3. A. If CD players are able to use the LDD strategy better than pure chance, then explain what happens to the signal reliability ratio as a CD player detects more cautiously.

B. Assume a population contains either CD or DD players, where each player is randomly matched with a partner taken from the whole population. Also assume the fear and greed payoff differences are equal. What are the expected payoff formulas for CD players [denoted E(CD*) ] and for DD players [ E(DD*) ] ] depending on the fraction of CD players in the population, denoted .

C. Use the expected payoff formulas of Part B to algebraically derive an inequality for the signal reliability ratio r/w that determines when the CD players will outperform the DD players.

D. Use this inequality with Part A, to explain how CD players can always outperform DD players starting from any positive initial fraction of CD players.