Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration | Zendy

Sylvain Sorin | Zendy

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Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration

Author(s) -

Sylvain Sorin

Publication year - 2017

Publication title -

mathematics of operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.619

H-Index - 83

eISSN - 1526-5471

pISSN - 0364-765X

DOI - 10.1287/moor.2017.0851

Subject(s) - mathematics , limit (mathematics) , zero sum game , zero (linguistics) , discrete time and continuous time , partition (number theory) , differential game , markov chain , mathematical economics , markov process , markov decision process , state (computer science) , discrete mathematics , combinatorics , mathematical optimization , game theory , mathematical analysis , algorithm , statistics , linguistics , philosophy

We consider two-person zero-sum games where the players control, at discrete times {tn} induced by a partition Π of ℝ+, a continuous time Markov process. We prove that the limit of the values υΠ exist as the mesh of Π goes to 0. The analysis covers the cases of (1) stochastic games (where both players know the state), and (2) games with unknown state and symmetric signals. The proof is by reduction to deterministic differential games.

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