IEOR E4407: Game Theoretic Models for Operations
Recitation 10
Problems
1. (Krishna 5.2)There is a single object for sale and there are two potential buyers. The value
assigned by buyer 1 to the object X1 is uniformly drawn from the interval [0, 1 + k] wh
Recitation - 7 / IEOR4407
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1. Two partners must dissolve a partnership. Partner P1 currently owns a share s of the partnership,
partner P2 owns share 1 s. The partners agree to play the following game: P1 names a price
p, for the whole partnership and P2
IEOR E4407: Game Theoretic Models for Operations
Recitation 1
Sep 13,2013
Solutions
1. Consumers are uniformly distributed along a boardwalk that is 1 mile long. Ice-cream prices
are regulated, and consumers go to the nearest vendor because they dislike w
Recitation - 2 / IEOR4407
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1. Discussion of Homework 2
2. Problem: Suppose N students go to a restaurant. They agree to split the total cost of the meal.
If a student orders a meal of cost C , and pays X her net payo is C X . Find a Nash
Equilibrium of t
Recitation - 4 / IEOR4407
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1. (Gibbons 2.11)
Observe that there are 2 NEs of the game, namely (T, L) and (M, C). (B, R) is not a NE,
since given player 2 plays R, player 1 is better o playing T. Hence, one should think of a trigger
strategy that would pu
Recitation - 3 / IEOR4407
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1. Discussion of subgame perfect outcome and equlibrium
2. Joe, Elliot and Nancy are senators who are voting on whether to give themselves a pay raise.
The raise is worth $b, but each person who votes for the raise incurs a cos
A Note on Mixed Strategy
November 1, 2012
Consider a two player game with set of strategies S1 = cfw_s1 , . . . , s1 and S2 = cfw_s2 , . . . , s2 .
m
n
1
1
Let the payo be given by matrices A, B Rmn where for any i = 1, . . . , m, j = 1, . . . , n, Aij
(
IEOR E4407: Game Theoretic Models for Operations
Recitation 6
Problems
1. Consider the following strategic situation. Two opposed armies are poised to seize an island.
Each armys general can choose either attack or not attack. In addition, each army is ei
IEOR E4407: Game Theoretic Models for Operations
Recitation 1
Problems
1. Consumers are uniformly distributed along a boardwalk that is 1 mile long. Ice-cream prices
are regulated, and consumers go to the nearest vendor because they dislike walking (assum
Consider the following auction where the seller has one unit each of four dierent items
cfw_A, B, C, D. There are three bidders who are interested in some bundles of the items. The
list of bundles that each bidder is interested in and the corresponding v
IEOR E4407: Game Theoretic Models for Operations
Recitation 8
Problems
1. (Krishna 2.5)Consider a two bidder rst-price auction in which bidders values are distributed
according to F. Let be the symmetric equilibrium (as derived in Proposition 2.2). Now
su
IEOR E4407: Game Theoretic Models for Operations
Recitation 5
Oct 11,2013
1. Problem 3.2 in Gibbons
Firm 1 has two types and has to pick an action for each type. Firm 2 has only one type and
has to pick one action. Hence the strategy space for rm 1 is S1
IEOR E4407: Game Theoretic Models for Operations
Recitation 6
Problems
1. Consider the following strategic situation. Two opposed armies are poised to seize an island.
Each armys general can choose either attack or not attack. In addition, each army is ei
1
Recitation - 8 / IEOR4407
1. Consider a third price sealed bid auction. Suppose there are N agents
(a) Show that the set of strategies in which each player bids her valuation is not a Nash equilibrium
(b) Show that for any player i the bid of vi (i.e. t
IEOR E4407: Game Theoretic Models for Operations
Fall 2013 Sample Final
1. Consumers are located uniformly along a linear city of length 1. Each consumer wants to buy
one unit of a good from one of the existing rms. The transportation cost for the consume