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This exercise is adapted from Dixit, Avinash K., and Barry J. Nalebuff (1991), Thinking Strategically, New York: W W Norton. 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? (e) Comparing the answers to (a) and (b), what can you say about the value of commitment for the US