. The existence of optimal Markov strategies is proven for finite stage Markov games using a shortcut of a proof by D erman for the analogous result for Markov decision processes. For Markov games with a countably infinite number of stages some results are summarized. Here again the results and the methods of proof have much in common with results and proofs for Markov decision processes. Actually the theory of Markov games is a generalisation. The paper contains short introductions into the theories of matrix games and tree games.