Microsoft and a smaller rival often have to select from one of two competing technologies. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. Describe the equilibrium of this game.

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Game Theory:

1) Consider the game given (see attachment)

a. how many subhistories of (terminal) histories?

b. how many subgames are there?

c. how many strategies does player 1 have? Calculate this number.

d.
solve for the subgame perfect equilibrium using backward induction.
Indicate in the game tree the subgame perfect equilibrium strategy of
each player by drawing for each history a line parallel to the edge
representing the action that the player chooses at this history.

2)
There are two players. Players move sequentially starting with player
1, followed by player 2, followed by player 1 again etc. Each time that a
player moves, she can choose a number from the set {1, 2, 3, 4, 5, 6,
7, 8, 9, 10}. The first player who brings the sum of all chosen numbers
to a total that is weakly larger 100 (larger than or equal to 100) wins
the game. Who wins the game in subgame perfect equilibrium? Explain.