Question

Consider the following market entry game. There are two firms : firm 1 is an incumbent monopolist on a given market. Firm 2 wishes to enter the market. In the first stage, firm 2 decides whether or not to enter the market. If firm 2 stays out of the market, firm 1 enjoys a monopoly profit of 2 and firm 2 earns 0 profit. If firm 2 decides to enter the market, then firm 1 has two strtegies : either firm 1 Fight or Accomodate. If firm 1 Fight, it gets a payoff -1. If firm 1 Accomodate, it gets a payoff 1. In any event, firm obtains a payoff 1.

a) Draw the extensive-form of the game, specifying the payoffs, who play at which node and the available strategies to that player. b) Solve the game by backward induction to find the subgame perfect Nash equilibrium.

Answer 1

A) Firm 2 starts the game by deciding whether to enter(and earn 1 payoff) or not(and earn 0 payoffs). If it chooses to enter firm 1 then decides at the next node whether to fight(and earn -1 payoff) or accommodate(and earn 1 payoff).

B)

Once the firm 2 decides to entire, it is in the interest of the Firm 1 to accommodate as the pay is higher as compared to when Firm 1 decides to fight. (1>-1)

Because Firm 2 knows that this will be the outcome at Firm 1 point, it will always choose to 'enter'. Thus backward induction leads to the final outcome will be Firm 2 'enter' and Firm 1 'accommodate' with both the firms receiving a profit of 1 each.