Consider the oil production of OPEC. We simplify the situation to only two countries' case. Each action in the payoff matrix represents the amount of oil produced by each player. For example, small" means a small amount of crude oil is produced; “large" means a large amount of crude oil s produced. The payoff pairs in the table represent each country’s profit, respectively. For example, Very high profit, Very low profit" pair in the bottom left cell denotes a pair of payoffs that Iran gets “Very high profit", and Saudi Arabia gets “Very low profit". Saudi Arabia Small Large Small High profit, High profit Very low profit, Very high profit Iran Large Very high profit, Very low profit Low profit, Low profit *Note: Very high profit > High profit > Low profit > Very low profit What outcome (Nash equilibrium) of this game between two countries would you predict? Use vour answer to explain why OPEC has failed to keep the oil price (profit) high in the long-run.

Suppose we’ve modelled a firm’s entry decision with a one-shot, simultaneous move game, determined payoffs and found the Nash equilibrium. Suppose with the payoffs we came up with, both firms have a clear dominant strategy such that there is a Nash equilibrium in which both firms play their dominant strategy. However, when we observe the actual actions of the firms, we see that they don’t choose the strategy wepredicted and the outcome of the game doesn’t match the Nash equilibrium. What are 4 reasons this might be? (Hint: The firms are rational.)

Make sure you clearly write your name and submission:. 1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. • "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper -1 0 1 rock 0 paper 1 scissors -1 (a) Show that this game does not have a pure Nash equilibrium. 1 X 3 (b) Show that…

Question 3: Represent Rock-Paper-Scissors 1 point, the loser gets -1 and in case of a tie each player gets 0. What are the dominant strategies? What is the Nash equilibrium? game in a matrix format. Note that the winner gets