Consider a two-player game between Raising Cane’s and Layne’…
Consider a two-player game between Raising Cane’s and Layne’s Chicken Fingers, each of which sells chicken basket combos (a uniform good). Each firm can set either a high or a low price. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000. Suppose the two firms play this game repeatedly forever. Let each of them use a grim-trigger strategy in which they both price high unless one of them “defects,” in which case they price low for the rest of the game. Suppose now that the firms know that there is a 90% probability that the game goes on after any given year. Under these circumstances, a firm has incentives to defect for all r greater than _______ (please enter an exact answer).