Consider the market interpretation of the basic threat game (although you can also think of the international-crisis interpretation as well). A potential entrant E can either enter a market or not, after which the local monopolist, M, can decide whether to fight by engaging in a price war or to acquiesce by sharing the market. One round of this game illustrates the situation: As we have seen in class, the backwards-induction solution to that game is that there are is no price war: E enters and M acquiesces. But this seems inconsistent with empirical observationthere are price wars in the real world. We might then ask what is going on in the world that we are not capturing in the model. One idea is "reputation": perhaps costly price wars take place so that the monopolist can establish a reputation for being tough and thereby deter others from challenging in the future. To investigate this, suppose that a chain-store is a local monopolist in two markets. In the first market, a potential entrant E1 can challenge or not. If it does challenge, the chain-store can fight or acquiesce. Meanwhile, a second potential entrant, E2, who can challenge the monopolist in the second market, is able to observe what happens in the first market before deciding whether or not to challenge in the second. Suppose that the total profit in first market is 2. If the entrant does not challenge, all of the profits go to the monopolist. If the challenger enters and the monopolist acquiesces, the firms split the profits: payoffs of (1,1). If the monopolist fights, each firm suffers costs and loses 1 on net. The total profit in the second market is also 2. So, for example, if the monopolist fights in the first market and acquiesces in the second, its total payoff is -1+1=0. (a) Write out the extensive form for this game if, as described above, the second entrant can observe what happened in the first market. (Note that there are three players in this game: the first entrant E1, the second entrant E2, and the monopolist M. Payoffs are cumulative for M: they add up over time as described above.) (b) How would the extensive form for this game be different if the second entrant cannot observe what happened in the first market? (c) Solve for the subgame perfect equilibrium (a). Does the monopolist fight in the first market in equilibrium in order to deter the second entrant from challenging? (d) Suppose there were ten local markets instead of two and each entrant knows what happened in all of the previous markets. Explain why the monopolist would fight or not in the first market in the SPE. (Think the problem through without writing down the very long tree.) 1