A game between an incumbent firm (a firm already in the market) and a potential new entrant lasts for two periods.  At the beginning of each period, the potential entrant decides whether or not it will participate in the market that period (whether it will be “in” or “out” of the market that period).  For each period, the incumbent observes the entrant’s “in” or “out” choice and, if the entrant is “in”, the incumbent chooses its response to entry: “fight” or “accommodate”.  In order to choose “in” in period 2, the entrant must have chosen “in” in period 1.  In other words, once the entrant chooses “out”, it is “out” for good.  Payoffs are as follows:

The entrant earns 0 for each period in which it is “out” of the market.  The entrant earns $1 for each period in which it is “in” the market and the incumbent “accommodates”.  The entrant loses $1 for each period in which it is “in” the market and the incumbent “fights”.  

The incumbent earns x for each period in which it has a monopoly (i.e., each period in which the entrant is “out”).  The incumbent earns z for each period in which the entrant is “in” and the incumbent “accommodates”.  The incumbent earns y for each period in which the entrant is “in” and the incumbent “fights”.  Assume that x>z>y and x+y>2z.  

For each player, the whole-game payoff is the sum of the period 1 and period 2 payoffs (there is no discounting).  

Draw the extensive form for this game.  Use backward induction to find the unique Subgame Perfect Nash Equilibrium.
Now consider the following modification of the game described above.  Everything is the same as before, except that the entrant faces a credit constraint which means that, if it were to sustain a loss in period 1 because the incumbent chooses to “fight” entry, the entrant will be denied the option to enter the market in period 2.  Draw the extensive form for this modified game.  Use backward induction to find the unique subgame perfect Nash equilibrium.