Econ 398 Homework 2
Sketchy Solutions 1. There are four Nash Equilibria; each one involves one of the four writing down $3, while the other three each write down $10. Notice that in a strategy profile where two players, say Alice and Bertha, write do
10/9/2008
Mixed Strategies Matching Pennies
In Matching Pennies, we found there was no Nash Equilibrium
Guildenstern Heads Rosencrantz Heads Tails 1, -1 -1, 1 Tails -1, 1 1,-1
Why Mixed Strategies?
If you were to play the same opponent repeatedly, you wou
Solutions to Chapter 11 Exercises SOLVED EXERCISES
S1. False. The players are not assured that they will reach the cooperative outcome. Rollback
reasoning shows that the subgame-perfect equilibrium of a finitely played repeated prisoners dilemma will enta
Solutions to Chapter 12 Exercises SOLVED EXERCISES
S1. (a) (b) The number choosing X should decrease to move the population division between X and Because the line for action X is above the line for action Y when 100 people choose X,
Y away from the unsta
Solutions to Chapter 13 Exercises SOLVED EXERCISES
S1. (a) The payoff table for the two types of travelers is: High High Low 100, 100 70, 30 Low 30, 70 50, 50
(b)
The graph is:
(c)
There are three possible equilibria: a stable monomorphic equilibrium of a
Solutions to Chapter 14 Exercises SOLVED EXERCISES
S1. Some examples of incentive schemes that help induce more care on the part of policy holders: 1. The insurer can provide a multiyear contract or otherwise establishes an ongoing relationship in which f
Solutions to Chapter 15 Exercises SOLVED EXERCISES
S1. (a) In the pure-threat case, the unions expected payoff is 50(1 p) 100p = 50 150p. The
unions expected payoff goes to zero for p = 1/3 and is negative for p > 1/3. Thus the pure threat is too big from
Solutions to Chapter 16 Exercises SOLVED EXERCISES
S1. Under truthful voting, A should match Geology and Sociology in the first vote, with the winner (Geology) to face Philosophy in the second round. Under strategic voting, A should match Philosophy and S
Solutions to Chapter 17 Exercises SOLVED EXERCISES
S1. The painter can compare her estimated cost to a jobs true cost only when she does the job. But
the painter does a job only when she agrees (through the bidding process) to do it for less than anybody
Solutions to Chapter 18 Exercises SOLVED EXERCISES
S1. The father and daughter were implicitly negotiating about how much freedom from parental
control she would have. The fathers BATNA was low: breakdown of negotiation would lead to a tantrum or a scene
Solutions to Chapter 19 Exercises SOLVED EXERCISES
S1. (a) The existence of buyer B2 means that buyer B1 will not be able to buy at any price below
200. If B1 tried to strike a deal at (for example) 190, B2 could offer to pay 191; if B2 bought at that pri
Solutions to Chapter 2 Exercises SOLVED EXERCISES
S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is
simply making a decision. If some flavors of yogurt were in short supply, then it would be a game, because shop
Solutions to Chapter 3 Exercises SOLVED EXERCISES
S1. (a) There is one initial node (I) for Hansel making the first move; three decision nodes (D)
including the initial node, which represent the points where either Hansel or Gretel make a decision; and si
12/4/2008
Evolutionary Game Theory
Darwin's Origin of Species explained evolution of organisms
Certain members of a species are better adapted to their environment (more fit) The traits that make those members more fit are embedded in genes More fit membe
12/2/2008
Collective Action Games
N = population n = # of participants who take an action N-n = # of shirkers who do not take the action Participant g p gets: p( ) p(n) Shirker gets: s(n)
Collective Action Games
Suppose there are n participants and N-n-1
10/14/2008
Mixed Strategies Matching Pennies
We denote the strategies on the game bi-matrix
Guildenstern q Heads Rosencrantz R t p 1-p Heads H d Tails 1 , -1 1 -1 , 1 1-q Tails -1 , 1 1 1 , -1
Preferences Involving Gambles
We revisit our description of pa
9/10/2008
Personnel for Econ 398: Strategy
Econ 398: Strategy
A Study of Strategic Interaction in Games Chris Proulx Lorch Hall M107 rabbit@umich.edu Office Hours: Tu, Th 10:30-11:30
Instructor: Chris Proulx, rabbit@umich.edu Office Hours: TuTh 10:30-11:3
9/10/2008
Analyzing Games
We need three things to specify a game
Players Possible strategies for each player Payoffs for eac p aye o e ou co es ayo s o each player over outcomes
Analyzing Games
Players have well-defined and well-behaved preferences over o
10/29/2008
Expert Advice
We often rely on professionals to diagnose problems and recommend and carry out fixes
Doctors Auto Mechanics and Repair Technicians p Lawyers Financial Advisors and Real Estate Agents Teachers and Researchers
Expert Advice
A custo
10/16/2008
Mixed Strategies Matching Pennies
We denote the strategies on the game bi-matrix
Guildenstern q Heads Rosencrantz R t p 1-p Heads H d Tails 1 , -1 1 -1 , 1 1-q Tails -1 , 1 1 1 , -1
Mixed Strategies Matching Pennies
Rosencrantz's & Guildenstern
10/30/2008
Midterm 2: Next Tuesday
Exam focuses on new material
Chapter 5 to beginning of Chapter 9 Lectures 8-16, HW 4-6
Signaling with Strategic Uncertainty
Otto Stag Ludwig Stag Hare 2,2 1,0 Hare 0,1 1,1
Come early and bring a UMID No cellphones or i-p
11/10/2008
Spence: Education as a Screen
Education does not affect productivity Two types of people
Able types worth $150,000 Challenged types worth $100,000 $100 000 Types are indistinguishable, can't be tested
Spence: Education as a Screen
Self-Selectin
11/13/2008
Strategic Moves
Change the rules of the game to benefit yourself Usually involves making a pre-game move 1st Actions must be
Observable Irreversible
Strategic Moves
Strategic moves are to deter or compel
Unconditional commitments
Try to change
11/20/2008
The Entry Game
(-200,-100)
Fight
Burning Money
I E Challenger F A (-200, -100) (100, 100)
INCUMBENT SO Don t Don't Invest
Acquiesce
(0, (0 300)
(100,100) Incumbent I Invest E A Challenger (100, 0) F (-200, 10)
CHALLENGER
Enter
Stay Out
(0,300)
12/2/2008
Collective Action Problems
Often, the welfare of society is best served if individuals take a particular "socially responsible" action. On the other hand, individuals may not find it in their interest to take the "socially socially responsible"
Solutions to Chapter 4 Exercises SOLVED EXERCISES
S1. False. A dominant strategy yields you the highest payoff available to you against each of your
opponents strategies. Playing a dominant strategy does not guarantee that you end up with the highest of a