On a Friday night, Husband and Wife simultaneously decide whether to Go Home or Work Late. If both opt to Go Home, the payoffs are (1, 3) to Husband and Wife, respectively. If both opt for Work Late, the payoffs are (5, 3). If Husband chooses to Go Home and Wife chooses to Work Late, the payoffs are (1, 5). Finally, if Husband chooses to Work Late and Wife chooses to Go Home, the payoffs are (5, 1). Choose ALL correct statements:Group of answer choicesHusband’s dominant strategy is to Work Late.The Nash equilibrium is (Work Late, Work Late); this is a prisoners’ dilemmaThe Nash equilibrium is (Work Late, Work Late); this is a dominant strategy equilibriumThe Nash equilibria are (Work Late, Work Late); (Go Home, Go Home); this is a coordination gameNone of the answers are correct.
Question
On a Friday night, Husband and Wife simultaneously decide whether to Go Home or Work Late. If both opt to Go Home, the payoffs are (1, 3) to Husband and Wife, respectively. If both opt for Work Late, the payoffs are (5, 3). If Husband chooses to Go Home and Wife chooses to Work Late, the payoffs are (1, 5). Finally, if Husband chooses to Work Late and Wife chooses to Go Home, the payoffs are (5, 1). Choose ALL correct statements:Group of answer choicesHusband’s dominant strategy is to Work Late.The Nash equilibrium is (Work Late, Work Late); this is a prisoners’ dilemmaThe Nash equilibrium is (Work Late, Work Late); this is a dominant strategy equilibriumThe Nash equilibria are (Work Late, Work Late); (Go Home, Go Home); this is a coordination gameNone of the answers are correct.
Solution
The correct statement is: "The Nash equilibrium is (Work Late, Work Late); this is a dominant strategy equilibrium".
Here's why:
A dominant strategy is one where a player will always prefer one action, regardless of what the other player does. In this case, the Husband's payoffs are higher if he chooses to Work Late, regardless of the Wife's choice. Therefore, the Husband’s dominant strategy is to Work Late.
A Nash equilibrium is a set of strategies where no player can improve their payoff by unilaterally changing their strategy, given the other player's strategy. In this case, if the Husband is working late, the Wife gets a higher payoff by also working late. Similarly, if the Wife is working late, the Husband gets a higher payoff by also working late. Therefore, the Nash equilibrium is (Work Late, Work Late).
This is not a prisoner's dilemma because in a prisoner's dilemma, each player has a dominant strategy and they are better off if they both betray each other. However, in this case, the Wife does not have a dominant strategy.
This is not a coordination game because in a coordination game, there are multiple Nash equilibria and the players need to coordinate to achieve the best outcome. However, in this case, there is only one Nash equilibrium.
Therefore, the correct statement is: "The Nash equilibrium is (Work Late, Work Late); this is a dominant strategy equilibrium".
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