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TC Timber is a company owned by Mark Adams and located in Skaneateles, New York. The company manufactures wooden train sets. Brio is the largest producer of wooden train sets and Mark Adams is deciding whether to make TC Timber train sets compatible with sets manufactured by Brio. Brio is also interested in acquiring TC Timber which Mark Adams is well aware of. Suppose that after Mark Adams decides whether or not to make TC Timber sets compatible with Brio, Brio makes an offer to acquire TC Timber. In terms of notation, let Pc be the take-it-or-leave-it price Brio offers Mark Adams for TC Timber if he decided to make the TC Timber wooden sets compatible. Let Pnc be the take-it-or-leave-it price Brio offers Mark Adams for TC Timber if he decided to make the TC Timber wooden sets not compatible with Brio. After Brio makes an offer, Mark Adams can either accept the offer (i.e., sell TC Timber to Brio) or reject the offer. In terms of payoff, suppose TC Timber is worth $20M to Mark Adams if he makes the sets compatible and does not sell to Brio. TC Timber is worth $12M to Mark Adams if he does not make the sets compatible and does not sell to Brio. The maximum Brio is willing to pay for TC Timber is $40M if Mark Adams chose to make the TC Timber sets compatible with Brio. The maximum Brio is willing to pay for TC Timber is $55M if Mark Adams chose not to make the TC Timber sets compatible with Brio. Below is the game tree associated with the extensive form game described above. a. Suppose Mark Adams has decided to make the wooden sets compatible and Brio has offered a price of Pc. What is the minimum price Mark Adams will accept? Explain. b. Suppose Mark Adams has decided to make the wooden sets compatible? Based on backward induction/subgame perfection, what price (Pc) should Brio offer? Explain. c. Based on the Subgame Perfect Equilibrium, what would you expect the outcome of this game to be? In other words, would Mark Adams make the wooden sets compatible or would he make the wooden sets not compatible? What offer would Brio make in terms of price and would Mark Adams accept or reject this price? Explain. d. What if we change the game above and allowed Mark Adams to negotiate the price with Brio at the same time he negotiates whether or not to make the wooden sets compatible. Provide intuition as to how this could change the outcome of the above game. Mark Adams Make Compatible Don't Make Compatible Brio Brio Pac Mark Adams Mark Adams Accept Reject Accept Reject Mark Adams: Pc 20M Pac 12M Brio: 40M- Pc 0 55M- Pac