Economics 2052: Game Theory
Spring 2014
Monday 4-7 pm
Robinson Hall 107
Instructor: Drew Fudenberg, 310 Littauer, [email protected]
Office hours: Wednesday 1:30-3:30pm
Teaching fellow: Jonathan L
NON-EQUILIBRIUM ADJUSTMENT PROCESSES AND LEARNING IN GAMES
Overview
When and why will observed play to approximate an equilibrium?
What sort of equilibrium?
Rationality, even common knowledge of ratio
Back to Strategic Form Games:
Other adjustment processes and other techniques.
1. Imitation Processes: like REL dont require agents to know payoff matrix,
and stochastic even w/o mutations.
Examples:
Generalizations of Repeated Games
1. Stochastic Games
Per-period payoffs depend on a publicly observed state; state evolution depends
on actions played.
Shapley (1953): General definition and minmax t
Common Learning (CEMS [2008])
Two players, finite set of payoff-relevant states, common prior p.
Each period t each agent i sees (exogenous) private signal zit
State space = Z
When do players come to
Repeated Games
No tangible link between periods, but players can condition current play on
their information about past actions; can allow new equilibria because players
know have the ability to "rewa
Reputation Effects
Basic idea: Repeatedly playing a given action can generate a reputation for
playing that action and induce opponents to play a best response to it.
Tradeoff short term cost vs. long
Equilibrium Refinements:
Overview/Interpretation
Payoffs are common knowledge (CK) or common certainty, and no sequence
of observations to the contrary changes anyones belief about this, even zeroprob
ECON 2052 SPRING 2014: SOLUTIONS TO PROBLEM SET # 1
Problem 0
Claim. Ki (E) = Ki (Ki (E)
Proof. Want to show that
cfw_ : hi () Ki (E) = cfw_ : hi () E.
To see that this equality holds, suppose hi () K
Spring 2014
Economics 2052
Problem Set 1
Due Monday Feb. 24
0.
(warm up exercise, do not hand in)
In the standard state-space model of knowledge presented in class, prove that
Ki ( E ) = Ki ( Ki ( E )
Extensive form games and self-confirming equilibrium
Extensive form games: agents observe (at most) the terminal nodes that are
reached in their own plays of the game.
(strategy method results in a di
ECON 2052 SPRING 2014: SOLUTIONS TO PROBLEM SET # 2
Problem 1
[Solution due to Annie Liang]
(a) (A1 C2 , B2 D2 ) is the unique SPNE by backwards induction: At the last node, 2 will
choose D2 , which i
Last time: steady states of rational Bayesian learning->SCE.
(quasi) Converse: any SCE in strategies that arent weakly dominated is a steady
state of the overlapping generations model of FL.
Also know
Problem Set 2
Ec 2052, Spring 2014
Due March 24, 2014
1. Consider the following game of perfect information:
1
A1
A2
(0,0)
2
B1
B2 B3
(0,0)
(1, -1)
1
C1
C2
(-2, -1)
2
D1
(-3, 0)
D2
(-1, 1)
(a) What is
SFP with Heterogeneous Agents (Fudenberg-Takahashi [2011])
Non-strategic behavior in SFP doesn make sense with one agent per role.
t
What happens in large populations of agents each of whom only sees
Problem Set 3
Ec 2052, Spring 2014
Due April 21, 2014
1. Consider a repeated game between I players, each player i simultaneously choosing
an action ai Ai in each stage game. Player is stage game payo