Notable features of auctions
Ancient market mechanisms.
use. A lot of varieties.
Common auctions &
Revenue equivalence &
Simple and transparent games (mechanisms). Universal rules (does not depend on the ob
14.126 GAME THEORY
Department of Economics, MIT,
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
14. 126 Game Theory
Based on Lectures by Paul Milgrom
Definitions: lattices, set orders, supermodularity
Games with Strategic Complements
Dominance and equilibrium
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
14.129 Advanced Contract Theory
February 23, 2005
A general incomplete information setting
A nite group of players (economic agents), denoted by N = cfw_1, . . . , n, interact. Any interaction can
Unit 3: Producer Theory
Q = f L, K);
M RT S =
MR = MC
MR = P
P = MC
P < min AV C
P = MC
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)
14.126 Lecture Notes on Rationalizability
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
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
Interdependent (common) values.
Each bidder receives private signal Xi [0, wi].
(wi = is possible)
(X1, X2, . . . , Xn) are jointly distributed according to commonly known F (f > 0).
Interdependent Values &
Vi = vi(X1, X2, . . . , Xn).
M units of the same object are oered for sale.
Each bidder has a set of (marginal values) V i =
(V1 , V2 , . . . VM ), the objects are substitutes, Vk
Multiunit Auctions &
Extreme cases: unit-demand, th
IPV and Revenue Equivalence:
Each bidder has u : R+ R with u(0) = 0,
u0 > 0, and u00 < 0.
Independence of values.
Proposition: With risk-averse symmetric bidders the
expected revenue in a rst-pri
14.126 Game Theory
There will always be small but positive
probability of mutation.
Then, some of the strict Nash equilibria will
not be stochastically stable.