Consider an extensive form game in which there are two players, Kodak and

P olaroid. In this extensive form game, the initial node is associated with

Kodak, and at this node Kodak has two available actions, Out and In$.$ When

Kodak chooses Out, then the game ends with the payoff allocation $($uK $,$ uP $)=$

$(0,2$$).$ When Kodak chooses In$,$ then Kodak and P olaroid come to compete

in the instant photography market, where each of them can choose either F ight

or Accomodate without knowing the other$$s action. Moroever, after they choose

their actions, the game ends. The payoff allocations are specified according to

their choice of actions in the market competition as follows:

$($i$)$ if both choose F ight, then the payoff allocation is $($uK $,$ uP $)=($$,$$).$

$($ii$)$ if P olaroid chooses F ight and Kodak chooses Accomodate, then the

payoff allocation is $($uK $,$ uP $)=($$,$ $)$;

$($iii$)$ if Kodak chooses F ight and P olaroid chooses Accomodate, then the

payoff allocation is $($uK $,$ uP $)=($$,$$)$;

$($iv$)$ if both choose Accomodate, then the payoff allocation is $($uK $,$ uP $)=$

$($$,$ $),$

where $>$ $>0$ and $>$ $>0.$

Given this extensive form game, answer the following questions:

$(1)$ Describe the game tree of this game.

$(2)$ Describe the game matrix of this game.

$(3)$ Compute what pure strategy Nash equilibria are in this game.

$(4)$ Compute what subgame perfect equilibria in this game.

$(5)$ Is there a pure strategy Nash equilibrium which is based on an incredible

commitment of Kodak? If yes, specify which of pure strategies is incredible? If

no$,$ explain why there is no incredible pure strategy for Kodak.

$3$