Reference no: EM13906856

(Extension of the Stag hunt) Extend the n-hunter Stag Hunt by giving each hunter K (a positive integer) units of effort, which she can allocate between pursuing the stag and catching hares. Denote the effort hunter i devotes to pursuing the stag by ei, a nonnegative integer equal to at most K. The chance that the stag is caught depends on the smallest of all the hunters' efforts, denoted minj ej . ("A chain is as strong as its weakest link.") Hunter i's payoff to the action profile (e1,... , en) is 2 minj ej - ei. (She is better off the more likely the stag is caught, and worse off the more effort she devotes to pursuing the stag, which means she catches fewer hares.) Is the action profile (e,..., e), in which every hunter devotes the same effort to pursuing the stag, a Nash equilibrium for any value of e? What is a player's payoff to this profile? What is her payoff if she deviates to a lower or higher effort level? Is any action profile in which not all the players' effort levels are the same a Nash equilibrium? (Consider a player whose effort exceeds the minimum effort level of all players. What happens to her payoff if she reduces her effort level to the minimum?)