Concrete Mathematical Modeling Problem: Write down the system of equations describing the Rock-Paper-Scissors game dynamics and explain why the system looks the way it does. Numerically solve the system. Use initial conditions a) xR = 0.2, xP = 0.7, xS = (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

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Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "uYHSkhaIKd7Mcnn6IkrYSWIxROPM7Cv9yG4YAtmNMRY375LAIeSGq9u8NTtXl3zy"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "uYHSkhaIKd7Mcnn6IkrYSWIxROPM7Cv9yG4YAtmNMRY375LAIeSGq9u8NTtXl3zy"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "uYHSkhaIKd7Mcnn6IkrYSWIxROPM7Cv9yG4YAtmNMRY375LAIeSGq9u8NTtXl3zy", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    Concrete Mathematical Modeling Problem:
Write down the system of equations describing the Rock-Paper-Scissors game dynamics and explain why the system looks the way it does. Numerically solve the system. Use initial conditions a) xR = 0.2, xP = 0.7, xS =  (2024)

    FAQs

    How do you solve rock paper scissors game theory? ›

    Quite simple! If Player 2's strategy is Rock, Player 1 should choose Paper, but if Player 1 chooses Paper, it is profitable for Player 2 to deviate and choose Scissors instead. When player 2 chooses Scissors, Player 1 would want to deviate and choose Rock, and so forth.

    What is the theory of the game Rock Paper Scissors? ›

    Well, in theory, the game has 3 outcomes: a win, loss, or tie. Rock defeats scissors, scissors defeats paper, and paper defeats rock. Players who play Rock-Paper-Scissors have an equal probability of winning, assuming that both players choose options completely randomly.

    What is the methodology of rock paper scissors game? ›

    To play, find an opponent and stand facing each other with one hand flat in front of you and your other hand making a fist on your palm. Then, count down by saying “rock, paper, scissors, shoot!” On “shoot,” play either a rock, paper, or scissors with your hand. Whoever makes the winning item with their hand wins!

    Is the game of rock-paper-scissors mathematically a fair game? ›

    This means that mathematically, there is no best option when it comes to playing rock-paper-scissor. No matter how often you play rock-paper-scissors, if you randomly choose a strategy, there is a ⅓ chance that you win.

    What is the logic for rock-paper-scissors? ›

    A player who decides to play rock will beat another player who chooses scissors ("rock crushes scissors" or "breaks scissors" or sometimes "blunts scissors"), but will lose to one who has played paper ("paper covers rock"); a play of paper will lose to a play of scissors ("scissors cuts paper").

    What is the statistical analysis of rock-paper-scissors? ›

    On average, over 100 trials we found 31.8% selections of rock, 34.8% paper, 33.3% scissors, respectively.

    What is the result of the rock-paper-scissors game? ›

    If both players show the same sign, the round is a draw. If the players show different signs, this rule determines the winner: scissors wins over paper, paper wins over rock, and rock wins over scissors. Is there a strategy for winning the game? This table shows all possible combinations of signs in the game.

    What is the Nash equilibrium in the rock-paper-scissors game? ›

    The two players will then fall into a cycle of rock, then paper, then scissors. Thus, there is no equilibrium – it just doesn't make sense for one player to ALWAYS pick one choice for the whole game – it's just too predictable.

    What is the conclusion of the Rock Paper Scissors game? ›

    There are only three possible outcomes besides a tie: rock beats scissors, paper beats rock, and scissors beat paper. If both players make the same gesture, the game is tied and usually replayed to break the tie.

    What are the mechanics of Rock Paper Scissors game? ›

    The rock is a closed fist; paper is a flat hand with fingers and thumb extended and the palm facing downward; and scissors is a fist with the index and middle fingers fully extended toward the opposing player. Rock wins against scissors; paper wins against rock; and scissors wins against paper.

    What is the method to rock paper scissors? ›

    Switch up your own move after your opponent plays the same move twice; if they play rock twice, they may play paper next, so go for scissors. Look for physical signs that may indicate their move, like a tucked thumb for a rock or a loosened grip for paper. Since paper is used most often, try throwing rock instead.

    What is the objective of the game Rock Paper Scissors? ›

    * The object of Rock, Paper, Scissors is to win a match by making a shape with your hand that defeats your partner based on specific rules.

    Is there a strategy behind rock-paper-scissors? ›

    Therefore, this is the best way to win at rock-paper-scissors: if you lose the first round, switch to the thing that beats the thing your opponent just played. If you win, don't keep playing the same thing, but instead switch to the thing that would beat the thing that you just played.

    What is the dominant strategy in rock-paper-scissors game theory? ›

    There is no dominant strategy for either player, no Nash Equilibrium, and no mixed equilibrium. The average expected payoff for each player is zero, so the only strategy for either player is to choose rock, paper, or scissors randomly in hopes that their choice will be the right one.

    How do you score the rock-paper-scissors game? ›

    We determine the winner of the match by the following rules:
    1. Rock blunts Scissors (Rock wins over Scissors)
    2. Scissors cuts Paper (Scissor wins over Paper)
    3. Paper covers Rock (Paper wins over Rock)
    4. A tie results if both players choose the same option; in this case, players play another round to break the tie.

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