(3) Games People Play (24 points) Colgate and Unilever are engaged in an innovation Ramp;D competition (game).

(3) Games People Play (24 points)

Colgate and Unilever are engaged in an innovation R&D competition (game). Each firm knows the structure of the game, including both its own and the other firm's payoffs from the various outcomes of this game. 

In the final stage of this R&D game, Colgate has up to three possible innovation R&D strategies:   Broad, Narrow, or Mixed. Unilever has two possible innovation R&D strategies: Complex or Disruptive. When the firms get to this final stage of the R&D game (in which each chooses one of its possible innovation strategies), the game will be a simultaneous one round game.  For this R&D game=, if there are all possible strategies and no side payments, the payoffs for each possible outcome are:

                                                                                   Colgate           Unilever

Colgate Broad, Unilever Complex                                    46                   36

Colgate Broad, Unilever Disruptive                                 34                   47

Colgate Narrow, Unilever Complex                                 45                   44

Colgate Narrow, Unilever Disruptive                               37                   48

Colgate Mixed, Unilever Complex                                   49                   35

Colgate Mixed, Unilever Disruptive                                 41                   43

The R&D game is played in several steps, however. 

1.  First, if Colgate wants to, Colgate has the ability to make an irrevocable and fully binding commitment for Colgate to make a side payment of 10 to Unilever, if and only if Unilever chooses the strategy "Complex" when Unilever makes a strategy choice in the game shown above. If Colgate decides to commit to the side payment, Unilever knows that it will receive the side payment of 10 if it chooses "Complex". (The side payment will be settled at the same time as the payoffs are made at the end of the R&D game.) Colgate must decide whether or not to commit to making this side payment.

2.  After Colgate announces whether or not it will commit to the side payment offer, Unilever then has the ability, if it wants to, to remove the strategy choice "Mixed" from the set of possible R&D strategies that Colgate could choose. Unilever must decide whether or not to prevent Colgate from being able to choose "Mixed".

3.  Once those two decisions are made by the firms, the game of selecting innovation R&D strategies is then played, using any rules from those two decisions in addition to the rules "simultaneous, non-cooperative, one-shot." For this game, if the game has one Nash equilibrium in pure strategies, then we expect each firm will then select its Nash-equilibrium strategy. If the game has no Nash equilibrium in pure strategies - or if the game has two or more Nash equilibriums in pure strategies - then the game will actually not be played. Instead, each company will receive a payoff of 40 in lieu of playing the game. (And, if the game is not actually played, then there will be no side payment.)

Here are these questions for you to answer for this R&D game: 

(a)  Should Colgate commit to making the side payment if and only if Unilever chooses "Complex", or should Colgate not offer a side payment?

(b)  Should Unilever remove the strategy "Mixed" from Colgate's possible strategies, or should Unilever allow Colgate to consider and potentially choose the strategy "Mixed"?

(c)  What is the outcome of the overall R&D game?

Offer a full explanation of why you reach your conclusions. In your answer, please be as precise as possible; show enough in your answer to show how you are solving for various aspects of the game