If the Battle of the Sexes game were played sequentially:a. Only the mixed strategy equilibrium would exist.b. One of the two pure strategy equilibria would become the only equilibrium.c. The two pure strategy equilibria would alternate in being the equilibrium seen ineach round of the game.d. Only the dominant strategy equilibrium would exist.e. The two pure strategy equilibria would exist.
Question
If the Battle of the Sexes game were played sequentially:a. Only the mixed strategy equilibrium would exist.b. One of the two pure strategy equilibria would become the only equilibrium.c. The two pure strategy equilibria would alternate in being the equilibrium seen ineach round of the game.d. Only the dominant strategy equilibrium would exist.e. The two pure strategy equilibria would exist.
Solution
The correct answer is b. One of the two pure strategy equilibria would become the only equilibrium.
Here's why:
In the Battle of the Sexes game, there are two pure strategy equilibria and one mixed strategy equilibrium in the simultaneous version of the game. However, when the game is played sequentially (one player moves first, and the other player moves after observing the first player's move), the game changes.
In the sequential version of the game, the player who moves first can commit to their preferred outcome. The second player, after observing the first player's move, will choose to match the first player's strategy (since the payoff from matching is higher than the payoff from not matching), leading to one of the two pure strategy equilibria.
Therefore, the mixed strategy equilibrium does not exist in the sequential version of the game, and the two pure strategy equilibria do not alternate or coexist. The dominant strategy equilibrium also does not exist because neither player has a dominant strategy in the Battle of the Sexes game.
Similar Questions
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A mixed strategy game can be solved by ______________.
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