Games Theory Essay Example for Free

Games Theory Essay In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute Nash equilibrium. Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phils decision, and Phil is making the best decision he can, taking into account Amys decision. Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best payoff for all the players involved; in many cases, all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium: e.g., competing businesses forming a cartel in order to increase their profits. The prisoners dilemma is a fundamental problem in game theory that demonstrates why two people might not cooperate even if it is in both their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the prisoners dilemma name (Poundstone, 1992). A classic example of the prisoners dilemma (PD) is presented as follows: Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full one-year sentence. If both remain silent, both prisoners are sentenced to only one month in jail for a minor charge. If each betrays the other, each receives a three-month sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? If we assume that each player cares only about minimizing his or her own time in jail, then the prisoners dilemma forms a non-zero-sum game in which two players may each either cooperate with or defect from (betray) the other player. In this game, as in most game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other players payoff. The unique equilibrium for this game is a Pareto-suboptimal solution, that is, rational choice leads the two players to both play defect, even though each players individual reward would be greater if they both played cooperatively. In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal. In the iterated prisoners dilemma, the game is played repeatedly. Thus each player has an opportunity to punish the other player for previous non-cooperative play. If the number of steps is known by both players in advance, economic theory says that the two players should defect again and again, no matter how many times the game is played. Only when the players play an indefinite or random number of times can cooperation be an equilibrium (technically a subgame perfect equilibrium), meaning that both players defecting always remains an equilibrium and there are many other equilibrium outcomes. In this case, the incentive to defect can be overcome by the threat of punishment. In casual usage, the label prisoners dilemma may be applied to situations not strictly matching the formal criteria of the classic or iterative games, for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation. Strategy for the classic prisoners dilemma The classical prisoners dilemma can be summarized thus: Prisoner B stays silent (cooperates) Prisoner B confesses (defects) Prisoner A stays silent (cooperates) Each serves 1 month Prisoner A: 1 year Prisoner B: goes free Prisoner A confesses (defects) Prisoner A: goes free Prisoner B: 1 year Each serves 3 months Imagine you are player A. If player B decides to stay silent about committing the crime then you are better off confessing, because then you will get off free. Similarly, if player B confesses then you will be better off confessing, since then you get a sentence of 3 months rather than a sentence of 1 year. From this point of view, regardless of what player B does, as player A you are better off confessing. One says that confessing (defecting) is the dominant strategy. As Prisoner A, you can accurately say, No matter what Prisoner B does, I personally am better off confessing than staying silent. Therefore, for my own sake, I should confess. However, if the other player acts similarly then you both confess and both get a worse sentence than you would have gotten by both staying silent. That is, the seemingly rational self-interested decisions lead to worse sentences—hence the seeming dilemma. In game theory, this demonstrates that in a non-zero-sum game a Nash equilibrium need not be a Pareto optimum. Although they are not permitted to communicate, if the prisoners trust each other then they can both rationally choose to remain silent, lessening the penalty for both of them. We can expose the skeleton of the game by stripping it of the prisoner framing device. The generalized form of the game has been used frequently in experimental economics. The following rules give a typical realization of the game. There are two players and a banker. Each player holds a set of two cards, one printed with the word Cooperate (as in, with each other), the other printed with Defect (the standard terminology for the game). Each player puts one card face-down in front of the banker. By laying them face down, the possibility of a player knowing the other players selection in advance is eliminated (although revealing ones move does not affect the dominance analysis[1]). At the end of the turn, the banker turns over both cards and gives out the payments accordingly. Given two players, red and blue: if the red player defects and the blue player cooperates, the red player gets the Temptation to Defect payoff of 5 points while the blue player receives the Suckers payoff of 0 points. If both cooperate they get the Reward for Mutual Cooperation payoff of 3 points each, while if they both defect they get the Punishment for Mutual Defection payoff of 1 point. The checker board payoff matrix showing the payoffs is given below. These point assignments are given arbitrarily for illustration. It is possible to generalize them, as follows: Canonical PD payoff matrix Cooperate Defect Cooperate R, R S, T Defect T, S P, PWhere T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Suckers payoff. To be defined as prisoners dilemma, the following inequalities must hold: T R P S This condition ensures that the equilibrium outcome is defection, but that cooperation Pareto dominates equilibrium play. In addition to the above condition, if the game is repeatedly played by two players, the following condition should be added.[2] 2 R T + S If that condition does not hold, then full cooperation is not necessarily Pareto optimal, as the players are collectively better off by having each player alternate between Cooperate and Defect. These rules were established by cognitive scientist Douglas Hofstadter and form the formal canonical description of a typical game of prisoners dilemma. A simple special case occurs when the advantage of defection over cooperation is independent of what the co-player does and cost of the co-players defection is independent of ones own action, i.e. T+S = P+R. The iterated prisoners dilemma If two players play prisoners dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoners dilemma. The iterated prisoners dilemma game is fundamental to certain theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modelled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoners dilemma has also been referred to as the Peace-War game. If the game is played exactly N times and both players know this, then it is always game theoretically optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to punish the player. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit. Unlike the standard prisoners dilemma, in the iterated prisoners dilemma the defection strategy is counterintuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoners dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one. For cooperation to emerge between game theoretic rational players, the total number of rounds N must be random, or at least unknown to the players. In this case always defect may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Nobel Prize winner Robert Aumann in his 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.

