Speaker: |
T.E.S. Raghavan (University of Illinois at Chicago Department of Mathematics, Statistics and Computer Science 851, S. Morgan Chicago, IL 60607-7045 United States of America) |

Organiser: |
Sandeep K Juneja |

Date: |
Wednesday, 11 Mar 2015, 11:30 to 12:30 |

Venue: |
AG-66 (Lecture Theatre) |

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While zero sum two person stochastic games with finitely many states and actions admit stationary optimal strategies for discounted payoffs, the existence of value with Cesaro payoff is possible only in the space of behavioral strategies. At each move players may have to peg on the entire history so far to make their randomized action choices. The seminal theorem of Mertens and Neyman on the existence of value for Cesaro payoff stochastic games is made quite simple and transparent by an application of the above theorem of Martin on perfect information Gale Stewart games. It simply bypasses many complicated constructions and technical estimates that view solution to the discounted Shapley value equation as an elementary sentence in the space of the ordered field of Laurentz series in fractional powers of the discount factor, namely the real closed field of Puiseux series and hence relies on many tools fromĀ real algebraic geometry. The talk will present this proof due to Ashok Maitra and Sudderth. Their theorem is applicable to much more general classes of payoffs besides Cesaro payoffs. This is a fruitful interplay between mathematical logic and game theory.