Question

An incumbent firm (I) faces the possibility of entry by a challenger firm (C). If C enters, I may either accommodate or fight. If C does not enter, its payoff is 1, while I's payoff is 2. If C enters, and I accommodates, their payoffs are 2 and 1, respectively. However, if C's entry is met with a fight by I, their payoffs are 0 and 1, respectively. Which one of the following is a subgame perfect Nash equilibrium (SPNE) under perfect information ?

• A. enter; accommodate
• B. enter; fight
• C. not enter; accommodate
• D. not enter; fight

Answer 1

The Correct Option is A

To determine the subgame perfect Nash equilibrium (SPNE) under perfect information, we need to analyze the sequential game between the incumbent firm (I) and the challenger firm (C). In a SPNE, strategies form a Nash Equilibrium in every subgame of the original game.

1. Consider the decision tree's sequential structure: First, C decides whether to enter or not. If C does not enter, I automatically receives a payoff of 2 while C receives 1.
2. If C enters, I can choose to either accommodate or fight. Let's evaluate these:
   • Accommodate: C's payoff is 2, I's payoff is 1. 
   • Fight: C's payoff is 0, I's payoff is 1.
3. Next, consider C's decision-making process. Knowing I's potential responses:
   • If C expects I to accommodate, C's payoff for entering is 2, which is better than not entering (1).
   • If C expects I to fight, C's payoff for entering is 0, which is worse than not entering (1).
4. Given that C will anticipate I's best response, the rational choice for I, when C enters, is to accommodate since it results in a higher payoff (2) for C than fighting (0).
5. Thus, the strategy pair where C enters and I accommodates is a subgame perfect Nash equilibrium, as it considers the best responses at each decision node within the game.

The SPNE is therefore: enter; accommodate.