TEW - Stochastic Processes, Optimization and Game Theory (2020)

Speakers and Syllabus


Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Prof. Rahul Roy

6

Stochastic Processes: Elementary concepts: Experiments, Outcomes, Sample space, Events. Discretesample spaces and probability models. Conditional probability and independence. Random variables-discrete and continuous: Expectation, variance and moments of random variables. Jointly distributed random variables, Conditional expectation. Generating functions. Limit theorems. Discrete Markov chains with countable state space. Classification of states- recurrence, transience, periodicity. Random walks, Gambler's ruin problem.

Prof. Aparna Mehra

6

Optimization: Non-linear programming: feasible directions, basic constraint qualification, first order necessary conditions, KKT conditions, special cases of linear and quadratic program. Convexity, applications of nonlinear programs in machine learning. One dimensional line search methods and convergence, Golden section and Fibonacci method, Steepest descent method, conjugate gradient method in n-dimensional space.

Dr. Satyanarayana Arikatla

6

Combinatorial Optimization: Equivalence of seven Major theorems: Menger's thorem, Konig's thorem for matrices, Konig-Egervary theorem, Hall's Marriage theorem, Birkhoff Vonneumann theorem, Dilworth's thoerem and  Max Flow-Min cut theorem. Few applications of these theorems in various fields.

Dr. Jyotirmoy Bhattacharya

6

Game Theory: Games in normal form: Nash equilibrium, dominance solvability and rationalizability. Bayes Nash equilibrium for games of incomplete information. Games in extensive form: subgame perfection.

 

References:

  1. W. Feller: Introduction to the Theory of Probability and its Applications, Vol. 1

  2. P.G. Hoel, S.C. Port and C.J. Stone: Introduction to Stochastic Processes

  3. S.M. Ross: Stochastic Processes

  4. S. Karlin and J. Taylor: Stochastic Processes, Vol. 1

  5. J.G. Kemeny, J.L. Snell and A.W. Knapp: Finite Markov Chains

  6. Alexander Schrijver: A Course in Combinatorial Optimization (Onlines notes: https://homepages.cwi.nl/~lex/files/dict.pdf)

  7. Luca Trevisan: Combinatorial Optimization-Exact and Approximate Algorithms (Online notes: http://theory.stanford.edu/~trevisan/books/cs261.pdf)

  8. John Lee: A first course in Combinatorial optimization, Cambridge University Press

  9. T. Cormen, C. Leiserson, R. Rivest: Introduction to Algorithms, McGraw Hills, 2001

  10. M.J. Osborne and A. Rubinstein: A Course in Game Theory, MIT Press

  11. M. Maschler, E. Sorin, and S. Zamir: Game Theory, Cambridge University Press

  12. D.Fudenberg and J. Tirole: Game Theory, MIT Press


Time Table

Day

Date

Lecture 1

(9.30–10.30)

10.35
to
10.55

Lecturer 2

(11.00–12.00)

Lecture 3

(12.00–1.00)

1.00
to
2.20

Lecture 4

(2.30-3.30)

3.35
to
3.55

Discussion

(4.00-500)

5.05
to
5.30

(Speaker’s name)

(Speaker’s name)

(Speaker’s name)

(Speaker’s name)

(Tutor’s name)

Thu

30.4.20

RR

T
e
a

RR

AM

 L
u
n
c
h

AM

T
e
a

AM

S
n
a
c
k
s

Fri

1.5.20

AM

AM

RR

RR

RR

Sat

2.5.20

SA

SA

RR

RR

RR

Mon

4.5.20

JB

JB

AM

AM

AM

Tue

5.5.20

SA

SA

JB

JB

JB

Wed

6.5.20

JB

JB

SA

SA

SA+SC

  •  RR: Prof. Rahul Roy
  • AM: Prof. Aparna Mehra
  • SA: Dr. Satyanarayana Arikatla
  • JB: Dr. Jyotirmoy Bhattacharya
  • SC: Ms Shivani Chauhan (Research Scholar)

Ttutors:

Sr..

Name

Affiliation

1

Prof. Rahul Roy

ISI, Delhi

2

Prof. Aparna Mehra

IIT, Delhi

3

Dr. Satyanarayana Arikatla

ShivNadar University, Uttar Pradesh

4.

Dr. Jyotirmoy Bhattacharya

Ambedkar University, Delhi

5.

Ms. Shivani Chauhan

Research Scholar, Departement of Mathematics, SNU

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