Wozza, an entrepreneur, can either Enter (E) or Hold (H). Shazza, a rival entrepreneur, observes Wozza’s choice, then can choose to either play E or H. The payoffs are as follows: Following (E, E) (played by Wozza, then Shazza) the payoffs are (20, 50) to Wozza and Shazza, respectively. Following (E, H) the payoffs are (30, 80). Following (H, E) the payoffs are (60, 20). Finally, following (H, H), the payoffs are (20, 15) to Wozza and Shazza. Which statement is FALSE?Group of answer choicesH (played by Shazza) following E is credibleThe observed outcome in the credible (subgame perfect) equilibrium is H then E.If the order that the players get to choose E and H is reversed, the observed outcome (and actions) of the entrepreneurs will be different.H (played by Shazza) following H is credible.The sum of the payoffs to the entrepreneurs in the credible (subgame perfect) equilibrium is 80.
Question
Wozza, an entrepreneur, can either Enter (E) or Hold (H). Shazza, a rival entrepreneur, observes Wozza’s choice, then can choose to either play E or H. The payoffs are as follows: Following (E, E) (played by Wozza, then Shazza) the payoffs are (20, 50) to Wozza and Shazza, respectively. Following (E, H) the payoffs are (30, 80). Following (H, E) the payoffs are (60, 20). Finally, following (H, H), the payoffs are (20, 15) to Wozza and Shazza. Which statement is FALSE?Group of answer choicesH (played by Shazza) following E is credibleThe observed outcome in the credible (subgame perfect) equilibrium is H then E.If the order that the players get to choose E and H is reversed, the observed outcome (and actions) of the entrepreneurs will be different.H (played by Shazza) following H is credible.The sum of the payoffs to the entrepreneurs in the credible (subgame perfect) equilibrium is 80.
Solution
The false statement is: "The observed outcome in the credible (subgame perfect) equilibrium is H then E."
Here's why:
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"H (played by Shazza) following E is credible" - This is true. If Wozza plays E, Shazza will play H to maximize her payoff (80 > 50).
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"The observed outcome in the credible (subgame perfect) equilibrium is H then E" - This is false. The subgame perfect equilibrium would be E then H. Wozza knows that if he plays E, Shazza will respond with H, giving him a payoff of 30. If he plays H, Shazza will respond with E, giving him a payoff of 60. However, Shazza will not play E following H because her payoff would be 20, which is less than if she played H (15). Therefore, Wozza will choose E and Shazza will respond with H.
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"If the order that the players get to choose E and H is reversed, the observed outcome (and actions) of the entrepreneurs will be different" - This is true. If Shazza gets to choose first, the outcome could be different.
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"H (played by Shazza) following H is credible" - This is true. If Wozza plays H, Shazza will play H to maximize her payoff (15 > 20).
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"The sum of the payoffs to the entrepreneurs in the credible (subgame perfect) equilibrium is 80" - This is true. In the subgame perfect equilibrium (E, H), the sum of the payoffs is 30 (Wozza) + 50 (Shazza) = 80.
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