Amazon.com :: GCSE Business Marketing Coursework

Amazon.com In 1994, Jeffery Bezos noticed an important statistic about the Internet -- the fact that its usage was growing at 2300 percent a year. He was quick to become a part of such rapid growth; he began selling books on-line. He chose books over the vast number of products that could be sold on-line because of their volume. There were 1.5 million English-language books in print and 3 million books in all languages worldwide, while the largest physical bookstore in the world only carried 175,000 of the 1.5 million titles. Bezos made several decisions while starting his company; all of them seeming to be wise ones. For example, although it would seem unimportant for a virtual business, he was very selective in choosing a good location to start his business. He decided on Seattle: a place with lots of technical talent, near a large number of books; a nice place to live, and most importantly, it was in a small state -- to avoid customers having to pay sales tax due to the business’s presence in that state. Amazon.com was launched in July 1995. Sales picked up rapidly. By the end of 1996, its revenues reached $15.6 million, which was three times larger than the revenues of a large Barnes & Nobles superstore. The firm continued to expand and revenues continued to increase to a whopping $147 million in 1997. Despite the growth and huge revenues that Amazon.com made, the company still had net losses for 1996 and 1997. Bezos seems to have a good feel of the market. He has several services and functions that â€Å"cater† to the needs of the customers. His number one focus is customer service. Every decision, change, or acquisition that he makes is based, he claims, on making things better for the customer. After learning about Bezos technological and operational advances and efficiency, as well as his number one concern to satisfy the customer, one would wonder why his company is still experiencing loss year after year.

