Solve all please

7.3. Ericsson v Nokia. Suppose that Ericsson and Nokia are the two primary competitors in the market for 4G handsets. Each firm must decide between two possible price levels: $100 and $90. Production cost is $40 per handset. Firm demand is as follows: if both firms price at 100, then Nokia sells 500 and Ericsson 800; if both firms price at 90, then sales are 800 and 900, respectively; if Nokia prices at 100 and Ericsson at 90, then Nokia's sales drop to 400, whereas Ericsson's increase to 1100; finally, if Nokia prices at 90 51 and Ericsson at 100 then Nokia sells 900 and Ericsson 700. (a) Suppose firms choose prices simultaneously. Describe the game and solve it. (b) Suppose that Ericsson has a limited capacity of 800k units per quarter. Moreover, all of the demand unfulfilled by Ericsson is transferred to Nokia. How would the analysis change? (c) Suppose you work for Nokia. Your Chief Intelligence Officer (ClO) is unsure whether Ericsson is capacity constrained or not. How much would you value this piece of info? 7.7. HDTV standards. Consider the following game depicting the process of standard setting in high- definition television (HDTV).12 The US and Japan must simultaneously decide whether to invest a high or a low value into HDTV research. If both countries choose a low effort then payoffs are (4,3) for US and Japan, respectively; if the US chooses a low level and Japan a high level, then payoffs are (2,4); if, by contrast, the US chooses a high level and Japan a low one, then payoffs are (3,2). Finally, if both countries choose a high level, then payoff are (1,1). (a) Are there any dominant strategies in this game? What is the Nash equilibrium of the game? What are the rationality assumptions implicit in this equilibrium? (b) Suppose now the US has the option of committing to a strategy ahead of Japan's decision. How would you model this new situation? What are the Nash equilibria of this new game? (c) Comparing the answers to (a) and (b), what can you say about the value of commitment for the US? (d) \"When pre-commitment has a strategic value, the player that makes that commitment ends up 'regretting' its actions, in the sense that, given the rivals' choices, it could achieve a higher payoff by choosing a different action.\" In light of your answer to (b), how would you comment on this statement? 7.12. Ad games. Two firms must simultaneously choose their advertising budget; their options are H or L. Payoffs are as follows: if both choose H, then each gets 5; if both choose L, then each gets 4; if firm 1 chooses H and firm 2 chooses L, then firm 1 gets 8 and firm 2 gets 1; conversely, if firm 2 chooses H and firm 1 chooses L, then firm 2 gets 8 and firm 1 gets 1. (a) Determine the Nash equilibria of the one-shot game. (b) Suppose the game is indefinitely repeated and that the relevant discount factor is = .8. Determine the optimal symmetric equilibrium. (c) Now suppose that, for the first 10 periods, firm payoffs are twice the values represented in the above table. What is the optimal symmetric equilibrium? 7.15. Advertising levels. Consider an industry where price competition is not very important: all of the action is on advertising budgets. Specifically, total value S (in dollars) gets splits between two competitors according to their advertising shares. If al is firm 1's advertising investment (in dollars), then its profit is given by ay Sa ay +az (The same applies for firm 2). Both al and a2 must be non-negative. If both firms invest zero in advertising, then they split the market. (a) Determine the symmetric Nash equilibrium of the game whereby firms choose ai independently and simultaneously