<h3>MA6312 MATHEMATICAL THEORY OF GAMES</h3>
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<h4>Course Details</h4>
PART I: STATIC GAMES<br> 1. Two-person zero-sum finite games: MAtrix games, Pure and mixed strategies, saddle point equilibrium strategies, extensive form games.<br> 2. N-person finite games: Nash equilibrium, Refinements of Nash equilibirum, N-person games in extensive form.<br> 3. Infinite games: Equilibrium strategies, continuous-kernel games, stackelberg equilibirum.<br> PART II: DYNAMIC GAMES<br> 3. Formulation of dynamic games: Discrete-time dynamic games, continuous-time dynamic games, mixed and behaviour strategies in dynamic games, representations of strategies along trajectories, time-consistency of optimal policies.<br> 5. Equilibria of dynamic games: Open-loop and feedback equilibria for dynamic games in discrete-time, informational properties of Nash equilibrium in discrete-time dynamic games, Open-loop and Feedback equilibria for differential games.<br> 6. Pursuit-evasion games: Necessary and sufficient conditions for equilibrium, captuability, singular surfaces.
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<h4>Course References:</h4>
TEXT BOOKS:<br>
T.Basar and G.J.Olsder, Dynamic Noncooperative Game Theory, SIAM, 2nd edn, 1999<br>
REFERENCES:<br>
1. R. B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1999<br>
2. M. J. Osborne and A.Rubinstein, A course in Game Theory, MIT Press, 1994<br>
3. D. Fudenberg and J. Tirole, Game Theory, MIT Press, 1991