**Mathematics 483 ** (Game Theory)

Homework Assignment vi

prepared by:

Joseph Malkevitch

Mathematics Department

York College (CUNY)

Jamaica, NY 11451

email: joeyc@cunyvm.cuny.edu

web page: http://www.york.cuny.edu/~malk

1. (i) Write down a 2x2 non-zero sum game with asymmetric payoff to Row and Column where simultaneously:

a. Row has a dominating row.

b. Column has a dominating column.

c. The "rational way" for each player to play the game results in each having a worse payoff than would occur if the players had played some other way.

(ii) Write down the motion diagram for the game you give above.

2. (i) Write down a 2x2 non-zero sum game with symmetric payoffs to Row and Column where there are two inequivalent equilibrium payoffs for the players.

(ii) Write down the motion diagram for the game you give above.

3. For the game bel;ow, write down the motion diagram. Is there any equilibrium for this game in pure strategies? If not, can you find a Nash equilibrium for this game?

Column I | Column II | |

Row 1 | (3, -1) | (-2, 3) |

Row 2 | (-6, 2) | (4, -6) |