THIS IS GAME THEORY QUESTION

Question 3. [32 total points] Ad competition Two computer game companies, A and B, are both trying to introduce their products to teenagers in a new-market economy. The market has the feature that the rm that spends the most on advertising \"wins\" the entire demand. Winning the market is worth $60M, regardless of the total amount of advertising. If both rms spend the same amount on advertising, they split the market. Thus, for example, if rm A spends $30M on advertising and rm B spends $20M on advertis- ing, then rm A will win the market and earn $30M (2 $60M $30M) while rm B will earn $20M. If each rm spends $20M, then each rm will earn $10M (= $60M/2 $20M). The rms choose their levels of advertising simultaneously. To keep things simple, assume that each rm can choose to spend either $0, $10M, $20M, or $30M on advertis- ing. No other amounts are possible. Assume throughout that each rm's only aim is to maximize its expected prots. Thus the payoff matrix for this game is as follows (where all numbers are in $M). 0 10 20 30 40 40 10 10 10 (a) [7 points] For each player in this game, nd the strategies that are strictly domi- nated (if there are any) and that are weakly dominated (if there are any). Explain your answer carefully: in particular explain why any dominated strategies are dom- inated and whether the domination is strict or weak. (b) [10 points] Either nd a purestrategy Nash Equilibrium in this game (if there is one), or explain why none exist. Show some working or explain your answer. (0) [5 points] Suppose that the government in the new market economy is considering banning all advertising of computer games: that is, there is proposed legislation that would make it illegal for any rm to spend any amount other than $0 on advertising for this market. If you were a consultant for these rms, would you advise them to lobby for or against this proposed legislation. Why? Return to the original game before the advertising ban. Suppose now that each rm can choose to spend either $0, $10M, $20M, $30M, or $40M on advertising. That is, we have added a new strategy to the game, spending $40M on advertising. The payoffs follow the same rules as before. So for example, if rm A spends $30M on advertising and rm B spends $40M, then rm B will win the market and earn $20M (= $60M $40M) while rm A will earn $30M. If each rm spends $40M then each will earn $10M (= $60M/2 $40M). ((1) [10 points] Construct the payoff matrix for this new game. Either nd a pure- strategy Nash Equilibrium in this game, or explain why none exists. Show some working or explain your