The payoff for SS will be .1 and .03, if it chooses to reduce the price in conjunction with two different strategies by SIA.
Ans 3) Yes there exists Nash equilibrium (Non-cooperative equilibrium) as the firms will not cooperate or collude as there can be no legally binding contract among them to keep the prices same and in absence of which each firm would fear that even if keeping price normal offers highest pay out overall and higher than what they would get in case they don’t cooperate, the other firm may cut the price an take the market share away from the firm keeping price normal. Thus both firm fearing this would play safe and reduce the price. The combination of these two price cutting strategy by both the firm will entail a Nash equilibrium which is represented in cell D.
Ans 4) No they are not likely to achieve their best outcome which would have been in cell C and B for SIA and SS respectively. In fact they would have been happier in cell A also but the irony is, fearing that they might be suckered by their competitor, they will avoid reaching such outcome and settle for the one that offers them utmost safety and not payoff.
Ans 5) Repeated games can be classified in two categories finitely repeated and infinitely repeated. In the former case the number of games is fixed and each player is aware of such number, while in the latter the number of such repetition is not known. In repeated games the firms may achieve cooperative equilibrium as each firm can punish the other one for suckering it in the next game and thus “Tit for tat” plays out which leads to cooperation in repeated games. Each firm over a period builds a reputation and they start trusting each other. But in case of finite games the theoretical understanding says they will not cooperate as in the last game both would like to defect and since in the last game no cooperation is expected in the second last game both would also like to defect and working backwards in