Firm V and Firm Z are engaged in a product design game. The game is a simultaneous, noncooperative, one-shot game.

Firm V has three possible design strategies: Beaded, Plated, or Mixed.

Firm Z has two possible design strategies: Contoured or Rough.

The payoffs for each possible outcome are:

                                                                                    Firm V            Firm Z

Firm V Beaded, Firm Z Contoured                                 45                    34

Firm V Beaded, Firm Z Rough                                       37                    36

Firm V Plated, Firm Z Contoured                                   46                    41

Firm V Plated, Firm Z Rough                                         35                    52

Firm V Mixed, Firm Z Countered                                   53                    29

Firm V Mixed, Firm Z Rough                                         39                    38

Explain why the combination Mixed and Rough is probably the outcome for this game.

Before the game shown in your answer to question A is played, the game has changed. It will actually be played in several steps:

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

2.   After Firm V has announced to everyone whether or not it will commit to the side payment offer, Firm Z then has the ability, if it wants to, to remove the strategy choice “Mixed” from the set of possible strategies that Firm V could choose. Firm Z must decide whether or not to prevent Firm V from being able to choose “Mixed”.

3.   Once those two decisions are made and announced to everyone, the game of selecting design strategies is then played, using any changes in structure from those two decisions. This game is still simultaneous, non-cooperative, one-shot.

      For this game, if the game has one Nash equilibrium in pure strategies, then each firm will 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 firm 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 the questions for you to answer:

For this mega-game:

• Should Firm V commit to making the side payment if and only if firm Z chooses “Contoured”, or should Firm V offer no side payment?
• Should Firm Z remove the strategy “Mixed” from Firm V’s possible strategies, or should Firm Z allow Firm V to consider and possibly to choose the strategy “Mixed”?
• What is the outcome of the overall 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, so that I can clearly see how you are solving for various aspects of the possible game outcomes.