1. Consider a market entry game (of complete information) between a...

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1. Consider a market entry game (of complete information) between a start-up and an incumbent. The start-up first decides whether to enter the market (I) or stay out of it (O). If the start-up stays out, the game ends with the start-up having 0 payoff and the incumbent enjoys 2 units of payoff. If the start-up enters the market, then both firms simultaneously choose whether to fight (F) a price war or to accommodate (A) each other. The payoff matrix for the post-entry subgame is as follows: Incumbent F A F -3, 1 1,-2 Start-up A -2,-1 3,1 (a) Draw the extensive form game for this situation. (b) Find all Nash equilibria of the market entry game. There is exactly one Nash equilibrium in which only the incumbent makes a non-credible threat on an off-equilibrium path. In other words, all of the start-up's actions in this equilibrium are best responses at their respective information sets. (c) Propose a belief for the incumbent that justifies its choice in the aforementioned equilibrium. In other words, find a belief for the incumbent such that, based on this belief, it is optimal for the incumbent to choose the strategy in the aforementioned equilibrium. (d) Solve for all the beliefs that can justify the incumbent's choice in this equilibrium. (e) Do any of the beliefs you find in (d) satisfy the consistency requirement, which is a part of the definition of perfect Bayesian equilibrium?

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