1
Notable features of auctions
Ancient market mechanisms.
use. A lot of varieties.
Auctions 1:
Common auctions &
Revenue equivalence &
Optimal mechanisms
Widespread in
Simple and transparent games (mechanisms). Universal rules (does not depend on the ob
14.126 GAME THEORY
MIHAI MANEA
Department of Economics, MIT,
1.
orward Induction in Signaling Games
Consider now a signaling game. There are two players, a sender S and a receiver R.
There is a set T of types for the sender; the realized type will be deno
Final Exam: 15:818
Extract from "With Select Apps, iPad is More Than a Pretty Face", New York Times, April 2010
Travelers can download 1,000 Experiences from Lonely Planet ($10), a graphically rich look at a wide variety of
trips. Lonely Planet cut the pr
Supermodularity
14. 126 Game Theory
Muhamet Yildiz
Based on Lectures by Paul Milgrom
1
Road Map
Definitions: lattices, set orders, supermodularity
Optimization problems
Games with Strategic Complements
Dominance and equilibrium
Comparative statics
2
1
Two
Applied Economics
For Managers
D. Richards
Summer, 2003
Final Exam
1. (20 points) The weekly demand for beer in Maltown is described by: P = 1000 2Q, where Q is
measured as the number of six-packs consumed each week and P is the price of a six-pack. The m
Bayesian-Nash games
Sergei Izmalkov
14.129 Advanced Contract Theory
February 23, 2005
1
A general incomplete information setting
1.1
Primitives
A nite group of players (economic agents), denoted by N = cfw_1, . . . , n, interact. Any interaction can
be re
Unit 3: Producer Theory
Q = f L, K);
MC =
MC =
dT C
dQ
M RT S =
w
r
4T C
4Q
MR = MC
MR = P
P = MC
P < min AV C
P = MC
Q=0
P < min AV C
P = M C = AC
P = min AC
q = arg min AC
Unit 4: Welfare Economics
Unit 5: Monopoly and Oligopoly
T R = P Q) Q
AR = P Q)
M
14.126 Lecture Notes on Rationalizability
Muhamet Yildiz
April 9, 2010
When we dene a game we implicitly assume that the structure (i.e. the set of players, their strategy sets and the fact that they try to maximize the expected value of
the von-Neumann a
14.01: Final Review
December 3, 2010
Unit 5: Market Power
1
Lecture 17: Oligopoly Continued (Chapter 12)
I. Cournot Math
Cournot: All rms set quantities at the same time
Calculate residual demand for a given rm and solve its prot maximization problem to
1
Interdependent (common) values.
Each bidder receives private signal Xi [0, wi].
(wi = is possible)
Auctions 3:
(X1, X2, . . . , Xn) are jointly distributed according to commonly known F (f > 0).
Interdependent Values &
Vi = vi(X1, X2, . . . , Xn).
h
i
M units of the same object are oered for sale.
Each bidder has a set of (marginal values) V i =
i
i
i
i
(V1 , V2 , . . . VM ), the objects are substitutes, Vk
i
Vk+1.
Auctions 4:
Multiunit Auctions &
Cremer-McLean Mechanism
Extreme cases: unit-demand, th
1
IPV and Revenue Equivalence:
Key assumptions
2
Risk-averse bidders
Each bidder has u : R+ R with u(0) = 0,
u0 > 0, and u00 < 0.
Independence of values.
Risk-neutrality.
Proposition: With risk-averse symmetric bidders the
expected revenue in a rst-pri
LearningAdjustment with
persistent noise
14.126 Game Theory
Mihai Manea
Muhamet Yildiz
Main idea
There will always be small but positive
probability of mutation.
Then, some of the strict Nash equilibria will
not be stochastically stable.
1
General Procedu