Firm Y and Firm Z are engaged in an innovation mega-game. Each firm knows the entire structure

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Question:

Firm Y and Firm Z are engaged in an innovation mega-game. Each firm knows the entire structure of the game, including both its own payoffs and the payoffs to the other firm from the various possible outcomes of the game.

In the final stage of this mega-game, Firm Y has up to three possible innovation strategies:

Broad, Narrow, or Mixed. Firm Z has two possible innovation strategies: Complex or Disruptive. When the firms get to this final stage of the mega-game (in which each chooses one of its possible innovation strategies), the game will be a simultaneous, non cooperative, one-shot game.

For the full basic version of this mega-game, if there are all possible strategies and no side payments, the payoffs for each possible outcome are:

Firm Y Firm Z

Firm Y Broad, Firm Z Complex 46 36

Firm Y Broad, Firm Z Disruptive 34 47

Firm Y Narrow, Firm Z Complex 45 44

Firm Y Narrow, Firm Z Disruptive 37 48

Firm Y Mixed, Firm Z Complex 49 35

Firm Y Mixed, Firm Z Disruptive 41 43

The mega-game is actually played in several steps.

1. First, if Firm Y wants to, Firm Y has the ability to make an irrevocable binding commitment for Firm Y to make a side payment of 10 to Firm Z, if and only if Firm Z chooses the strategy “Complex” when firm Z makes a strategy choice in the game shown above. If Firm Y decides to commit to the side payment, Firm Z 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 mega-game.) Firm Y must decide whether or not to commit to making this side payment.

2. After Firm Y announces 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 Y could choose. Firm Z must decide whether or not to prevent Firm Y from being able to choose “Mixed”.

3. Once those two decisions are made, the game of selecting innovation 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 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 Y commit to making the side payment if and only if firm Z chooses “Complex”, or should Firm Y offer no side payment?

Should Firm Z remove the strategy “Mixed” from Firm Y’s possible strategies, or should Firm Z allow Firm Y to consider and possibly to choose the strategy “Mixed”?