2023 MAT3172_The Mathematics of Games

CompetencyThis competency will allow you to demonstrate your ability to analyze discrete probability distributions and expected value.InstructionsYou have recently applied for an analyst position at GB Consulting and have been invited in for an interview. A part of the interview requirements for the job is presenting a thorough knowledge of probability and statistics. Some of your future potential coworkers are given the opportunity to interview you and wish to test your knowledge.What to SubmitTo complete this assignment, you must first download the word document .Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem not completed.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 2 – Binomial Distribution AnalysisCompetencyThis competency will allow you to demonstrate your ability and skill in applying counting principles and analyzing binomial distributions.InstructionsYou have just been hired by G&B consulting and given your first assignment. A local independently wealthy citizen who happens to enjoy both gambling and baseball, but not math, has asked you to help him determine the likelihood of some different outcomes for the upcoming season.What to SubmitTo complete this assignment, you must first download the word document .Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided. If you use Excel for any of your calculations that file must also be included in the drop box.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem not completed.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 3 – Nash Equilibria AnalysisCompetencyThis competency will allow you to demonstrate your ability and skill in applying concepts of Nash equilibrium.InstructionsA local law firm has hired G&B consulting to help determine a business strategy. There is a competing firm in the area and recently the two firms have begun talks in regards to a merger. The merger would mean there are more shared resources than either had before individually. There would also be less competition for both companies. Both would be able to operate more efficiently, however it would take a strong commitment from both sides for the merger to be successful. The law firm that has hired you wants to know their optimum strategy in this situation.What to SubmitTo complete this assignment, you must first download the word document. Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem not completed.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 4 – Optimal Strategy with Zero-Sum GameCompetencyThis competency will allow you to demonstrate your ability and skill in analyzing zero-sum games and synthesizing optimal strategies within them.InstructionsA night club owner has just changed ownership and the new owner has contracted G&B consulting to help decide the direction the club will take. Based on the local music scene, it would make the most sense to book either rock bands or country bands. The new owner is aware that a competing night club is hoping to attract new customers while the new club is getting itself established. Since these are the only two night clubs in town competing to book the same bands, whatever market share is gained by one is lost by the other making this a zero-sum game. The new club owner has hired you to find the optimum strategy for this situation.What to SubmitTo complete this assignment, you must first download the word document .Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem left blank.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 5 – Optimal Strategy with a Nonzero-Sum GameCompetencyThis competency will allow you to demonstrate your ability and skill in analyzing nonzero-sum games and synthesizing optimal strategies within them.InstructionsDuring the city’s mayoral race one of the candidates hires G&B Consulting. This candidate is a challenger from the same party as the incumbent mayor and is vying to be put on the ticket in the general election. She believes that the nomination will likely come down to what stance she takes on a proposed tax bill. The bill is for a tax increase that would subsidize education grants. Staying within traditional party lines would be advantageous to gaining support from the core constituency, but going against party lines on the issue would help sway swing voters and independents. The issue is bound to come up at an upcoming debate and she wants the help of G&B Consulting to determine an optimum strategy.InstructionsTo complete this assignment, you must first download the word document .Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem left blank.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 6 – Construct and Analyze a Game TreeCompetencyThis competency will allow you to demonstrate your ability and skill in analyzing nonzero-sum games and synthesizing optimal strategies within them.InstructionsA telecom company is considering upgrading their infrastructure in your city and they have hired G&B Consulting. The telecom company would be willing to invest in upgraded lines that offer higher speeds and bandwidth, but it is costly to do so and they are afraid they might make the investment but not have customers willing to upgrade their services which would be needed to recoup their profits. The alternative would be to keep the old infrastructure, but there are already a high amount of service complaints from the customer base. The telecom company needs to determine if investing in the improved service will pay off for them by having a sufficient amount of customers buy the upgraded service. You have been tasked with helping them determine their optimum strategy.What to SubmitTo complete this assignment, you must first download the word document .Your step-by-step breakdown of the problems, including explanations and all work shown, should be present within the PowerPoint you create. Do not submit the Word document with instructions.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem not completed.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.
Deliverable 7 – Presentation on Game Theory ApplicationsCompetencyThis competency will allow you to demonstrate your ability and skill in applying game theory to real world scenarios.InstructionsAfter working for 18 months in your analyst position at G&B Consulting, you are now being considered for a project manager position that would put you in charge of several team members. As part of the interview process, you have been asked to make a presentation to highlight what you think are the most compelling reasons you should get the position.You are to put together a PowerPoint presentation that explains all of the key components that you feel will factor into why you should get the position.What to SubmitTo complete this assignment, you must first download the word document. Use the questions on the worksheet as your guide for the contents of your presentation.Your step-by-step breakdown of the problems, including explanations and all work shown, should be present within the PowerPoint you create. If you use Excel for any of your calculations that file must also be included in the drop box. Do not submit the Word document with instructions.Grading RubricFFCBA01234No PassNo PassCompetenceProficiencyMasteryNot SubmittedDid not correctly solve a majority of the problems or at least one problem not completed.Correctly solved a majority of the problems.Correctly solved almost all the problems.All problems are solved correctly.Not SubmittedVery few steps are provided to explain how to solve the problem OR the steps provided have several errors.Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors.Mostly complete and detailed steps are provided to explain how to solve the problem.Complete and detailed steps are provided to explain how to solve the problem.Not SubmittedExplanations generally lack a basic understanding of the concepts or lack of proper terminology.Explanations demonstrate a basic understanding of most of the concepts and terminology, but some explanations may be incomplete or incorrect.Explanations demonstrate a proficient understanding of most of the concepts and terminology, but with small errors.Explanations demonstrate a mastery of understanding of the concepts and terminology.Not SubmittedThe majority of mathematical expressions and any graphs or tables are not properly formatted OR some are not present.The majority of mathematical expressions and any graphs or tables are properly formatted.Almost all mathematical expressions and any graphs or tables are properly formatted.All mathematical expressions and any graphs or tables are properly formatted.

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