6
The Principle of Optimality
Denition 1 A T shot deviation from a strategy si is a strategy si such that there exists
b
T such that
for all ht 2 H with t
T:
si (ht ) = si (ht )
b
Denition 2 A one-sho
11
Global Games
Common complaint about Nash equilirium is that there is an extreme amount of coordination built into the notion of equilibrium.
Global games is a device to model situations where coord
12
Adverse Selection and Insurance; The Case with a
Monopoly
Suppose that there are two typesof consumers. Call them fH; Lg
Type H has a probability of an accident given by
Type L has a probability of
13
Social Choice
The fundamental question in social choice theory is the following: Given a collection of agents with
preferences over dierent alternatives ( allocations, outcomes), how should society
14
Mechanism Design
The basic point with mechanism design is that it allows a distinction between the underlying
economic environment and the rules of the game We will take as given some set of possib
10
Dynamic Games of Incomple Information
DRAW SELTEN HORSE
S
In game above there are no subgames. Hence, the set of subgame perfect equilibria
and the set of Nash equilibria coincide.
However, the sor
9
Games of Incomplete Information
9.1
Cournot Duopoly With Unknown Costs
Assume that two rms produce a homogenous good with inverse demand P (Q) = max f2
Q; 0g ;
where Q is interpreted as the total qu
1
Games on Normal Form
1.1
Examples of Normal Form Games
A Game in Normal (sometimes strategic) form consists of:
1. A set of players I; which we assume is a nite set I = f1; :; ng
2. A strategy space
2
Extensive Form Games
Denition 1 A nite extensive form game is an object
K = fI; (T; ) ; P; A; H; u; g ;
where
I = f0; 1; :; ng is the set of agents (0 denotes nature
)
(T; ) is the game tree
P is th
3
Alternating Oers Bargaining
Consider the following setup following Rubinstein (1982) extension of a model by Stahl
s
(1972):
Two players bargain over a pie with size normalized to 1.
Given a divisio
8
Mixed Strategies
Rock
Scissors
Paper
Rock
0,0
1,-1
-1,1
Scissors
1,-1
0,0
1,-1
Paper
1,-1
-1,1
0,0
Figure 1: A Game with no Pure Strategy Nash Equilibrium
Clearly, there is no pure strategy equilibr
15
Optimal Auctions with Private Values and Independent Types
15.1
Set-up
A seller seeks to sell a single indivisible good. There are n potential buyers (aka bidders We
).
denote the set of of bidders