Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich choos (2024)

Table of Contents
Question Video Answer Request a Custom Video Solution More Than Just Video Answers to Similar Questions More Solved Questions in Your Textbook NO COMMENTS YET

Rate your experience

Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (1)

Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (2) Bad

Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (3) Decent

Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (4) Love it!

Submit your feedback

Please review us on

Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (7)

Games of Strategy Avinash K. Dixit, Susan Skeath 2nd Edition

Chapter 3, Problem 10

`}function getSectionHTML(section, chapter_number){ if (section.has_questions){ const current_section_id = ''; const active_str = current_section_id == section.id ? 'active' : ''; return `

  • ${chapter_number}.${section.number} ${section.name}

    • ` } return '';}function getProblemHTML(problem, appendix){ var active_str = problem.active == true ? 'active' : '' return `

  • Problem ${problem.number}${appendix}

    • `}function getProblemsHTML(problems, section_id){ var output = ''; var abc = " ABCDEFGHIJKLMNOPQRSTUWXYZ".split(""); var idx = 0; var last_problem = 0; for (let i = 0; i < problems.length; i++) { if (section_id == 0){ var times = Math.floor(idx/25)+1; var appendix = abc[idx%25+1].repeat(times) }else{ var appendix = ''; } output += getProblemHTML(problems[i], appendix) if (last_problem != problems[i].number){ idx = 1; }else{ idx = idx + 1; } last_problem = problems[i].number } return output;}function getChaptersHTML(chapters){ var output = ''; for (let i = 0; i < chapters.length; i++) { output += getChapterHTML(chapters[i]) } return output;}function getSectionsHTML(section, chapter_number){ var output = ''; for (let i = 0; i < section.length; i++) { output += getSectionHTML(section[i], chapter_number) } return output;}$(function(){ $.ajax({ url: `/api/v1/chapters/`, data:{ book_id : '27602' }, method: 'GET', success: function(res){ $("#book-chapters").html(getChaptersHTML(res)); $(".collapsable-chapter-arrow").on('click',function(e){ var section = $(this).siblings(".section-container"); var chapter_id = $(this).data('chapter-id') var chapter_number = $(this).data('chapter-number') if(section.is(":visible")){ $(this).removeClass('open'); section.hide('slow'); }else{ $(this).addClass('open'); section.show('slow') if (section.children('li').length == 0){ $.ajax({ url: `/api/v1/sections/`, data:{ chapter_id : chapter_id }, method: 'GET', success: function(res){ section.html(getSectionsHTML(res, chapter_number)) $(".collapsable-section-arrow").off('click').on('click',function(e){ var problems = $(this).siblings(".problem-container"); if(problems.is(":visible")){ $(this).removeClass('open'); problems.hide('slow'); }else{ var section_id = $(this).data('section-id'); var question_id = $(this).data('current-problem'); $(this).addClass('open'); problems.show('slow') if (problems.children('li').length == 0){ $.ajax({ url: `/api/v1/section/problems/`, data:{ section_id : section_id, question_id: question_id }, method: 'GET', success: function(res){ problems.html(getProblemsHTML(res, section_id)) }, error: function(err){ console.log(err); } }); } } }); if(first_section_load){ $(".collapsable-arrow.open").siblings(".section-container").find(`.collapsable-section-arrow[data-section-id=${current_section}]`).click(); first_section_load = false; } }, error: function(err){ console.log(err); } }); } } }); if(current_chapter && first_chapter_load){ $(`.collapsable-chapter-arrow[data-chapter-id=${current_chapter}]`).click(); first_chapter_load = false; } }, error: function(err){ console.log(err); } }); });

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (9)

    Question

    Answered step-by-step

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is $x$ for Rich, $y$ for Kelly, and $1-x-$ $y$ for Rudy; similarly, the probability of winning when Rich chooses Give Up is $z$ for Kelly and $1-z$ for Rudy. Further, suppose that Rich's chance of being picked by the jury is $p$ if he has won immunity and has voted off Rudy; his chance of being picked is $q$ if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two.
    (a) What is the algebraic formula for the probability, in terms of $p, q, x$, and $y$, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information?
    (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( $p, q, x, y$ ) that summarize these two conditions.
    (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up.

    Video Answer

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (10) Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (11) Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (12)

    33 people are viewing now

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (13)

    Get the answer to your homework problem.

    Try Numerade free for 7 days

    Input your name and email to request the answer

    Numerade Educator

    Like

    Report

    Request a Custom Video Solution

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (14)

    We will assign your question to a Numerade educator to answer.

