Question

This Question: 10 pts Accept SX 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 $10 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? CM High Price Reject GM Accept GM 515 SX S11 Low Price SX CHE SY510 O A. The subgame-perfect equilibrium is for GM to offer a high price and for Securitex to reject the offer. OB. The subgame-perfect equilibrium is for GM to offer a high price and for Securitex to accept the offer OC. The subgame-perfect equilibrium is for GM to offer a low price and for Securitex reject the offer OD. A subgame-perfect equilibrium does not exist for this game O E The subgame-perfect equilibrium is for GM to offer a low price and for Securitex to accept the offer Reject

Answer 1

Answer:

The subgame perfect Nash equilibrium is for GM to offer low price and for Securitex to accept the offer.

reason: Subgame perfect Nash equilibrium can be found in a sequential game where the responses of the second mover can be manipulated by the first mover to the latter's advantage.

If GM offers a high price, SX will either accept it (he will then get a payoff 14),  or reject it (his payoff willl be 10). SX will choose to accept it because accepting the high price gives SX a higher payoff (14>10). If GM offers a low price, SX will accept it (11>10). Between these two responses of SX, GM will gain better with the second option (15>7). So, GM will offer a low price and SX will follow and accept it.