Suppose Securitex is a small firm that has developed a new​ anti-theft device for automobiles. Securitex currently sells its device online and earns profit of ​$1515 million per year. GM is considering installing​ Securitex's system on its automobiles. The two firms​ first, however, must bargain over what price GM will pay Securitex for its software. GM chooses how much to offer Securitex for its system and then Securitex chooses whether to accept the offer and install its system on​ GM's automo

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Question:

Suppose Securitex is a small firm that has developed a new​ anti-theft device for automobiles. Securitex currently sells its device online and earns profit of ​$1515 million per year. GM is considering installing​ Securitex's system on its automobiles. The two firms​ first, however, must bargain over what price GM will pay Securitex for its software. GM chooses how much to offer Securitex for its system and then Securitex chooses whether to accept the offer and install its system on​ GM's automobiles. The strategies and corresponding profits for GM​ (GM) and Securitex​ (SX) are depicted in the decision tree to the right. Profits are in​ millions, and​ GM's payoffs represent the additional profit it can earn on its automobiles with​ Securitex's anti-theft system. What is the​ subgame-perfect equilibrium

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Answer:The data is missing, so I looked for a similar question (see attached image). in a subgame perfect equilibrium, players take turns, one player (GM) will take turn an make an offer to the second player (Securitex), and then the second player will decide whether to accept the offer or not. The situations where the offer is rejected are not really an equilibrium since basically GM and Securitex get nothing out of the deal. The two remaining options where Securitex accepts the offer must be analyzed in the following way:After GM makes its move, is Securitex going to be better off or not. If GM makes a high offer and Securitex accepts it, then both will be better off. But if GM makes a low offer and Securitex accepts, it, GM will be better off but Securitex will be worse off, so that is not a real equilibrium. The only option where a real equilibrium happens and is accepted by both, is that GM makes a high offer and Securitex accepts it. This would be option C.

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