14.12: Problem Set 5 Solution
Ruitian Lang December 3, 2010
1
(a) There are two players, 1 and 2, with A1 = cfw_U, D and A2 = cfw_L, R. The type spaces are T1 = cfw_-1, 1, T2 = cfw_-1, 1, and the beliefs are p1 (t2 |t1 ) = p2 (t1 |t2 ) = 1/2 for all t1 T1

14.12 Game Theory Muhamet Yildiz Fall 2010
Homework 1 Solutions
Due on 9/28/2010 (in class) 1. In the following pair of games, for each player, check whether the player' preferences s over lotteries are the same? L M R a 2,-1 1,0 3,-2 b 0,0 1,1 2,0 c 1,-3

14.12 Game Theory Prof. Muhamet Yildiz Fall 2010
Homework 2 Solutions
Due on 10/12/2010 (in class) You need to show your work in all questions. 1. Consider the following game: L A (3; 2) B (0; 0) C (1; 4) D (0; 0) M (0; 0) (2; 4) (1; 3) (0; 0) N (6; 0) (1

14.12 Game Theory Muhamet Yildiz Fall 2010
Homework 1
Due on 9/28/2010 (in class) 1. In the following pair of games, for each player, check whether the player's preferences over lotteries are the same? L M R a 2,-1 1,0 3,-2 b 0,0 1,1 2,0 c 1,-3 2,2 1,4 2.

14.12 Game Theory Prof. Muhamet Yildiz Fall 2010
Homework 2
Due on 10/12/2010 (in class) You need to show your work in all questions. 1. Consider the following game: L A (3 2) B (0 0) C (1 4) D (0 0) M (0 0) (2 4) (1 3) (0 0) N (6 0) (1 2) (0 5) (0 -1) R

14.12 Game Theory Prof. Muhamet Yildiz Fall 2010
Homework 3
Due on 1028/2007 (in class) You need to show your work in all questions. 1. Find a subgame-perfect equilibrium of the following game:
2. Consider the following two-stage Cournot competition. Ther

14.12 Game Theory Prof. Muhamet Yildiz Fall 2010
Homework 4
Due on 11/9/2010 (in class) You need to show your work in all questions. 1. Consider a finitely repeated game with the following stage game (in which players decide between a soccer game or a mov

14.12 Game Theory Prof. Muhamet Yildiz Fall 2010
Homework 5
Due on 12/2/2010 (in class) You need to show your work in all questions. 1. Consider the following two-player game in which the payoffs and the actions are as follows: L R U 2 0,0 D 0,0 2 Here, c

14.12 Game Theory - Midterm I 10/19/2010 Prof. Muhamet Yildiz Instructions. This is an open book exam; you can use any written material. You have one hour and 20 minutes. Each question is 25 points. Good luck! 1. Consider the following game.
(a) Using bac

14.12 Game Theory Midterm II Solution 11/18/2010 Prof. Muhamet Yildiz Instructions. This is an open book exam; you can use any written material. You have one hour and 20 minutes. Each question is 25 points. Good luck! 1. Find all subgame-perfect equilibri

14.12: Problem Set 3 Solution
Ruitian Lang October 27, 2010
1
There are three subgames: the whole game, the game following L, and the game following R. The subgame following L is the following normal form: a x 1,0 b 0,1
1 2x 1 + 2 y, 1 a + 1 b , and Playe

14.12: Problem Set 4 Solution
Ruitian Lang November 14, 2010
1
The stage game has three Nash equilibria: (S, S), (M, M ), and associated with these equilibria are (2, 1), (1, 2) and
2 2 3, 3 2 3S 1 + 1 M, 3 S + 2 M , and the payoffs 3 3
. Therefore, the p

18.445 Take Home Exam (Due May 12th)
1. Suppose is a continuous time Markov Chain taking non-negative integer values. Moreover, suppose (1) (2) ; has independent increments property; and such that when ,
(3) There exist
. Let for all and non-negative inte

9/27/2011
15.501/15.516 Financial Accounting Fall 2011 Session 6
Nemit Shroff MIT Sloan School of Management
Recap of last class
TAccounts and journal entries are two ways of representing a business transaction. Debits increase assets and decrease liabil

Stochastic Processes 18.445
MIT, fall 2011
Practice Mid Term Exam 1
October 25, 2011
Problem 1: . Let X1 , X2 , X3 , . . . be a Markov chain on a finite state space S = cfw_1, . . . , N with transition matrix P . Among the following statements, say which

10/23/2011
15.501/15.516 Financial Accounting Fall 2011 Session 11
Nemit Shroff MIT Sloan School of Management
Recap of last class.
The "ins" of inventory accounting The "outs" of inventory accounting
Acquisition costs Cost of goods available for sale Beg

MATH 56A: FALL 2006 HOMEWORK AND ANSWERS
2. Math 56a: Homework 2 p. 35 #1.1, 1.2, 1.3 1.1. Every morning a newspaper is added to a pile. With probability 1/3 the pile is emptied emptied. But if the pile has 5 newspapers, it is always emptied. Make this in

Problem Set 4 Solutions
1
1 Problem 4.1
a. Simply verify that P = and that 0 + 1 = 1 0 1 0 1 1 b. Obviously f00 = P00 = 1 : For higher n; because the only path starting from 0 and reaching 0 after n steps without passing 0 is 01 10; its probability (n) n

Lecture12.5AdditionalIssues
ConcerningDiscreteTimeMarkov
Chains
Topics
Review of DTMC
Classification of states
Economic analysis
First-time passage
Absorbing states
DiscreteTimeMarkovChain
Astochasticprocesscfw_XnwherenN=cfw_0,1,2,.iscalleda
discrete