Three friends are voting on a holiday destination. Each player chooses a destination to vote for, and the winner is the destination with the most votes. If all three are tied, then one destination is randomly selected from the three, where each has a third probability of winning. The players of the game are F1, F2 and F3, and fortunately for us, they all obey the von- Neumann-Morgenstern axioms. All three rank a lottery which gives them their worst outcome with 20 percent chance and their best outcome with 80 percent chance as equivalent to getting their second-best outcome with certainty. The ordinal preferences of the holiday destinations Argentina, Bolivia and Columbia (A, B and C) are given by: F1: A > B> C
F2: B_2C2 A
F3: C-3A3 B.
(a) Write this game out as a strategic game where the maximum payoff for every player is 100, and the minimum payoff is 0. (Hint, you should have three tables where every cell contains three numbers be- tween 0 and 100. Also, the value of a draw is uniquely defined here, as it's a lottery over three values.)
(b) For each player, list their weakly dominated strategies.
(c) List the six pure-strategy Nash equilibria (Hint: Use p, q and r as the probability of playing their favorite destination, and use the indifference probability to find an equilibrium where p=q=r.)