In experimental economics, it is impossible to repeat a game infinitely many times. Instead, the experimentor applies the following technique: Players start by playing a stage game once. Then, a coin is flipped that has a probability 0 < < 1 of landing on Heads and a probability 1 of landing on Tails. If the coin lands on Tails, the game ends and players receive their payouts thus far. If the coin lands on Heads, the game is repeated again, with another coin-flip at the end of that game to determine if the game continues or not. After a Tails is flipped, players earn the payoffs that they have received so far.

(a) Show that the expected payoff from this procedure is the same as the payoff from a player who plays the stage game infinitely many times with a discount rate of 0 < < 1.

(b) Is the set of strategies the same under the experimental technique and the infinitely repeated game? Explain: