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Steph is deciding on whether to Open (O) a flower shop or Not (N) next to Woolworths, who already sell flowers. If Steph chooses to Open, Woolworths then can choose to Fight (F) or Accommodate (A). If Woolworths chooses F, following Stephs choice to Open, the payoff is (-5, 5) to Steph and Woolworths, respectively. If Steph chooses to Open, then Woolworths opts for A payoffs are (10, 15). If Steph opts for N, the payoff to Steph is 0 and Woolworths gets 20. Which of the following is a Nash Equillibrium that is NOT a subgame perfect equillibrium:Group of answer choices(O,F)(O,A)(N,F)(N,A)

Question

Steph is deciding on whether to Open (O) a flower shop or Not (N) next to Woolworths, who already sell flowers. If Steph chooses to Open, Woolworths then can choose to Fight (F) or Accommodate (A). If Woolworths chooses F, following Stephs choice to Open, the payoff is (-5, 5) to Steph and Woolworths, respectively. If Steph chooses to Open, then Woolworths opts for A payoffs are (10, 15). If Steph opts for N, the payoff to Steph is 0 and Woolworths gets 20. Which of the following is a Nash Equillibrium that is NOT a subgame perfect equillibrium:Group of answer choices(O,F)(O,A)(N,F)(N,A)

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Solution

The Nash Equilibrium that is not a subgame perfect equilibrium in this scenario is (O, F).

Here's why:

A Nash Equilibrium is a set of strategies where no player can do better by unilaterally changing their strategy, given the strategies of the other players. In this case, (O, F) and (N, A) are Nash Equilibria.

However, a subgame perfect equilibrium is a refinement of a Nash Equilibrium that also satisfies the principle of sequential rationality. This means it must represent a Nash Equilibrium in every subgame of the original game.

In the subgame where Steph has chosen to Open, Woolworths' best response is to Accommodate (A), not Fight (F), because 15 > 5. Therefore, (O, F) is not a subgame perfect equilibrium, even though it is a Nash Equilibrium.

On the other hand, (N, A) is a subgame perfect equilibrium because it is a Nash Equilibrium in the subgame where Steph chooses Not to open.

This problem has been solved

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