Strategic Form Games: Barebones Definitions
An strategic form game is a collection G = (N, cfw_Si iN , cfw_%i iN ) where
1. N = cfw_1, ., n, a finite set of players. For i N :
2. Si is player is nonempty strategy set; and
3. %i is player is complete and t

Open Question
In the usual notation let
d(p, w) = cfw_y B(p, w) | y % x for every x B(p, w)
be the demand correspondence, where B(p, w) = cfw_x X | p x w is the budget set (for
(p, w) > 0) X = R+
+ is the consumption set, and % X X is an arbitrary binary

ECN 712: Microeconomic Analysis I
FALL 2016
E Schlee
Office: CPCOM 455G; ph: (480) 965-5745; email: ed.schlee@asu.edu
Hours: Mainly by appt; walk-in times are Mondays 230 -320 and just after class.
TA: Mehrdad Esfahani, <Mehrdad.Esfahani@asu.edu>.
Well be

The two-good quasilinear economy
There are J firms, I consumers, and L = 2 goods. Good 1 is a consumption good and an output for each firm. Good
2 is both a consumption good and an input for each firm. The relative price of good 1 in terms of good 2 is p

Demand Properties: Summary Fall 2015
In what follows u is a continuous and locally nonsatiated real-valued function representing a preference relation % on the consumption set X = RL
+ . For (p, w) > 0, define d(p, w) =
cfw_x B(p, w) | u(x) u(y) for every

Nash Equilibrium of the Cournot Game:
Existence and Uniqueness
Consider a Cournot game with n 1 firms. Let p() : R+ R+ be an inverse demand satisfying
the usual conditions: it is continuous and nonincreasing with p(0) > 0; and on cfw_Q 0 | p(Q) > 0,
it is

Extensive Form Games
An extensive form game is a collection = (N, A, H, T, , I, cfw_Ui iN ).
1. N , a finite set of players.
2. A, a set of actions.
3. H, a set of histories (sometimes called nodes), with
(a) h0 H, where h0 is the empty history.
(b) h H c

Covariance Inequality
Let F be a cumulative distribution function on R with bounded support D that contains at least
two elements. Let f and g be real-valued functions on D.
Covariance Inequality: If f and g are either both increasing or both decreasing,

Comparative Risk Aversion (The Arrow-Pratt Theorem)
For t = 0, 1, let ut be a C 2 vN-M utility with u0t > 0 on R+ . And let L be the set of
cumulative distribution functions on R with F (0) = 0 and F (z) = 1 for some number z < .1
u00 (z)
For t = 0, 1, de

Convex and Quasiconvex Functions
Let f : D R for some nonempty convex subset D of Rn . The function f is convex if, for
any x and y in D and [0, 1], f (x + (1 )y) f (x) + (1 )f (y). Is is quasiconvex
if, for any x, y in D and [0, 1], f (x + (1 )y) maxcfw_

Concave Programming
Let f : Rn+ R for some positive integer n, and let g : Rn+ Rm for some positive integer
m be continuously differentiable functions. Consider the problem
max f (x)
(1)
xRn
+
subject to the constraint that g(x) 0. Let L(x, ) = f (x) g(x)

Essential Goods
Let u be a continuous and locally nonsatiated real-valued function representing a preference relation
% on the consumption set X = RL
+ . For (p, w) > 0, define
d(p, w) = cfw_x B(p, w) | u(x) u(y) for every y B(p, w)
where B(p, w) = cfw_x

Properties of indirect utility functions
Let u be a real-valued, continuous, locally nonsatiated function on the consumption set RL
+ and let
L
B(p, w) = cfw_x R+ | p x w be the budget set at (p, w) > 0. Consider
V (p, w) =
max u(x).
xB(p,w)
Theorem (Prop

Game 2
Game 1
a
1
0
5
1
L
d
R
2
2
-2
-2
r
l
r
l
2
-2
-2
1
1
r
l
0
5
1
1
0
0
1s Srategy Set = cfw_a,d
1s Srategy Set = cfw_L,R
2s Srategy Set = cfw_l,r
2s Srategy Set = cfw_ll,lr,rl,rr
NE= cfw_(L,rr), (L,rl),(R,ll
NE= cfw_(a,l), (d,r)
ll
r
l
lr
rl
rr
a
0,5