Consider this following sequential game played by two investors. Cat chooses either to go long (L) of short (S). Cat’s choice is observed by rival Cutter. Cutter then can choose to either play Hard (H) or Diverse (D). The payoffs are as follows. Following (L, H) the payoffs are (300, 500) to Cat and Cutter, respectively. If the actions are L then D, the payoffs are (0, 0). If the actions are S and then H, the payoffs are (0, 0). Finally, if the actions are (S, D) the payoffs are (300, 500). In the credible (subgame perfect) equilibrium we observe:Group of answer choicesS then DL then HS then HS then LS then D, or L then H.
Question
Consider this following sequential game played by two investors. Cat chooses either to go long (L) of short (S). Cat’s choice is observed by rival Cutter. Cutter then can choose to either play Hard (H) or Diverse (D). The payoffs are as follows. Following (L, H) the payoffs are (300, 500) to Cat and Cutter, respectively. If the actions are L then D, the payoffs are (0, 0). If the actions are S and then H, the payoffs are (0, 0). Finally, if the actions are (S, D) the payoffs are (300, 500). In the credible (subgame perfect) equilibrium we observe:Group of answer choicesS then DL then HS then HS then LS then D, or L then H.
Solution
To find the subgame perfect equilibrium, we need to use backward induction. This means we start from the end of the game and move backwards, determining the optimal strategy for each player at each stage.
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In the second stage, after Cat has chosen L, Cutter has two options: H or D. The payoffs are (300, 500) for H and (0, 0) for D. Cutter will choose H because 500 > 0.
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In the second stage, after Cat has chosen S, Cutter again has two options: H or D. The payoffs are (0, 0) for H and (300, 500) for D. Cutter will choose D because 500 > 0.
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Now, in the first stage, Cat knows Cutter's strategies from the second stage. If Cat chooses L, the payoff will be 300 (because Cutter will choose H). If Cat chooses S, the payoff will also be 300 (because Cutter will choose D).
So, in the subgame perfect equilibrium, we can have either S then D, or L then H. Both of these strategies give the same payoff to both players.
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