AMS335/ECO355 Spring 2015
Homework 4
Due Date: March 23rd, 2015
1. Approval voting (40 points)
In the system of approval voting, a citizen may vote for as many candidates as she wishes. If there are two candidates, say A and B, for
example, a citizen may
AMS335/ECO355 Fall 2014
Homework 2
Due Date: Oct. 29th, 2014
1. Approaching cars (100 points)
Two cars are approaching an intersection from dierent directions. The
driver of each car can either stop or continue. The drivers preferences are
represented by
AMS335/ECO355 Fall 2014
Homework 3
Due Date: Nov. 5th, 2014
1. Examples of extensive games with perfect information (45 points.)
(a) Represent in a diagram (see the following diagram for the entry game
for an example) the two-player extensive game with pe
AMS335/ECO355 Fall 2014
Homework 4
Due Date: Nov. 25th, 2014
1. Extensive game with simultaneous moves
Find the subgame perfect equilibria of the following game. First player
1 chooses either A or B. After either choice, she and player 2 simultaneously ch
AMS335/ECO355 Fall 2015
Homework 2
Due Date: Feb. 18th, 2015
1. Variant of Prisoners Dilemma with altruistic preferences (80 Points)
Each of two players has two possible actions, Quiet and Fink ; each action
pair results in the players receiving amounts o
AMS210 Homework 1
due Friday 1/9
Sec 1.2, Problem 4a
Consider the oil renery model. There are three reneries: 1,2, and 3 and from each barrel of
crude petroleum, the dierent reneries produce the following amounts (measured in gallons) of
heating oil, dies
AMS335/ECO355 Fall 2015
Homework 3
Due Date: Feb. 25th, 2015
1. A joint project (50 Points)
Two people are engaged in a joint project. If each person i puts in the
eort xi , a nonnegative number equal to at most 1, which costs her c(xi ),
the outcome of t
AMS 335/ECO355 Fall 2014
Homework 1
Due Date: Oct. 22nd, 2014
1. Games with mixed strategy equilibria (30 points).
Find all the mixed strategy Nash equilibria of the strategic games in Table
1. Keep in mind that pure strategy equilibria are special cases
AMS335/ECO355 Fall 2014
Homework 4
Due Date: Nov. 19th, 2014
1. (Subgame perfect equilibria of the ultimatum game with indivisible units)
Find the subgame perfect equilibria of the variant of the ultimatum game
in which the amount of money is available on
10
Games with incomplete information:
the general model
Chapter summary
In this chapter we extend Aumanns model of incomplete information with beliefs in
two ways. First, we do not assume that the set of states of the world is nite, and allow
it to be any
Extensive form games
Dynamic Games
Game Theory
Stony Brook University
Prof. Yair Tauman
Instructor: Tilsa Ore Monago
In the previous slides we dealt mostly with simultaneous strategic interactions
where players choose their actions simultaneously.
Our n
Strategic Form Games
Game Theory
Stony Brook University
Prof. Yair Tauman
Games in Strategic Form
These games are characterized by
a set of players that are relevant to a specific conflict situation
a set of possible strategies for each player
a payoff
Extensive form games
Dynamic Games
Game Theory
Stony Brook University
Prof. Yair Tauman
Instructor: Tilsa Ore Monago
In the previous slides we dealt mostly with simultaneous strategic interactions
where players choose their actions simultaneously.
Our n
Mixed Strategies
Game Theory
Stony Brook University
Prof. Yair Tauman
The Princess Bride (video)
The battle of wits: the man in black (Wesley) is to poison one of two
wineglasses out of Vizzinis sight, and Vizzini is to decide who will drink from
which gl
MaxMin Strategies
Game Theory
Stony Brook University
Prof. Yair Tauman
MaxMin Strategies (The Safety
Level)
Consider
a game, G, in strategic form. Namely, G = (, ) where N = cfw_1, 2, is the set
of players, Si is the set of pure strategies of and
hi : R
Extensive form games - Dynamic Games
ECO355 - Game Theory
ECO 355 Game Theory
Department of Economics
Stony Brook University
Instructor: Tilsa Ore-Monago
tilsa.oremonago@stonybrook.edu
Tilsa Ore (SUNY SB)
1 / 22
Extensive form games
Extensive form games
R
MaxMin Strategies
Game Theory
Stony Brook University
Prof. Yair Tauman
MaxMin Strategies (The Safety Level)
Consider a game, G, in strategic form. Namely, G = (, ()=1 , ()=1 ) where N =
cfw_1, 2, is the set of players, Si is the set of pure strategies of
Mixed Strategies
Game Theory
Stony Brook University
Prof. Yair Tauman
The Princess Bride (video)
The battle of wits: the man in black (Wesley) is to poison one of two
wineglasses out of Vizzinis sight, and Vizzini is to decide who will drink from
which gl
AMS335/ECO355 Spring 2015
Homework 7
Due Date: April 22nd, 2015
1. Finding subgame perfect equilibria (30 points)
Find the subgame perfect equilibria of the game in Figure 1.
