Question

5. [20 points] Bruster's and Rita's both sell equally delicious ice cream and compete for the same customers. Each can offer customers a rewards card (offering free ice cream after a certain number of purchases) or not. Profits at each firm are greater if neither firm offers a rewards card than the case in which both do offer rewards cards. If one firm offers a rewards card and the other doesn't, the one offering the rewards card earns higher profits than in the case where neither firm offers a rewards card, while the firm that does not offer a rewards card earns lower profits than in the case where both firms offer rewards cards. a. [8 points) Write the payoff matrix. Be sure to label the players and the strategies in your payoff matrix. NOTE: For the purposes of simplifying the grading process, please use {0, 1, 2, 3} to denote the payoffs. b. [6 points] Conduct the best-response analysis and find the Nash equilibrium/equilibria. c. [3 points] Does either player have a strictly dominant strategy in this game? If so, what is it? d. [3 points] Is this game a Prisoners’ Dilemma? Explain your answer. If you think this is a Prisoners' Dilemma state which strategy you consider to be the cooperative strategy.

Answer 1

Brusher Reward - Neel Rewand Rita II 13,0 Nat 0,3 1 2,2 when Ritar chooses Reward, Brushes will choose Record as to when, Brusher chooses Reward, Rita will choose Reward as xo so, Rewa Rewald, Ruvard) is a noush equilibrium. O Rita chooses Not Reward, then , Bonster will choose Revard as 372. Yes, both players have strictly deaminant strategy which which is is Revat rewat kinward Runward as ito and 372.

I di Yes, this game is from Priseness' Dilemma type game, because there is a strictly dominant strategy which gives lower pay off if both of them cooperate and choose opposite stalegy. IR both will choose Neet Rever Reward then, they will get highn pay off which is 2 l