Now suppose that the third hunter joins the game. Assume that Hunter 1 moves first, Hunter 2 moves second, and Hunter 3 moves last and players observe other players’ past moves. It is still the case that at least two hunters are needed to catch a stag and they share the stag evenly. Thus, when three hunters chase a stag, the payoff of each hunter is 20, that is, (Hunter 1, Hunter 2, Hunter 3) = (20, 20, 20). Payoffs for other cases are still the same. For example, if Hunter 1 and Hunter 3 chase a stag and Hunter 2 chases a hare, then their payoffs are (Hunter 1, Hunter 2, Hunter 3) = (30, 25, 30). As another example, Hunter 1 chases a stag and Hunter 2 and Hunter 3 chase hares, then their payoffs are (Hunter 1, Hunter 2, Hunter 3) = (0, 25, 25) because Hunter 1 cannot catch the stag alone. Hunter 3’s problem 1: when both Hunter 1 and Hunter 2 chose to chase a stag, Hunter 3’s best response is .  Hunter 3’s problem 2: when one of Hunter 1 and Hunter 2 chose to chase a stag and the other hunter chose to chase a hare, Hunter 3’s best response is .  Hunter 2 makes a decision after observing Hunter 1’s decision. Moreover, Hunter 2 takes into account of Hunter 3’s response. Hunter 2’s problem 1: when Hunter 1 chose to chase a stag, Hunter 2’s best response is .  Hunter 2’s problem 2: when Hunter 1 chose to chase a hare, Hunter 2’s best response is .  Hunter 1 knows how Hunter 2 and Hunter3 will respond according to Hunter 1’s decision. Hunter 1’s problem: Hunter 1’s best response is .  Therefore, the subgame perfect Nash equilibrium of this game is as follows:Hunter 1 chooses , Hunter 2 chooses , and Hunter 3 chooses . 

In the long run, more firms enter the market. 

Now assume that Hunter 1 moves first. That is, Hunter 1 makes a decision, then Hunter 2 observes Hunter 1’s decision and make a decision. Draw the game tree in your scratch notes and check all the subgame perfect Nash equilibria in this game. (The answer can include one or multiple equilibria.)  [Hint: Use Backward induction] 

In the short run (the market price was given as before), firms earn positive profit. 

Identify the AUTHOR of the following passage: In proportion as I gain power over words, shall I lose dominion over sentiments; in proportion as my tale is deliberate and slow, the incidents and motives which it is designed to exhibit will be imperfectly revived and obscurely pourtrayed.

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