{"id":212608,"date":"2025-05-07T09:53:31","date_gmt":"2025-05-07T09:53:31","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=212608"},"modified":"2025-05-07T09:59:57","modified_gmt":"2025-05-07T09:59:57","slug":"consider-the-following-parthe-correct-answer-and-explanation-is","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/07\/consider-the-following-parthe-correct-answer-and-explanation-is\/","title":{"rendered":"Consider the following parThe Correct Answer and Explanation is"},"content":{"rendered":"\n

Consider the following parThe Correct Answer and Explanation is:. Each player beginswith three chips: one red, one white, and one blue. Each chip can be used only once. Tobegin, each player selects one of her chips and places it on the table, concealed. Both playersthen uncover the chips and determine the payoff to the winning player. In particular, if bothplayers play the same kind of chip, it is a draw; otherwise, the following table indicates thewinner and how much she receives from the other player. Next, each player selects one of hertwo remaining chips and repeats the procedure, resulting in another payoff according to thefollowing table. Finally, each player plays her one remaining chip, resulting in the third andfinal payoff.<\/p>\n\n\n\n

The Correct Answer and Explanation is<\/mark><\/strong>:<\/p>\n\n\n\n

To answer the question, we need to understand the game mechanics and the payoff structure. While you referenced a “table” indicating the winner and payoff, you didn’t provide that specific table. However, based on classic versions of this type of game (often inspired by Rock-Paper-Scissors<\/strong> mechanics but with colors or objects), a likely structure for the payoff could be:<\/p>\n\n\n\n

Assumed Payoff Table:<\/h3>\n\n\n\n
<\/th>Red wins over<\/th>White wins over<\/th>Blue wins over<\/th><\/tr><\/thead>
Red<\/td>Blue<\/td>(loses to White)<\/td>(loses to White)<\/td><\/tr>
White<\/td>Red<\/td>(loses to Blue)<\/td>(loses to Blue)<\/td><\/tr>
Blue<\/td>White<\/td>(loses to Red)<\/td>(loses to Red)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Each win may result in a payoff of +1 to the winner and -1 to the loser, while draws give 0.<\/p>\n\n\n\n

Key Assumptions:<\/h3>\n\n\n\n
    \n
  • Each player has exactly one of each chip: red, white, blue.<\/li>\n\n\n\n
  • Players choose their chip in secret each round.<\/li>\n\n\n\n
  • The same chip results in a draw.<\/li>\n\n\n\n
  • There are 3 rounds; each chip is used exactly once.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Strategic Analysis:<\/h3>\n\n\n\n

    This game is a zero-sum<\/strong>, non-cooperative<\/strong>, and sequential<\/strong> game with perfect information<\/strong> about previous outcomes (if observed), but simultaneous moves<\/strong> each round.<\/p>\n\n\n\n

    Since players must use each chip exactly once, the game becomes one of ordering<\/strong>. There are 6 possible orders to play the 3 chips (3! = 6 permutations). Hence, each player has 6 strategies.<\/p>\n\n\n\n

    The optimal strategy depends on predicting the opponent\u2019s order<\/strong>. Because of symmetry, there is no dominant strategy<\/strong>. Thus, the best option is to randomize<\/strong> the play order\u2014choosing uniformly at random from the six permutations. This approach ensures fairness and prevents exploitation, as any deterministic pattern can be anticipated.<\/p>\n\n\n\n

    Therefore, the game has a mixed-strategy equilibrium<\/strong>, where each player randomizes their chip order with equal probability. Over time, this strategy evens out payoffs, assuming rational players.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Consider the following parThe Correct Answer and Explanation is:. Each player beginswith three chips: one red, one white, and one blue. Each chip can be used only once. Tobegin, each player selects one of her chips and places it on the table, concealed. Both playersthen uncover the chips and determine the payoff to the winning […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-212608","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212608","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=212608"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212608\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=212608"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=212608"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=212608"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}