roblem 2: Strategic Defense 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 p, 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 {q.}, {p:}?? 2) If you knew {41,-...qN} in advance, how should you choose {p:} to maximize the probability you successfully prevent an attack? 3) If you are the attacker, and you know that the defender is going to choose the best strategy they can to maximize the probability of preventing an attack, how should you choose your strategy to maximize the probability of a successful attack? 4) Questions 2.1, 2.2, 2.3 address the probability of a successful defense from the perspective of the attacker thinking about the best possible defender. Consider as well the perspective of the defender thinking about the best possible attacker. Re-do 2.1, 2.2, 2.3 from this perspective, then argue what the 'final' strategies for each player will be in this game. the quest that follow we imag cesvful attack site i will cost the defende
roblem 2: Strategic Defense 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 p, 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 {q.}, {p:}?? 2) If you knew {41,-...qN} in advance, how should you choose {p:} to maximize the probability you successfully prevent an attack? 3) If you are the attacker, and you know that the defender is going to choose the best strategy they can to maximize the probability of preventing an attack, how should you choose your strategy to maximize the probability of a successful attack? 4) Questions 2.1, 2.2, 2.3 address the probability of a successful defense from the perspective of the attacker thinking about the best possible defender. Consider as well the perspective of the defender thinking about the best possible attacker. Re-do 2.1, 2.2, 2.3 from this perspective, then argue what the 'final' strategies for each player will be in this game. the quest that follow we imag cesvful attack site i will cost the defende
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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