Finding Nash Equilibria

Question 1.

  Player 2
  XY
Player 1A 10 , 10 15 ,  5
B  5 , 15 12 , 12
What is the equilibrium of the above game?

Question 2.

  Player 2
  XY
Player 1A 0 , 0 0 , 1
B 2 , 0 0 , 0
What is/are the equilibrium/equilibria of the above game?

Question 3.

  Player 2
  XYZ
Player 1A  6 ,  6  8 , 20  0 ,  8
B 10 ,  0  5 ,  5  2 ,  8
C  8 ,  0 20 ,  0  4 ,  4
What is the unique equilibrium of the above game?

Question 4.

  Player 2
  RockPaperScissors
Player 1Rock  0 ,  0 -1 ,  1  1 , -1
Paper  1 , -1  0 ,  0 -1 ,  1
Scissors -1 ,  1  1 , -1  0 ,  0
How many equilibria (in pure strategies) does the above game have?

Question 5.

Two firms are involved in developing a new technology that will allow consumers to taste food over the Internet. This has potential, for example, in restaurant promotion. Given the risks and the relatively small expected size of this market, compatibility of the technologies is very important. Firm DigiTaste is far advanced in developing its RemoteTaste technology. WebOdor has been expanding into the Internet taste arena with its incompatible product, BitterWeb. The two companies agree that if they both adopt the same technology, they each may gross $200M from the developing industry. If they adopt different technologies, consumers will make fun of both companies, and purchase neither product, leading to a gross of $0. Retooling one's factory to make the competing (nonproprietary) technology would cost WebOdor $100M and DigiTaste $250M. By the wave of an economist's wand, their production decisions must be made simultaneously.

Set up the above scenario as a normal form (simultaneous) game.

What is the equilibrium outcome?





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