IA168 — Problem set 2
Throughout this problem set, “game” means “two-player perfect-information extensive-form game with pure
strategies only”, unless stated otherwise.
Problem 1 [5 points]
Consider the game depicted below:
1
2 2
(-1,3) (2,2) (0,1) (-2,-3)
a b
x y x z
a) Give a formal description of this game as an extensive-form game.
b) Give a description of this game as a strategic-form game (formal definition or table).
Problem 2 [7 points]
Consider this real-life situation: Bob tells his wife Alice: “If you are ever unfaithful to me, I will kill you.”
Then, Alice decides to be either faithful or unfaithful. If she is unfaithful, Bob eventually finds it out and either
keeps quiet or really kills her and then, with probability p, is proved guilty and put in prison.
We model this scenario as the game depicted below:
A
B(10, 10)
(15, −10) (−100, −40p)
f u
q k
In dependence on the parameter p, 0 ≤ p ≤ 1, list all:
a) never-best-response strategies;
b) maxmin strategies;
c) Nash equilibria;
d) subgame-perfect equilibria.
Problem 3 [8 points]
Find a game where all of the following conditions are satisfied:
• there is a strategy profile whose outcome is for both players better than that of any Nash equilibrium;
• there is a Nash equilibrium whose outcome is for both players better than that of any subgame-perfect
equilibrium;
• there are exactly two subgame-perfect equilibria s, s , and the outcome of s is for both players better than
that of s .
Should you fail to find such a game, try your best (for partial points) to find a game which matches the
requirements as closely as you can.