Temple University

Department of Economics

Economics 92, Principles of Microeconomics (Honors)

Homework 10
Trade Negotiations
A Static Game with Incomplete Information

  USA
Tough   Accommodating
No Concessions Make Concessions   No Concessions Make Concessions
China No Concessions 0, 0 -2, 0   -2, 0 5, -2
Make Concessions -2, 7 5, 5   0, 5 7, 7

In this game the US and China are negotiating a new trade treaty.  The payoffs are indices of change from the status quo that include things like economic gain, perceptions of residents of the home country, and stature in the world.   The USA negotiator, Carr Ben Steele, knows his type.  But the Chinese negotiator, Hai Lo, doesn't know know Carr's type.

Name 

Social Security Number

1. If USA is tough, do they have a dominant strategy?
Yes, No Concessions.

2. If USA is accommodating, do they have a dominant strategy?
No.

3. Suppose that China is expected to play 'no concessions', what is the best USA response from a tough USA? If USA is tough then they are indifferent between No Concessions and Make Concessions.  If the USA is accommodating then they should play 'No Concessions.'

To answer the remaining questions you need to construct the normal form of the game. Instead of beta, use b.

    USA
    No Conc(T), No Conc(A) No Conc(T), Conc(A) Conc(T), No Conc(A) Conc(T), Conc(A)
China No Conc -2(1-b), (0,0) 5(1-b), (0, -2) -2b-2(1-b), (0,0) -2b+5(1-b), (0,-2)
Conc -2b, (7,5) -2b+7(1-b), (7,7) 5b, (5,5) 5b+7(1-b), (5,7)

4.  Write out the normal or strategic form of the game.  Can you eliminate any dominated strategy plans for the USA?

Yes No

Yes.  {No Conc(T), No Conc(A)} dominates {Conc(T), No Conc(A)}, and {No Conc(T), Conc(A)} dominates {Conc(T), Conc(A)}.

5. Let ß be China's prior for the probability that USA is a tough player.  For what values of ß will china want to play 'no concessions' against both kinds of USA player after eliminating any dominated USA strategies?
For a given strategy of the USA, we want China to be indifferent between No Concessions and Concessions.  For example, use the first column to find -2(1-b)=-2b; or, b=1/2.

Note that Conc(T), Conc(A) is a dominated strategy for the USA.  Furthermore, Conc(T), No Conc(A) is not a credible strategy for the USA since Ben Steele will never concede if he is a tough negotiator.

When b=1/2 the payoff table -- normal form becomes

    USA
    No Conc(T), No Conc(A) No Conc(T), Conc(A) Conc(T), No Conc(A) Conc(T), Conc(A)
China No Conc -1, (0,0) 2.5, (0, -2) -2, (0,0) 1.5, (0,-2)
Conc -1, (7,5) 2.5, (7,7) 2.5, (5,5) 6, (5,7)

But remember that the last two columns can be disregarded when b=1/2.

6. For values of ß below your answer to 4, what might happen? That is, will China have a dominant strategy? .  What strategy profile will be the solution to the game?

Yes. For b<1/2 Concession becomes China's dominant strategy.  When b=1/4 the game table becomes 

    USA
    No Conc(T), No Conc(A) No Conc(T), Conc(A) Conc(T), No Conc(A) Conc(T), Conc(A)
China No Conc -6/4, (0,0) 15/4, (0, -2) -2, (0,0) 13/4, (0,-2)
Conc -1/4, (7,5) 19/4, (7,7) 5/4, (5,5) 26/4, (5,7)

7. For values of ß above your answer to 4, what might happen? That is, will China have dominant strategy?    What strategy profile will be the solution to the game?

No. When b=3/4 the game table becomes 

    USA
    No Conc(T), No Conc(A) No Conc(T), Conc(A) Conc(T), No Conc(A) Conc(T), Conc(A)
China No Conc -1/2, (0,0) 5/4, (0, -2) -2, (0,0) -1/4, (0,-2)
Conc -6/4, (7,5) 1/4, (7,7) 15/4, (5,5) 22/4, (5,7)

China does not have a dominant strategy, but recall that the last two columns are dominated strategies for the USA.  The solution to the game is [No concession, {No C(T), No C(A)}]