Scoliosis Research Paper

Karmin Extra Source Paper Scoliosis is a complex deformity or curvature of the spine and entire torso and has been recognized clinically for centuries (Asher, Marc A. ). â€Å"For a few of the patients an underlying cause can be determined, including congenital changes, secondary changes related to neuropathic or myopathic conditions, or later in life from degenerative spondylosis. However, the cause of most scoliosis is not known and since about 1922 such patients have been diagnosed as having idiopathic scoliosis (Asher, Marc A. ). Based on the observation of three distinct periods of climax, scoliosis has been sub-divided into three groups; infantile, before the age of 3; juvenile, age 5 to 8; and adolescent, age 10 until the end of growth. This categorization is now extensively used. â€Å"Eighty percent or more of idiopathic scoliosis is of the adolescent variety. As it is often not possible to determine the age of onset, age at presentation/detection is more accurate (Canaves e, Federico). † â€Å"The prevalence is very dependent on curve size cut-off point, decreasing from 4. 5% for curves of 6 degrees or more to only 0. 9% for curves of 21 ° or more. It is also very dependent on sex, being equal for curves of 6–10 ° but 5. 4 girls to 1 boy for curves of 21 ° or more (Asher, Marc A. ). † Adolescent idiopathic scoliosis can probably best be considered as a complex genetic trait disorder. There is often a positive family history but the pattern of inherited susceptibility is not clear. Current information suggests that there is genetic heterogeneity. This indicates that multiple potential factors are acting either dependently or independently in its pathogenesis (Asher, Marc A. ).Up to moderate deformities, recognized at a 40 degree curvature, bracing is the most common treatment. Brace treatment has been mainly simulated by directly applying external forces on the rib cage and on the lumbar spine. However, its ef? ciency in prev enting the progression of scoliotic deformities is still controversial and the biomechanics of brace treatment is still poorly understood. For instance, there is still no concurrence about the favorable design of a brace. The shape of the brace, the location of pads attached to the brace, and openings vary amongst orthotists (Clin, Julien).Nevertheless, brace treatment is favorable in comparison to no treatment at all. For example, the Scoliosis Research Society conducted a study in 1985 to scrutinize the correctness of the bracing treatment. â€Å"Patients of the same age, same curve pattern and severity were divided into two groups: one treated with bracing; and the other, untreated. Results published in 1993 demonstrated that brace treatment is effective compared to natural history (Canavese, Federico). † Studies conducted on the number of hours per day of brace-wearing show that the more hours per day the brace is worn, the better the result.The brace is usually prescribe d for fulltime wear with some time set aside for bathing, swimming, physical education and sport. The patient should be encouraged to be pursue sporting activities while continuing to wear the brace if possible. Contact sports are not allowed with the brace to protect other participants, as the brace can significantly injure another if contacted the right way. These activities generally represent an average of two to four hours a day to ensure that the brace is worn 21 to 23 hours daily (â€Å"Minimally Invasive†).Other treatments of scoliosis include surgical treatment to straighten the curve of the spine (Asher, Marc A. ). â€Å"Surgical treatment was initiated in 1914. When the results were evaluated in 1941 they were found to be poor. As a result of the untiring work of John Moe, Paul Harrington, and many others these results had considerably improved by 1962. Due to advances in surgery the number of scoliosis curves greater than 100 ° had dropped considerably by 1973. The indications for surgery as an adult are pain, appearance, and pulmonary problems, i. . shortness of breath. However, it is unusual for these symptoms to be severe enough to warrant surgery. In addition only those with surgery had pain management problems (Asher, Marc A. ). † Although there are some risks associated with surgery they have decreased substantially. Death is very unlikely but can occur, especially in patients operated as adults (Horn, Pamela). â€Å"Knowledge of the natural history of adolescent idiopathic scoliosis has expanded greatly in the last two decades.It has become clear that only about one in ten curves progresses to the point that treatment with bracing is warranted, and only one in 25, or 0. 1%, to the point that surgery is warranted. Bracing appears to prevent about 20% to 40% of appropriately braced curves from progressing 6 ° or more. Surgery, consisting of instrumentation and arthrodesis has virtually eliminated large thoracic curves. Altho ugh most patients are satisfied with their results, follow-up at 20+ years shows significant, clinically relevant decrease in function and increase in pain compared to controls.Re-operation is required in 6 to 29%. And, a very few have pain management problems (Asher, Marc A. ). † Works Cited Asher, Marc A. , and Douglas C. Burton. â€Å"Scoliosis. †Ã‚  Adolescent Idiopathic Scoliosis: Natural History and Long Term Treatment Effects  1 (2006): 1-10. Web. 23 Sept. 2012. Clin, Julien, Carl-Eric Aubin, Stefan Parent, and Hubert Labelle. â€Å"Biomechanical Modeling of Brace Treatment of Scoliosis. †Ã‚  Effects of Gravitational Loads  (2011): 743-53. International Federation for Medical and Biological Engineering 2011, 02 Feb. 2011. Web. 3 Sept. 2012. Canavese, Federico, and Andre Kaelin. â€Å"Adolescent Idiopathic Scoliosis: Indications and Efficacy of Nonoperative Treatment. † Indian Journal of Orthopaedics 45. 1 (2011): Academic Search Complete. Web. 2 3 Sept. 2012. â€Å"Minimally Invasive Scoliosis Surgery: An Innovative Technique In Patients With Adolescent Idiopathic Scoliosis. † Scoliosis (17487161) 6. 1 (2011): 16-25. Academic Search Complete. Web. 23 Sept. 2012. Horn, Pamela. â€Å"Scoliosis. † Clinician Reviews 22. 8 (2012): 16-22. Academic Search Complete. Web. 23 Sept. 2012.

My Career Coach Career For A Nonprofit Agency - 1695 Words

When we first started this course, I was not quite sure what leading organization change meant and what we would accomplish during this time together. Over the next two months, this course presented us with different resources about the process of developing a leadership philosophy regarding organizational change, plus integrating our own workplace organizational context with concepts of vocation, organizational culture, differentiation, and progress. My favorite thing about this course was the many ways I was able to apply what we learned to my vocation and our agency’s organizational culture. As this course comes to a close, I am impressed about all topics we were able to cover. I have identified the use of emotional triangles and the†¦show more content†¦Working for a nonprofit agency, I serve a diverse group of clients, but some come from low socioeconomic background, some our ex-offenders who have recently been released from jail, some military veterans, some are new graduates recently out of high school, or community college, or a four-year college. Part of my role is connecting individuals to resources in our community to help them cope with their situation. Helping families find access to food pantries, shelter, gas and bus fare, and childcare makes me realize the pivotal role I play in their lives. I am supposed to help break down obstacles for them as they progress down the career and financial path. Prior to Luther, vocation typically referred to a special calling to religious life, as a priest or as a member of a vowed order. The reference to kingdom is from the Lutheran idea that God governs the world through two different â€Å"kingdoms† or governances. The first is the kingdom of Christ while the second is the kingdom of the civil realm. God governs both, but in different way. Christian vocation is theology for living. It informs how we earn our daily bread and how we live our daily lives. It shapes our sense of identity and our relationships with others. Viewing my career more as a Christian vocation changes my whole outlook of my work. There is a constant reminder that my work is the work that god wants we me to do, and so your approach