You and friend are playing game. You both are given number between 1 and 10, private to each of you. You then both simultaneously decide to put a chip in the pot or not. If you both decide to put a chip in the pot (so that there're now two chips in the pot) then you proceed to second betting round. You both should then again decide (simultaneously) whether to put another chip in the pot. These rounds continue till one person decides not to put chip in the pot, at which point other player wins the pot. If 10 chips are in pot (5 rounds), then betting stops, and each player reveals his or her number. The player with highest number wins. A tie results in splitting of the pot.
Supposing Strategy 1 refers to always putting chip in the pot, find out what Strategy two is, the optimal strategy against Strategy 1. Likewise, determine Strategy n, the optimal strategy against Strategy n-1. Do this for n up to 20. How many unique strategies does this produce? What can you infer from this?