Consider the location game with nine possible regions at which vendors may locate. Suppose that, rather than the players moving simultaneously and independently, they move sequentially. First, vendor 1 selects a location. Then, after observing the decision of vendor 1, vendor 2 chooses where to locate. Use backward induction to solve this game (and identify the subgame perfect Nash equilibrium). Remember that you need to specify the second vendor’s sequentially optimal strategy (his best move conditional on every different action of vendor 1).

Location game with 9 possible [tex]\text{regions}[/tex] and other than the players who are moving simultaneously and also independently, but they move in a sequential manner.

Vendor 1 selects a location.

After observing decision of vendor 1, vendor 2 chooses where to locate.

Using backward induction the game is solved as below :

-- [tex]\text{a retrogressive acceptance harmony of the division}[/tex] will be a Nash equilibrium.

-- Presently [tex]\text{ if applicant 1}[/tex] (vendor 1) picks first then he will likewise get the chance to pick last as this another move amusement.

-- In the end of the game, vendor 1 will have claimed five regions and candidate 2 (vendor 2) will have claimed four regions.

-- So vendor 2 will keep this in mind and apply backward induction and choose the best regions early on the game.

-- Vendor 2 will keep in mind that vendor 1 will choose last and will ensure that his choices take up the best locations first.

--- This will be his ideal technique for each activity of vendor 1.

Hence this is the Nash equilibrium.