{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Problem_set_11_solutions

Problem_set_11_solutions - Kaushik Basu Spring 2007 Econ...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Kaushik Basu Spring 2007 Econ 367: Game-Theoretic Methods Problem Set 11 1. Consider the symmetric normal-form game described below. H D H 1, 1 3, 0 D 0, 3 4, 4 (a) Locate all the Nash equilibria (pure and mixed-strategy) in this game. (b) Focusing on pure strategies alone, locate all the Evolutionarily Stable Strategies in this game. Answer: (a) Pure Strategy Nash Equilibria: (H, H) and (D, D) Mixed Strategy Nash equilibria: (H, H), (D, D), and (H with probability ½; D with probability ½) (b) H is an ESS D is an ESS 2. Consider a two-period game between a landlord and a laborer in which the landlord offers the worker a wage of w dollars (for a day’s work) and the worker can accept (A) or reject (R) the offer. A day’s work has a leisure cost of $4 for the worker. If the worker accepts the deal, the landlord gets an output of $10. If the worker rejects it, the landlord gets 0. (a) In the subgame perfect equilibrium of this two-period game what wage does the landlord offer? What payoffs do the two players receive in the equilibrium? Suppose the players meet in period 3 (after the above two-period interaction) to play the following simultaneous-move game. T B T 4, 4 0, 0 B 0, 0 2, 2 (b) In this 3-period game, what is the lowest wage offer that the laborer will accept in a subgame perfect equilibrium? Explain why such a wage is accepted.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Answer: (a) 10-w 0 w-4 0 Landlord offers wage = 4 to make the laborer indifferent between accepting or rejecting the offer and thus the landlord can maximize his own pay-off. Landlord’s payoff is 10 (output) – 4 (labor cost) = 6; worker’s payoff is 4 (wage) – 4 (leisure cost) = 0.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern