Suppose that there are two firms, A and B. Each is considering entering into a n

Question

Suppose that there are two firms, A and B. Each is considering entering into a new market. If neither enters, then both earn zero. If one enters and the other does not, the one who enters earns 50, while the other earns zero. If both enter, they both lose 100. The normal form of this game is given below. (The gamers symmetric so it does not matter which firm is the 'row' player and which is the 'column' player.) Which of the following statements is not correct? i). this game has multiple Nash equilibria B). if firm A has the opportunity to choose first, it will enter and firm B will not. iii). when the firms choose simultaneously, firm A entering and firmb B not entering is a Nash equilibrium. iv). if firm B has the opportunity to choose first, it will enter, and firm A will also choose to enter. h. The table below shows a payoff matrix for two firms. A and B, that must choose between a high-price strategy and a low-price strategy. (The game is symmetric so it does not matter which firm is the 'row' player and which is the 'column' player.) Which of the following statements is correct? i). setting a high price is a dominant strategy for firm B ii). doing the opposite to firm A is always optimal for firm B iii). there is no dominant strategy for firm A iv). when the firms decide simultaneously, both firms setting low prices is the unique Nash equilibrium

Explanation / Answer

g.

A game is the strategic interaction between two or more players in the process of economic decision making. Each agent who makes the decision in a game is called the player. Each player has a set of choices to decide upon, these choices are called the strategies. The strategies are tied to certain outcomes called payoffs.

The Nash equilibrium of the game occurs when both the player takes their best strategies in response to the strategies of the other players. The prisoner’s dilemma is a situation where the players choses a Nash equilibrium that is not associated with the highest payoff of the players.

The move that the player choses no matter what the other player do is called the dominant strategy. The move that a player never plays no matter what the other player do is called the dominated strategy. The equilibrium where each player plays their dominant strategies is called the dominant strategy equilibrium.

Therefore, the incorrect statement is:

iv) if firm B has the oppertunity to choose first, it will enter and firm B will also choose to enter.

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h.

In this game, if Firm A chooses “low price (LP)”, it will be best for Firm B to choose “High Price (HP)” that will get it a profit of 10 than to “LP” which will get him a profit of 5. On the other hand, if Firm A chooses to play “HP”, it will be best for Firm B to “HP” that will get him a profit of 25 than to “LP” which will get him 20. Hence, “HP” is the dominant strategy for Firm B. This means no matter what strategy Firm A choose, Firm B will choose “High Price (HP)”.

Therefore, the correct statement is

i) setting a high price is a dominant strategy for firm B.

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