Roll Number
12i190007
Category
TA
Topics for PhD Qualifiers
Compulsory Subject: (i) Optimisation Techniques, (ii) Stochastic Models
Elective 1:Game Theory
Elective 2:Probability Theory
Elective 1:Game Theory
Elective 2:Probability Theory
Elective1
Game Theory:
Strategic Form Games(Domination,Elimination of Dominated Strategies, Two-Player Zero sum games, Matrix Games, Minmax Solution Concept, Bimatrix Games, N-Person Games in Normal Form, Nash Equilibrium:Existence,Properties,Stability, Pure Strategy Solution, Mixed Strategies Solution, Games with Perfect Information, Games with Imperfect Information).
Games with Incomplete Information(Common Knowledge, Aumann's Model of Incomplete Information, Information Sets, Correlated equilibrium Concept: Definitions and Properties).
Extensive Form Games(Zero-Sum Games: Single and Multi Act Games, Non Zero Sum Games: Single Act Games(pure Nash Concept, Behavioral and Mixed Solutions Concept) and Multi Act Games(Pure Strategy Nash Equilibria, Behavioural and mixed equilibrium strategy), Sub Game Perfect Equilibrium, Rationalizibility, Backward Induction, Stackelberg Solution Concept).
Strategic Form Games(Domination,Elimination of Dominated Strategies, Two-Player Zero sum games, Matrix Games, Minmax Solution Concept, Bimatrix Games, N-Person Games in Normal Form, Nash Equilibrium:Existence,Properties,Stability, Pure Strategy Solution, Mixed Strategies Solution, Games with Perfect Information, Games with Imperfect Information).
Games with Incomplete Information(Common Knowledge, Aumann's Model of Incomplete Information, Information Sets, Correlated equilibrium Concept: Definitions and Properties).
Extensive Form Games(Zero-Sum Games: Single and Multi Act Games, Non Zero Sum Games: Single Act Games(pure Nash Concept, Behavioral and Mixed Solutions Concept) and Multi Act Games(Pure Strategy Nash Equilibria, Behavioural and mixed equilibrium strategy), Sub Game Perfect Equilibrium, Rationalizibility, Backward Induction, Stackelberg Solution Concept).
Elective2
Probability Theory:
Probabilty(Axioms, Conditional Probability and Independence, Construction of Probability Measures).
Random Variables and Integration(Random Variables on a Countable Space and Their Expectations, Markov's Inequality, Chebychev's Inequality, Independence, Convergence of Random Variables).
Conditioning and Martingales(Conditional Expectations, Martingales, Supermartingales, Submartingales, Martingale Inequalities, Martingale Convergence Theorems).
Basic Limit Theorems(Strong Law of Large Number, Central Limit Theorem).
Probabilty(Axioms, Conditional Probability and Independence, Construction of Probability Measures).
Random Variables and Integration(Random Variables on a Countable Space and Their Expectations, Markov's Inequality, Chebychev's Inequality, Independence, Convergence of Random Variables).
Conditioning and Martingales(Conditional Expectations, Martingales, Supermartingales, Submartingales, Martingale Inequalities, Martingale Convergence Theorems).
Basic Limit Theorems(Strong Law of Large Number, Central Limit Theorem).
PhD. Supervisor (if decided)
K.S. Mallikarjuna Rao