Consider the following sequential strategic situation, called the centipede game. The game has 100 stages. Two players take turns making decisions, starting with player 1. At stage t = 1, ..., 99, player 1 (if the stage is odd) or player 2 (if it is even) chooses wheter to "Terminate the Game" or to "Continue the Game." If the game is terminated at stage t = 1,...,99, the plater terminating the game recieves a payoff of t, while the other player recieves a payoff of zero. Finally, at stage t = 100, player 2 chooses between action A with a payoff of 99 for each player, or action B with a payoff of zero for player 1 and a payoff of 100 for player 2.
a) Draw the game tree for this strategic situation (the name of the game will become apparent then).
b) What is the backward induction solution to this game?