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 rationality, neither necessary
nor sufficient for Nash equil
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:
1) Imitation + aspiration Binmore -Samuelson JET [1997]
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 theorem for observed actions,
finite # states and action
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 have common q belief about the state for q->1?
(discus
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 "reward" or "punish" opponents.
Repeating the game doesnt ge
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 term benefit so may not be worthwhile for an
impatient
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 zeroprobability events that are inconsistent with CK of rationa
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 () Ki (E) = cfw_ : hi ( ) E. Then,
hi (), hi ( ) E hi () E
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 ) ) and Ki (Ki ( E ) Ki ( E ) (where " " means "not".)
1
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 different game)
Agents dont observe how the opponents wou
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 induces 1 to choose C2 , 2 to choose B2 , and 1 to choos
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 that steady states with patient rational learners-> Na
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 the set of subgame-perfect equilibria?
(b) Write down
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 outcomes
of own matches?
Need to specify the matching s
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 payos from action
prole a are denoted by gi (a). Suppose th