Nash Arbitration Methods: Game Theory for students without calculus
William P. Fox
Naval Postgraduate School
Abstract
We illustrate a method to obtain the solution to Nash arbitration using only methods involving college algebra. A necessary component of the Nash arbitration is the status quo point which is usually the security levels found from the Prudential Strategies. We use linear programming to find these security levels using the SimplexLP of the Solver. We show how golden section search, used as an iterative numerical method with Excel, is used to find the solution value for the x coordinate of the Nash arbitration scheme. Then we show how we find the y coordinate using the equation developed from the Pareto optimal line. Having
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His interests include applied mathematics, optimization (linear and nonlinear), mathematical modeling, statistical models for medical research, game theory, and simulation models. He is currently the Past-President of the Military Application Society of INFORMS.
Introduction
We teach a course in decision making titled modeling in conflict. Our main topics in this course are applications and algorithms in decision theory and game theory. In our game theory course, we cover such main topics as utility theory, zero sum games & constant sum with their methods of solutions, non-zero sum games with Nash equilibriums and strategic moves, three person zero sum and non-zero sum games, and Nash arbitration scheme for bargaining. To somewhat complicate our teaching is that the course requirement is college algebra, not calculus. Our other main issue is that we are limited to the technology that we use. Currently that technology is Excel since Excel is the software that our students will have after graduation in the careers.
Our colleague, Frank Giordano, developed a geometric approach to Nash arbitration involving triangles, mid-points, and similar triangles to obtain both the arbitration point and how strategically to play the arbitration game. We found that often geometry is harder to extract from our students memories than the basic algebra concepts. We also wanted to give the students some technology using Excel to assist them in their efforts also
Johnny Cueto VS John Lackey...The first pitch was to the Giants. Strike one. Then a fly out to center field. That was mostly for the rest of he 2-3 innings, it was back and forth. But in the fourth inning, John Lackey got his first hit of his pitch. It was going, looking like it was going out but it dropped and it went straight to Jason Heyward. He had the ball but he dropped it and the Giants had a double for an error. For the rest of that inning, they had only scored one run on a base hit into right field.
Because the case is nondirected, there is ample opportunity for students to be creative in their solution approaches. Thus, it is impossible to provide a single solution here that is applicable to every student's work. As a starting point in evaluating students' solutions, we provide a solution that is based on the questions contained in online Case Questions section. It is important, however, to recognize that this solution is merely a starting point, and student work should be graded at least as much on the
This paper presents my reflections on the Negotiations: Strategy and practice coursework in the MBA program at Said Business School, University of Oxford. My paper will present various reflections on different themes of negotiation simulation undertaken by me during the course. This course has allowed investigating and reflecting on key drivers of negotiation techniques for me. I have learned that transparency and coalition are the core tenet of negotiation for me. For the purpose of this reflective exercise, I will conduct a comparative analysis of the process, dynamics and outcomes based on the themes such as negotiation styles, bargaining zones, power, emotion, coalitions, value claiming vs value creation etc. for the below-mentioned simulations:
Games can be very hard. States can be only observes to a certain extend. Multiple agents choose Actions, stochastic pays off and state transition depends on state and other
The negotiators in these situations should mainly on the integrative bargaining. It means that negotiator should arrange a face to face meeting for both the parties by motivating them to practice integrative barging so that they can use the conflict strategy management to innovate positive solutions rather than dysfunctional conflicts. The negotiator should focus mainly on problem solving, compromising, smoothing and finding solutions. Motivating both the parties for a face-to-face meet is done so that, they can identify the problem and resolve it by an open discussion. Each team should give up something so that they can come to an agreement. The negotiator should use smoothing technique by reducing the conflicts while stressing common interests between both the teams. By compromising and smoothing both the parties should know about their common interests and goals and should create a shared goal. Once the negotiator make them realize that they need each other for achieving their goals, integrative positions solutions will be obtained instead of dysfunctional
Because the case is nondirected, students have ample opportunity to be creative in their solution approaches. Thus, it is impossible to provide a single solution here that applies to every student’s work. As a starting point in evaluating students’ solutions, we provide a solution based on the questions in the online Case Questions section. However, this solution is merely a starting point, and student work should be graded at least as much on thought processes, assumptions used, creativity, and the ability to
Student G will have assignments broken into chunks so that she won’t get overwhelmed with a lengthy assignment. Since she enjoys playing on the computer implementing technology into the assignment will help engage her in assignments. Given the opportunity to use technology Student G will achieve in the classroom because she will be motivated and highly engaged. Assignments that promote choice and are of personal interest to her will also help her develop self-regulation skills which will allow her to operate freely in the classroom.
Dr. Chris Ahrendt has an educational background in both mathematics and computer science. His doctorate degree was earned through the University of Nebraska-Lincoln. This directed his interest in artificial intelligence and machine learning. Throughout the interview we learned more about Dr. Ahrendt’s practical experience and ability to tangibly connect mathematics
To Negotiate is a part of every day life, and in most cases is absolutely critical to your success. (book) There are a multitude of advantages and disadvantages towards specific approaches to conflict and negation. With several references to Stitt Feld Handy Negotiation Simulations I will discuss with you my initial understanding and experience of negotiation, prior to this class. I will also discuss my personal experience with the Stitt Feld Handy Negotiation Simulations, and how many of my initial views towards negation have altered since completing them. Based on this I will introduce my newfound understanding and plans for negotiating. I will conclude, by providing an overall evaluation of the negotiation module, specifically the negotiation simulations.
Prepare responses to the questions below after viewing the Negotiation Strategy and Tactics Tutorial in this week's lecture. In drafting your answers to the questions, make sure that you apply course concepts in your answers.
As litigation continues to be a time-wasting, costly, distracted, and unsatisfactory practice for dispute resolution, alternative dispute resolution increases in popularity, specifically, mediation and arbitration. Arbitration is a cost efficient substitute to litigation that is the yielding of a dispute to an impartial party in order to receive a final incumbent decision in the form of an award. Arbitration is sensitive, classified, and modeled to be a swift, and inexpensive solution to dispute. Participating parties may include additional terms in the agreement identifying arrangements to their agreements’ arbitration clauses to meet the requirements of their discrete dispute. In summation, arbitration is process that is private, speedy, cost efficient, and customized to the liking of the parties involved.
I fully agree with your post. I like how you stated that despite even though each party may not get all the things they want and request however, being willing to compromise is what is important to good-faith bargaining. Essentially, good-faith bargaining commonly refers to the duty of the parties to meet and negotiate at reasonable times with willingness to reach an agreement on matters within the range of representation; however, neither party is required to cop out or agree to any proposal.
Looking at the parties involved in the negotiation, it was clear that each party would have agendas that would be in conflict with each other. For instance, the other ports in the region would like the highest compensation possible while Harborco would like the lowest compensation. Additionally, each party would also have a minimum threshold score that they would need from each outcome before they would support the project. Therefore, it is clear that this is an integrative negotiation which requires joint problem solving to achieve
This area of math has a great impact on the army and their needs. The long term goals of the Army’s mathematical research program is to help the Army advance in areas such as materials, systems, testing, evaluation, acquisition, training, and logistics. Math is a major factor when it comes to modeling systems, evaluating and regulating complex developments, and designing and improving systems in the Army.