MA6312 MATHEMATICAL THEORY OF GAMES


Course Details

PART I: STATIC GAMES
1. Two-person zero-sum finite games: MAtrix games, Pure and mixed strategies, saddle point equilibrium strategies, extensive form games.
2. N-person finite games: Nash equilibrium, Refinements of Nash equilibirum, N-person games in extensive form.
3. Infinite games: Equilibrium strategies, continuous-kernel games, stackelberg equilibirum.
PART II: DYNAMIC GAMES
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.
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.
6. Pursuit-evasion games: Necessary and sufficient conditions for equilibrium, captuability, singular surfaces.

Course References:

TEXT BOOKS:
T.Basar and G.J.Olsder, Dynamic Noncooperative Game Theory, SIAM, 2nd edn, 1999.
REFERENCES:
1. R. B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1999
2. M. J. Osborne and A.Rubinstein, A course in Game Theory, MIT Press, 1994
3. D. Fudenberg and J. Tirole, Game Theory, MIT Press, 1991