ECE 586RS
Each problem is worth 10 points.
Homework 4
Due: November 11
1. Consider the online convex optimization problem considered in the class. But now assume (in
addition to the assumptions in the class) that
52 f (x) M I, for some M > 0,
2f
where 52
Dynamic Programming
R. Srikant
ECE586RS
Shortest Path on a Directed Graph
4
7
2
5
8
3
6
9
1
S
Find
the shortest path from S to D.
is the distance from node I to node
j
D
Number
of paths from S to D is 3*3*3=27. In general, if there are T intermediate stag
Zero-Sum Dynamic
Games
R. Srikant
ECE586RS
Discrete-Time Formulation
Consider a dynamical system controlled by two players: we will call
the controller and the adversary or noise
Here, x, u, and w can all be vectors. The goal of the controller is to
min
ECE 586RS
Each problem is worth 10 points.
Homework 3
Due: November 4
1. Consider the following Pigou network:
(i) Show that the price of anarchy (PoA) when CB (x) is of the form ax2 + bx + c, a, b, c 0 is
3 3
upper bounded by 3
.
32
d
P
d+1
(ii) Show tha
ECE 586RS
Each problem is worth 10 points.
Homework 2
Due: September 23
1. (Exercise 1.6 (F & T) Show that the two-player game illustrated in the following figure has a
unique equilibrium. (Hint: Show that it has a unique pure-strategy equilibrium; then s
ECE 586RS
Each problem is worth 10 points.
Homework 1
Due: September 9
1. (Owen) A zero-sum matrix game is said to be symmetric if the payoff matrix A is skew-symmetric,
i.e., A = AT .
Find the value of a symmetric game.
In a symmetric game, show that i
ECE 586RS
Each problem is worth 20 points.
Midterm 1
Due: October 7
1. Consider a zero sum game with cost function
J(u, w) = (x + u + w)2 + u2 2 w2 ,
where x 6= 0 is a given real number, u R and w R are controlled by Players 1 and 2, respectively,
and is
ECE 586RS
Each problem is worth 20 points.
Midterm 2
Due: December 9
1. Consider an undirected graph with a set of n nodes and a set of edges E. Node i makes a
decision si cfw_0, 1 and receives a reward
X
ui (si , si ) = si (vi
sj ),
jNi
where vi is the