On a Saturday night, Husband and Wife simultaneously decide where to go for dinner. The options are Vietnamese restaurant (V) or Thai restaurant (T). If both opt for V, the payoffs are (8, 8) to Husband and Wife, respectively. If both opt for T, the payoffs are (7, 5). If Husband chooses V and Wife chooses T, the payoffs are (3, 5). Finally, if Husband chooses T and Wife chooses to V, the payoffs are (5, 7). In the Nash equilibrium, Husband gets a payoff of
Question
On a Saturday night, Husband and Wife simultaneously decide where to go for dinner. The options are Vietnamese restaurant (V) or Thai restaurant (T). If both opt for V, the payoffs are (8, 8) to Husband and Wife, respectively. If both opt for T, the payoffs are (7, 5). If Husband chooses V and Wife chooses T, the payoffs are (3, 5). Finally, if Husband chooses T and Wife chooses to V, the payoffs are (5, 7). In the Nash equilibrium, Husband gets a payoff of
Solution
8
Here's why:
A Nash equilibrium occurs when no player can improve their payoff by unilaterally changing their strategy, given the other player's strategy.
In this case, if both Husband and Wife choose V, neither player can improve their payoff by changing their strategy. So, (V,V) is a Nash equilibrium.
In the Nash equilibrium, the Husband gets a payoff of 8.
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