Information Games

1-3

(work to be done prior to commencement of course)

Questions relating to problem sets 1-3 will be discussed on Wednesday 28 January.

Lecture 1 Representation of Games:

normal-form representation, extensive-form representation, information sets, random moves, histories, pure strategies, relationship between extensive-form and normal-form, mixed strategies and expected utility.

Lecture 2 Static Games of Complete Information - Dominance:

(strictly) dominant strategies, (strictly) dominated strategies, iterated deletion of strictly dominated strategies, iterated deletion and rationality, mixed strategies and dominance.

Lecture 3 Static Games of Complete Information - Pure Strategy Nash Equilibrium in Finite Games:

definition of Nash equilibrium (NE), finding NE, best-response correspondences and NE, motivating NE, relation between NE and iterated deletion, existence of NE in pure strategies in finite games, multiplicity.

Lecture 4 Static Games of Complete Information - Mixed Strategy Nash Equilibrium in Finite (Discrete) Games:

definition of mixed strategy NE, finding mixed strategy NE, mixed best-response correspondences and mixed NE, motivating mixed NE, existence of (possibly mixed) NE in finite games.

5

(Wednesday 4 February)

Lecture 5 Static Games of Complete Information - Nash Equilibrium in Infinite (Continuous) Games:

finding NE in games with continuous strategy spaces, best-response correspondences and NE with continuous strategy spaces, strategic substitutes vs. strategic complements, applications in economics and finance, existence of NE in games with continuous strategy spaces.

(Problem Set 5)

6

(Wednesday 11 February)

Lecture 6  Dynamic Games of Complete Information - Subgame Perfect Nash Equilibrium in Finite Games:

incredible threats and incredible promises, subgames, definition of subgame perfect Nash equilibrium (SPNE), finding SPNEs in games of perfect information (Backward Induction Procedure), finding SPNE in games of imperfect information (Generalized Backward Induction Procedure), NE versus SPNE, existence of SPNE in finite games.

(Problem Set 6)

7

(Wednesday 18 February)

Lecture 7 Dynamic Games of Complete Information - Subgame Perfect Nash Equilibrium in Continuous Games with Perfect Information:

finding SPNE in continuous games of perfect information, SPNE outcome vs. SPNE, games of positive externalities vs. games of negative externalities, NEs of simultaneous-move vs. SPNE of sequential move games, costs and benefits of precommitment: first-mover advantage vs. second-mover advantage, strategic effect and direct effect of first-stage behaviour, applications.

(Problem Set 7)

8

(Wednesday 25 February)

Lecture 8 Dynamic Games of Complete Information - Subgame Perfect Nash Equilibrium in Continuous Games with Imperfect Information:

finding SPNE in continuous games of imperfect information, strategic precommitments to affect future interactions, formal analysis of incentives for precommitment, strategic effects and direct effects, Tirole’s animal terminology to characterize commitment strategies, a graphical analysis of precommitment effects.

(Problem Set 8)

9

(Wednesday 4 March)

Lecture 9  Dynamic Games of Complete Information - Subgame Perfect Nash Equilibrium in Games with (Potentially) Infinite Sequences of Moves:

finding SGPE in games with (potentially) infinite sequences of moves, motivation for repeated games, finitely and infinitely repeated games, finitely repeated games with unique and with multiple NE in stage-game, one-stage-deviation principle, infinitely repeated games and discounting, applications of infinitely repeated games (cooperation in social dilemmas, collusion), characterizing SPNE outcome paths in payoff space (folk theorems), infinite horizon, infinite action bilateral bargaining.

(Problem Set 9)

10

(Wednesday 11 March)

Lecture 10 Static Games of Incomplete Information - Bayesian Equilibrium in Finite (Discrete) Games:

incomplete information, Harsanyi transformation, definition of Bayesian equilibrium (BE), finding BE in finite games, correlated types, applications, existence of BE in finite games.

(Problem Set 10)

11

(Wednesday 18 March)

Lecture 11  Static Games of Incomplete Information - Bayesian Equilibrium in Infinite (Continuous Action and/or Continuous Type Spaces) Games:

definition of BE in games with continuous action and/or continuous type spaces , finding BE in games with continuous action and/or continuous type spaces, Cournot with asymmetric information on cost, purification of mixed strategies, first price auction.

(Problem Set 11)

12

(Wednesday 25 March)

Lecture 12 Dynamic Games of Incomplete Information - Perfect Bayesian Equilibrium in Finite Games:

motivation for definition of perfect Bayesian equilibrium (PBE), elements of PBE, definition of PBE, finding PBE, applications.

(Problem Set 12)

13

(Wednesday 1 April)

Lecture 13 Dynamic Games of Incomplete Information - Perfect Bayesian Equilibrium in Signalling Games:

definition of signalling game, translation of definition of PBE (for general games) to a definition of PBE for signalling games, finding PBE in signalling games, applications of signalling in economics and finance.

Lecture 14 Dynamic Games of Incomplete Information – Refinements of Perfect Bayesian Equilibrium:

implausible beliefs off-the-equilibrium-path, forward induction, domination-based refinements on beliefs, intuitive criterion, other refinements, applications.

(Problem Set 13)

(Problem Set 14)