You and a friend are in an Italian restaurant and the owner offers both of you an 8- slice pizza under the following conditions: each one of you must simultaneously announce how many slices you would like to have (i.e., each player i is belong {1,2} names her desired amount of pizza slices 0 <= s(i )<= 8 ). If s1 + s2 <= 8 the players get their demands. (The owner eats any left over pizza). If s 1 + s 2 >8 then the players get nothing. Assume that more pizza is better for both players.

Part a. Assigning utility indices for each player according to the number of slices of pizza that are both requested and received (utility being set to zero in all other situations), write the payoff matrix.

Part b. All strategies that survive iterated elimination of strictly dominated strategies (in two-player games) are said to be rationalizable strategies. Delineate the set of rationalizable strategies, explaining briefly.

Part c. How would you describe the general nature of the best responses that each player should choose?

Part d. Identify any and all pure strategy Nash equilibria for this game.