    Answer Delivery Time

    Est. 2-3 hours
    You are asking at 3:30PM Today

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is $x$ for Rich, $y$ for Kelly, and $1-x-$ $y$ for Rudy; similarly, the probability of winning when Rich chooses Give Up is $z$ for Kelly and $1-z$ for Rudy. Further, suppose that Rich's chance of being picked by the jury is $p$ if he has won immunity and has voted off Rudy; his chance of being picked is $q$ if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two.(a) What is the algebraic formula for the probability, in terms of $p, q, x$, and $y$, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information?(b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( $p, q, x, y$ ) that summarize these two conditions.(c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up.

    We’ll notify you at this email when your answer is ready.

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (15)

    More Than Just

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (16)

    We take learning seriously. So we developed a line of study tools to help students learn their way.

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (17)Ace Chat

    Your personal AI tutor, companion, and study partner. Available 24/7.

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (18)Ask Our Educators

    Ask unlimited questions and get video answers from our expert STEM educators.

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (19)Notes & Exams

    Millions of real past notes, study guides, and exams matched directly to your classes.

    Video Answers to Similar Questions

    Best Matched Videos Solved By Our Expert Educators

    More Solved Questions in Your Textbook

    Not your book?

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (20)

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (21)

    Games of Strategy

    Avinash K. Dixit, Susan Skeath 2nd Edition

    Chapter 3

    ​ Chapter 2

    ​ Chapter 3

    ​ Chapter 4

    ​ Chapter 5

    ​ Chapter 6

    ​ Chapter 12

    ​ Chapter 13

    ​ Chapter 14

    ​ Chapter 15

    ​ Chapter 16

    ​ Chapter 17

    ​ Chapter 18

    Sections

    Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10

    NO COMMENTS YET

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich chooses Continue is x for Rich, y for Kelly, and 1-x- y for Rudy; similarly, the probability of winning when Rich chooses Give Up is z for Kelly and 1-z for Rudy. Further, suppose that Rich's chance of being picked by the jury is p if he has won immunity and has voted off Rudy; his chance of being picked is q if Kelly has won immunity and has voted off Rudy. Continue to assume that, if Rudy wins immunity, he keeps Rich with probability 1 , and that Rudy wins the game with probability 1 if he ends up in the final two. (a) What is the algebraic formula for the probability, in terms of p, q, x, and y, that Rich wins the million dollars if he chooses Continue? What is the probability that he wins if he chooses Give Up? Can you determine Rich's optimal strategy with only this level of information? (b) The discussion in Section 3.7 suggests that Give Up is optimal for Rich as long as (i) Kelly is very likely to win the immunity challenge once Rich gives up and (ii) Rich wins the jury's final vote more often when Kelly has voted out Rudy than when Rich has done so. Write out expressions entailing the general probabilities ( p, q, x, y ) that summarize these two conditions. (c) Suppose that the two conditions from part b hold. Prove that Rich's optimal strategy is Give Up. | Numerade (22)

    Just now.

    Consider the Survivor game tree illustrated in Figure 3.9. Suppose that, unlike in Figure 3.9, you want to use only general values for the various probabilities. In particular, suppose that the probability of winning the immunity challenge when Rich choos (2024)
    Top Articles
    RIT and AT&T offer video game development camp for underrepresented students
    The Age from Melbourne, Victoria, Australia
    Declan Schuster's Hong Kong Selections and Analysis for Saturday, July 6, 2024
    Belmont Stakes Horse Racing Entries, Race Results, & More | DRF
    Parineeti 28th April 2024 Written Episode Update: Sanju insults Neeti for trying to harm Pari - Telly Updates
    Parineeti 28th May 2024 Written Episode Update: Pari finds out about an attack on her - Telly Updates
    Preise und Funktionen für Veranstalter
    Berlin, Deutschland: Events, Kalender und Tickets | Eventbrite
    Who Is Ficki Fiona
    What's In The Flu Shot, Anyway?
    Frequently Asked Questions
    Is Legacy a Real Credit Card? Truth about Financial Products
    Latest Posts
    Apple iPad Pro 11-inch (2024) - Send & Receive Messages - AT&T
    Malibu Kitchen, The Ned, London: restaurant review
    Article information

    Author: Rueben Jacobs

    Last Updated:

    Views: 6056

    Rating: 4.7 / 5 (77 voted)

    Reviews: 84% of readers found this page helpful

    Author information

    Name: Rueben Jacobs

    Birthday: 1999-03-14

    Address: 951 Caterina Walk, Schambergerside, CA 67667-0896

    Phone: +6881806848632

    Job: Internal Education Planner

    Hobby: Candle making, Cabaret, Poi, Gambling, Rock climbing, Wood carving, Computer programming

    Introduction: My name is Rueben Jacobs, I am a cooperative, beautiful, kind, comfortable, glamorous, open, magnificent person who loves writing and wants to share my knowledge and understanding with you.