GAME THEORY: SEQUENTIAL GAMES ARE PLAYED IN BUSINESS ALL THE TIME

Game theory was developed by the mathematician John Nash. It is a set of tool for analyzing gamesof strategy. Hewas awarded the Nobel Prize in Economics in 1994 and the Abel Prize in Mathematics in 2015.His tools for analysis have wide use, but in terms of economics many of the games he was able to articulate with game theory were quite old and well known to the economic literature, but Nash's solutions were elegantly stated. TheCournotduopoly game in the Discussion Preparation dates from the 1830s.

In our Managerial Economics textbook, we consider a sequential-move game in which an entrant is considering entering an industry in competition with an incumbent firm (see Figure 15-1). There are several possibilities of how this sequential game will be played. We want to use the Froeb rule of "look ahead and reason back."

sequential game, W tomorrow in response to each of our possiu Pen now the other player will react tomorrow, we can accurately forecast the col anticipating 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 ty thlove game illustrated in Figure 15.1. An entrant is deciding whether to ente. an industry currently controlled by a single incumbent firm. Beginning on " 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., by keeping Entrant In Out Incumbent 0, 10 Accommodate Fight 5 , 5 -5, -5 FIGURE 15.1 Entry Game