Is the incumbent ever in control of this game?
In sequential-move games, players take turns, and each player observes what his or her rival did before having to move. To compute the likely outcome of a sequential game, we look ahead and reason back, or predict what will happen tomorrow in response to each of our possible actions today. By anticipating how the other player will react tomorrow, we can accurately forecast the con- sequences of her own moves.
We represent sequential games using the extensive or tree form of a game, familiar to anyone who has ever used a decision tree. Consider the simple two- move game illustrated in Figure 15.1. An entrant is deciding whether to enter an industry currently controlled by a single incumbent firm. Beginning on the bottom of the left branch of the tree, we see that entry can lead to two dif- ferent outcomes depending on how the incumbent reacts. The incumbent has two choices: accommodate entry or fight it. Accommodation (e.g., b
Can, and how does, the entrant succeed? Is the incumbent ever in control of this game?
You may wish to review the old game known as Duopoly, as well as Antoine-Augustin Cournot, to help inform your post.