please send handwritten solution for Q5 There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack,and you must pick one to protect. Suppose that the attacker is going to attack site i with probability q:. You planon selecting a site to protect, with probability pi of selecting site i. If you select the same site to protect that theattacker chooses to attack, you successfully defend that site. The choice of {q;} and {p;} represent the attacker'sand defender's strategy, respectively.1) What is the probability that you successfully prevent the attack, given strategies {4:}, {p:}?? .2) If you knew {qı,...,qN} in advance, how should you choose {p:} to maximize the probability you successfullyprevent an attack?3) If you are the attacker, and you know that the defender is going to choose the best strategy they can to maximizethe probability of preventing an attack, how should you choose your strategy to maximize the probability of asuccessful attack? (4) Questions 2.1, 2.2, 2.3 address the probability of a successful defense from the perspective of the attackerthinking about the best possible defender. Consider as well the perspective of the defender thinking about thebest possible attacker. Re-do 2.1, 2.2, 2.3 from this perspective, then argue what the 'final' strategies for eachplayer will be in this game.In the questions that follow, we imagine that a successful attack on site i will cost the defender C;.5) What is the expected or average cost of an attack, given strategies {4;}, {p:}? ( *

Probability of a successful attack = 1 - 1/N2 Probability of defended attack = 1/N2 Expected Value…

There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability q;. You plan on selecting a site to protect, with probability pi of selecting site i. If you select the same site to protect that the attacker chooses to attack, you successfully defend that site. The choice of {q;} and {p;} represent the attacker's and defender's strategy, respectively. 1) What is the probability that you successfully prevent the attack, given strategies {4;}, {p:}?? 2) If you knew {q1,...,qN} in advance, how should you choose {pi} to maximize the probability you successfully prevent an attack? 3) If vou are the attacker, and vou kmow that the defender is going to choose the best strategy they can to maximize

There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability q;. You plan on selecting a site to protect, with probability pi of selecting site i. If you select the same site to protect that the attacker chooses to attack, you successfully defend that site. The choice of {q;} and {p;} represent the attacker's and defender's strategy, respectively. 1) What is the probability that you successfully prevent the attack, given strategies {4;}, {p:}?? 2) If you knew {q1,...,qN} in advance, how should you choose {pi} to maximize the probability you successfully prevent an attack? 3) If vou are the attacker, and vou kmow that the defender is going to choose the best strategy they can to maximize

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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