06CS763 - Game Theory |
PART – A |
UNIT 1 |
INTRODUCTION; STRATEGIC GAMES: What is game theory? The
theory of rational choice; Interacting decision makers. Strategic games;
Example: The prisoner’s dilemma; Nash equilibrium; Examples of Nash
equilibrium; Best-response functions; Dominated actions; Equilibrium in a
single population: symmetric games and symmetric equilibria. |
UNIT 2 |
MIXED STRATEGY EQUILIBRIUM: Introduction; Strategic games in
which players may randomize; Mixed strategy Nash equilibrium; Dominated
actions; Pure equilibria when randomization is allowed, illustration;
Equilibrium in a single population, illustration; The formation of players’
beliefs; Extensions; Representing preferences by expected payoffs. |
UNIT 3 |
EXTENSIVE GAMES: Extensive games with perfect information;
Strategies and outcomes; Nash equilibrium; Subgame perfect equilibrium;
Finding subgame perfect equilibria of finite horizon games. |
UNIT 4 |
EXTENSIVE GAMES: EXTENSIONS, COALITIONAL GAMES AND
THE CORE: Extensions: Allowing for simultaneous moves, illustration:
entry in to a monopolized industry; Discussion: subgame perfect equilibrium
and backward induction.Coalition games; The core; Illustration: ownership
and the distribution of wealth; Other solution concepts. |
PART – B |
UNIT 5 |
BAYESIAN GAMES: Motivational examples; General definitions; Two
examples concerning information; Illustration: auctions; Auctions with an
arbitrary distribution of valuations. Extensive games with imperfect
information; Strategies; Nash equilibrium; Beliefs and sequential equilibrium; Signaling games; Illustration: strategic information
transmission. |
UNIT 6 |
STRICTLY COMPETITIVE GAMES, RATIONALIZABILITY: Strictly competitive games and maximization; Maximization and Nash
equilibrium; Strictly competitive games; Maximization and Nash equilibrium
in strictly competitive games. Rationalizability; Iterated elimination of
strictly dominated actions; Iterated elimination of weakly dominated actions;
Dominance solvability. |
UNIT 7 |
EVOLUTIONARY EQUILIBRIUM, ITERATED GAMES: Monomorphic pure strategy eulibrium; Mixed strategies and polymorphic
equilibrium; Asymmetric contests; Variations on themes: Sibling behavior,
Nesting behavior of wasps, the evolution of sex ratio. Repeated games: The
main idea; Preferences; Repeated games; Finitely and infinitely repeated
Prisoner’s dilemma; Strategies in an infinitely repeated Prisoner’s dilemma;
Some Nash equilibria of an infinitely repeated Prisoner’s dilemma. |
UNIT 8 |
REPEATED GAMES: GENERAL RESULTS, BARGAINING: Nash
equilibria of general infinitely repeated games; Subgame perfect equilibria of
general infinitely repeated games; Finitely repeated gazmes; Imperfect
observability. Bargaining as an extensive game; Trade in market as an
illustration; Nash’s axiomatic model; Relation between strategic and
axiomatic models. |
REFERENCE |
TEXT BOOKS: |
1. An Introduction to Game Theory – Martin Osborne, Oxford
University Press, Indian Edition, 2004.
|
Reference Books |
1. Game Theory: Analysis of Conflict – Roger B. Myerson, Harvard
University Press, 1997.
2. Microeconomic Theory – Andreu Mas-Colell, Michael D.
Whinston, and Jerry R. Green, Oxford University Press, New York,
1995.
3. Game Theory and Strategy – Philip D. Straffin, Jr., The
Mathematical Association of America, January 1993. |