In this game theory question a take it or leave it scenario is given.

Question 12: Consider the 'take-it-or-leave-it' gameA referee has N times 10 kroner. He places 10 kroner on the table. Player 1 can either take the 10 kroner coin or leave it. If she takes them, the game ends. If she leaves it, the referee places a second 10 kroner coin on the table. Player 2 is now given the option of taking the 20 kroner or leaving them. If he takes them, the game ends. Otherwise the refere places a third 10 kroner coin on the table and it is again player 1's turn to take or leave the 30 kroner. The game continues in this manner with the players alternately being given the choice to take all the money the referee has so far placed on the table and where the referee adds 10 kroner to the total whenever a player leaves the money. If the last player to move chooses to leave the N times 10 kroner the game ends with the money going to the other player. Assume that N is public information. (a) If two of your co-students would be asked to play this game, what would you think would happen? Would it make a difference if N were very large (like one thousand) or quite small (like 5)? (b) What are the backward induction strategies for the two players? (c) What does your answers under (a) and (b) mean for the ability of backward induction to predict actual behavior