a) Let’s examine another strategy that we will call “Alternate.” The strategy is played as follows: start by colluding, then defect, and keep alternating (C,D, etc.) to the end of the game. Calculate the overall payoffs for the Tit-for-Tat strategy, the Trigger Price strategy, the Dominant strategy and the Alternate strategy in a tournament where each strategy plays against itself and the three other strategies (each in a 10-rounds game). Use the payoff matrix we used in class during that experiment. How does the Alternate strategy do in terms of overall payoffs compared to the tit-for-tat strategy and compared to the other strategies? Why is that? Note: You must show all your work for full credit. There will be no partial credit. Using Excel would facilitate calculations. You can attach an Excel spreadsheet to your submission -- make sure your answers are easy to be located.
b) Can you think of another strategy to add to the tournament (ignoring the random and Alternate strategies) such that the Tit-for-Tat strategy would do the best overall (in terms of payoffs)?
i. Explain the strategy.
ii. Calculate overall payoffs for the Tit-for-Tat strategy, the Trigger Price strategy, the Dominant strategy and your strategy in a tournament where each strategy plays against itself and the three other strategies (each in a 10-rounds game). Show that tit-for-tat does the best overall. Use the payoff matrix we used in class during that experiment.