uniqueness of the fixed point

In section 2.4.3 (Univalent mapping arguement) from 'game theory in SC analysis' by Cachon and Netessine, they claim that if best response function is one-to-one, then there is at most one fixed point(uniqueness of equilibrium). But why? It is possible that we can have x and y where x not equal to y such that x=f(x) and y=f(y). For example, f(x_1,x_2)=(x_2,x_1) is univalent mapping. But when x_1 = x_2=a in R, f(a,a)=(a,a). We can construct a trival game, player x and y write down a number, if x=y, then they both get 10, if not then their payoff is 10-(x-y)^2. In this game, the best response is f(x_1,x_2)=(x_2,x_1) .

Pros and cons of staying in a small university

The most advantage is that the relationship between prof. and students are close. But sometimes you will be shocked. There is only one student registering real analysis class, so that the class is cancelled. It is hard to imagine that this could happen to the basic graduate math courses in those bigger universities.

Very limited courses are offered in Lehigh. After my three years in Lehigh, there is no open course about heuristics, the stochastic process class only using introductory level of book 'Introduction to Probability Models' by Ross. It takes me waiting for 2 years to have IP open again. And there are many other regrets about courses in Lehigh.

More guns can be added into my powder magazine

Today, my wife gets and accepts her first offer. Now I can continue to my hobby to buy books. The books I plan to buy recently will be
Stochastic Calculus and Financial Applications
Nonlinear Programming: Theory and Algorithms
Theory and Practice of Revenue Management
An Annotated Timeline of Operations Research: An Informal History

Another new book in two days

Today my wife's sister comes to my home with book 'Real and Complex Analysis' I ordered from dangdang.com. It only cost me 39RMB (5 dollar).

Why Toy's R doesn't have sample for people to try

I also drop at Toy's R today due 25% gift certificate again. I try to get some gifts for my relatives and friends children. But there is no sample for most items for people to try except PS2 and Xbox 360. This setting loses the advantage to have a real store rather than online store only. Finally I get two idog mini which I already know what it is. But if I can try some other stuffs, I may buy more stuff. It seems that they don't know how to model customer behaviors

A new book comes to my book shelf

Today, I use 25% gift certificate of Border to get 'Game theory' by Fudenberg and Tirole. It is must have book for people doing game theory in SCM.

Crazy Tuesday and Thursday Next Semester

Finally I get my schedule for next semester. All the courses and meeting are concentrated in Tuesday and Thursday.
10:45-12:00 Advanced Stochastic Process II
12:10-1:00 IP Seminar (Th)
1:10:2:25 Real Analysis II
2:35-3:50 Financial Calculus II
4:00-5:00 Weekly Meeting with Larry(T)
7:00-8:15 Integer Programming
After crazy day, I will play tennis on Tuesday and Ping Pong on Thursday.

Wiki for Econ. Job Market

Is anything similar in IE or B-school.

Assignment of interview time slot

One of my friends from Econ. will graduate this year. He gets about 30 interviews during a conference at Chicago. Each interview lasts about half an hour. It is interesting to see how interviewees and interviewers agree on the time slot especially when there is no centralized system.

To queue or not to queue

It is not about the book To queue or not to queue. It is about my experience today.

Today, I sit in the Wendy's from 10:30am to 2:50pm to read and think. When I realized that I soon need to have lunch, there is waiting line. Then it becomes an optimization problem. My hungry degree increases by time. I don't want to waiting in the line waste my time not doing meaningful things. The length of waiting line is changing. What should I do?!

It turns out that I was poor to make that decision. I waited until that I cannot stand more and joined a long line. What is the form of best strategy under this situation? What if I have perfect information or not? Is any similiar situation in the real business situation?

Martingale and NP Complete problem

Last semester, I have two courses related to martingale. But how can it be used in inventory related problems. So far my limited literature reading hasn't touched any paper using martingale properties. I guess the reason is that it is not easy to find a martingale in inventory problem.

Today when I read 'The logic of Logistics', I found an application to use martingale difference sequence to develop average case analysis for Bin pack problem. Although it is not close related to inventory problems I am interests. It is a good start.

The reference is
Martingale inequalities and NP-complete problems

Wrong impression: any NP complete problem has no finite worst case bound for any heuristic

In network and graph class, we learn that there is no finite worst case bound for TSP. But I thought there is no finite worst case bound for any NP complete problem. Because of this wrong understanding, I argued with a speaker during Informs about his speech about bound of one multi-echolen problem. Of course, he cannot agree on my wrong opinion.

I realize this understand is wrong until today when I happen to read the bounds on Bin-Packing problem.