please send handwritten solution for bonus Question Problem 2: Strategic DefenseThere 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 qi. You planon selecting a site to protect, with probability p; 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 {pi} represent the attacker'sand defender's strategy, respectively.1) What is the probability that you successfully prevent the attack, given strategies {qi}, {pi}??2) If you knew {q1,..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 {q}, {p:}?6) If you knew {q1,...,qN} in advance, how should you choose {p:} to minimize the expected cost of an attack?7) If you were the attacker, and knew that your opponent was trying to minimize the expected cost of your attack,how should you choose {q;} to maximize the expected cost of an attack? (Assume that your strategy is goingto leak to your opponent.)8) Questions 2.5, 2.6, 2.7 address the problem of the expected cost of an attack from the perspective of the attackerthinking about the best possible defender. Consider as well the the perspective of the defender thinking aboutthe best possible attacker. Re-do 2.5, 2.6, 2.7 from this perspective, then argue what the 'final' strategies foreach player will be in this game.BonusRestricting ourselves to two sites, site A and site B, suppose that a successful attack onsite i gives a reuward of R, to the attacker, at cost C; to the defender. if the attacker wants to marimize their erpectedreward, and the defender wants to minimize their erpected cost, uwhat strategies should they follow, and why? Whatif they had the opportunity to negotiate beforehand, how would that change things? Note, this will depend heavily onhow {RA, RB}, {Ca,CB} relate to each other.

protection (number them 1 to N). Someone is going to pick one e ect. Suppose that the attacker is going to attack site i with probal with probability p, of selecting site i. If you select the same site t u successfully defend that site. The choice of {q} and {p.} repres etively. that you successfully prevent the attack, given strategies (q.), {p.} in advance, how should you choose {p,} to maximize the probabili d you know that the defender is going to choose the best strategy the ting an attack, how should you choose your strategy to maximize ti uddress the probability of a successful defense from the perspecti possible defender. Consider as well the perspective of the defender t e-do 2.1, 2.2, 2.3 from this perspective, then argue what the 'final me. re imagine that a successful attack on site i will cost the defender C average cost of an attack, given strategies {g.}, {p.}?

protection (number them 1 to N). Someone is going to pick one e ect. Suppose that the attacker is going to attack site i with probal with probability p, of selecting site i. If you select the same site t u successfully defend that site. The choice of {q} and {p.} repres etively. that you successfully prevent the attack, given strategies (q.), {p.} in advance, how should you choose {p,} to maximize the probabili d you know that the defender is going to choose the best strategy the ting an attack, how should you choose your strategy to maximize ti uddress the probability of a successful defense from the perspecti possible defender. Consider as well the perspective of the defender t e-do 2.1, 2.2, 2.3 from this perspective, then argue what the 'final me. re imagine that a successful attack on site i will cost the defender C average cost of an attack, given strategies {g.}, {p.}?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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