Figure 1
2. Voting by alternating veto (40 points)
(a) Two people select a polic
AMS335/ECO355 Spring 2015
Homework 5
Solution
1. Cournots duopoly game with linear inverse demand and dierent unit
costs. (25 points.)
Find the Nash equilibrium of Cournots game when there are two rms,
the inverse demand function is given by
cfw_
Q if Q
AMS335/ECO355 Spring 2015
Homework 8
Due Date: April 29th, 2015
1. Subgame perfect equilibria of the ultimatum game with indivisible units
Find the subgame perfect equilibria of the variant of the ultimatum game
in which the amount of money is available o
AMS335/ECO355 Spring 2015
Homework 4
Due Date: March 23rd, 2015
1. Approval voting (40 points)
In the system of approval voting, a citizen may vote for as many candidates as she wishes. If there are two candidates, say A and B, for
example, a citizen may
AMS335/ECO355 Fall 2015
Homework 3
Due Date: Feb. 25th, 2015
1. A joint project (50 Points)
Two people are engaged in a joint project. If each person i puts in the
eort xi , a nonnegative number equal to at most 1, which costs her c(xi ),
the outcome of t
Stony Brook University, Spring 2015
AMS 335/ECO 355 Game Theory Lecture 01
Instructor: Zhenning Wang
E-mail: Zhenning.Wang@stonybrook.edu
Oce Hours: 4:20pm5:20pm, Monday and Wednesday
Oce Address: N605, Social and Behavioral Sciences Building
Textbook: An
AMS 335/ECO355 Spring 2015
Homework 2
Due Date: Feb 18th, 2015
1. Variant of Prisoners Dilemma with altruistic preferences (40 Points)
Each of two players has two possible actions, Quiet and Fink ; each action
pair results in the players receiving amounts
AMS 335/ECO355 Spring 2015
Homework 1
Due Date: Feb 11th, 2015
1. Another way of modeling working on a joint project (30 points)
Formulate a strategic game that models a situation in which two people
work on a joint project in the case that their preferen
AMS 335/ECO355 Spring 2015
Homework 1
Solution
1. Another way of modeling working on a joint project (30 points)
Formulate a strategic game that models a situation in which two people
work on a joint project in the case that their preferences are the same
AMS335/ECO355 Spring 2015
Homework 5
Due Date: March. 30th, 2015
1. Cournots duopoly game with linear inverse demand and dierent unit
costs (25 points)
Find the Nash equilibrium of Cournots game when there are two rms,
the inverse demand function is given
1.
Consider the following two-person game in a tree form.
Mark all the true statements
A.
There is one Perfect Nash Equilibrium (PNE), and four Nash
Equilibrium points (including the PNE)
B.
The PNE is the only sensible equilibrium
C.
(r, Aa) (4, 2) is th
UC Berkeley
Haas School of Business
Economic Analysis for Business Decisions
(EWMBA 201A)
Game Theory II
Applications (part 1)
Lectures 6-7
Sep. 12, 2009
Outline
This week
[1] The main ideas review
[2] Strictly competitive games
[3] Oligopolistic competit
1
L
R
U
4, 4
0, 3
D
5, 0
1, 1
\ 2
If this game becomes a perfect information game and is played sequentially, two things can happen: (i)
case 1: player 1 moves first and player 2 moves second, and (ii) case 2: player 2 moves first and player 1
moves later
Given the above tree game, transform the game in its strategic form and mark the true statements:
A.
By playing (D1,U2), player 1 would get -1 and player 2 would
get 10.5
B.
Player 2 do not receive any payoff since she does not make
moves in this game
C.
ECO 355 / AMS 355 - GAME THEORY
Winter 2017
Department of Economics
Stony Brook University
Course code and section: ECO 355 - section 01
Credit hours: 3 credit hours
Instructor: Tilsa Ore-Monago
Office hours: Available online on M., W. & F. 4:00pm-5:30pm