Вопрос с экзамена по Quantitative Methods in Economics. Задача на английском языке. Two players green and blue are opponents. They are playing matching pennies, and each can choose tails or heads, resulting in one winning and the other losing. The first player green player, will win 30 if both choose head and will win 20 if the both choose tail simultaneously. If the green player chooses head while the blue chooses tail, then the green will win 10. Finally, if the green chooses tails and the blue heads, the green will lose 20. 1.Represent the problem In its conventional tabular form. 2. Solve and indicate what type of strategy the players should use in the game and explain why.? 3.Indicate if there is a saddle point as well as the value of the game. 4. In the case of mixed strategy, indicate how long each player should play each strategy
Вопрос с экзамена по Quantitative Methods in Economics. Задача на английском языке. Two players green and blue are opponents. They are playing matching pennies, and each can choose tails or heads, resulting in one winning and the other losing. The first player green player, will win 30 if both choose head and will win 20 if the both choose tail simultaneously. If the green player chooses head while the blue chooses tail, then the green will win 10. Finally, if the green chooses tails and the blue heads, the green will lose 20. 1.Represent the problem In its conventional tabular form. 2. Solve and indicate what type of strategy the players should use in the game and explain why.? 3.Indicate if there is a saddle point as well as the value of the game. 4. In the case of mixed strategy, indicate how long each player should play each strategy
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The players should use mixed strategies in this game. This means that each player should choose their strategies randomly based on a probability distribution. This is because if a player consistently chooses one strategy, the opponent can easily exploit their pattern and win consistently. By using mixed strategies, the players can make their choices unpredictable and prevent the opponent from gaining an advantage.
There is a saddle point in this game, as there is a pair of mixed strategies in which each player's expected payoff is equal to the value of the game. The value of the game in this case is 0.
In the case of mixed strategy, each player should play each strategy with the following probabilities:
Green: head with probability 3/5, tail with probability 2/5Blue: head with probability 1/5, tail with probability 4/5.