Assignment: Introduction to Game Theory
1. "Rock - Paper -Scissors" can be modeled as a strategic form game between players 1 and 2 with strategy sets S1 = S2 = {R, P, S}. Assume that payoffs are 1, 0 or -1 depending on who wins the game.
(a) Create the corresponding payoff matrix.
(b) Evaluate u2(R, P) and u1(S, S).
(c) Does any player have a dominant strategy?
(d) Is there a pure strategy NE?
(e) Evaluate u2([¼R, ¾S], P).
(f) What is the best pure strategy response for player 2 to [½R, ½S]?
(g) What is the best response for player 2 to [½R, ½S]?
(h) Show that ([1/3R, 1/3P, 13S], [1/3R, 1/3P, 1/3S]) is a NE of the game.
2. Three persons, Ann, Bob and Chad, have to decide to work or shirk in a group project. Payoffs are given according to the following information.
• The three group members will receive the same grade.
• If at least two group members work the grade assigned will be good, giving each student four units of payoff.
• If only one group member works the grade assigned will be mediocre, giving each student two units of payoff.
• If no group member works the grade assigned will be bad, giving each student zero units of payoff.
• Working implies an effort worth losing one unit of payoff.
(a) Create the payoff matrix for this three-player game.
(b) Does any player have a dominant strategy?
(c) What are the pure strategy NE of the game?
3. Find all the pure and mixed NE of the following games:
4. Find all the pure and mixed NE of the following game:
