Game theory Essay Example for Free

Game theory Essay Game theory is a broad field of study that involves examining ways in which strategic decisions are derived. The study is applied in areas where strategic interactions among rational players produce outcomes with respect to the preferences of those players (Fudenberg Tirole 1991). Game theory is a branch of applied mathematics that is mostly used in the social sciences situations like, economics, psychology, political science, and philosophy. The theory is also used in other fields like, biology, engineering, political science, international relations and computer science. Game theory can be classified as; non-cooperative (or strategic) games and co-operative (or coalitional) games (Fernandez Bierman 1998). Non-cooperative games are involved with how intelligent individuals interact with one another in an effort to achieve their own goals. Co-operative games are where players co-operate in their moves (strategies) to achieve the desired common goals. ‘Strategic-form’ or ‘normal form’ games and ‘extensive form’ games. ‘Strategic form’ games are games where actions by players are taken simultaneously and order of the play is irrelevant to the game’s outcome. ‘Extensive form’ games are games where actions are taken by the players in a sequence and order of play is relevant to a games outcome. They are usually presented in a tree diagram. Symmetric and Asymmetric games; Asymmetric games are where the payoffs for playing a particular move depend only on the other player’s strategies. Symmetric game is where identities of the players can be changed without changing the payoff to the strategies. Zero-sum games and non-zero sum games; Zero-sum games are where the total benefits to all players add up to zero (Camerer 2003). In non-zero sum games, the total benefits do not necessarily adds up to zero. Discrete and continuous games; discrete games have finite number of players, moves, events and outcomes. Continuous games have infinite numbers. The basic elements of game theory are; an agent (an entity with preferences/options), game (All situations in which at least one agent can only act to maximize his utility through anticipating responses to his actions by one or more other agents), utility (amount of benefits/welfare an agent derives from occurrence of an event), payoff (an ordinal utility number assigned to a player at event of a certain outcome), outcome (an assignment of a set of payoffs, one to each player in the game), strategy (player’s plan on which action to take to achieved his/her desired payoff) and trees and matrices (ways of representing games that is based on order of play) (Fernandez Bierman 1998). Game theory is based on the following assumptions: Players in a game are able to make their own preferences i. e. they are free agents. Players are economically rational and they can, assess outcomes, calculate paths to outcomes and choose actions that they think will yield their preferred outcomes. Agents’ purpose is to maximize their utility. Game outcome depends on the actions taken by the players (Camerer 2003). Game theory has been used to explain in different fields to explain varied phenomena. In economics, game theory has been employed to explain business behaviors and economic conditions. Economic theories have embraced game theory in explaining and exhibiting certain economic behaviors. Economists have used other related theories in trying to understand rational interaction of strategic economic decisions that are made by people. These theories are closely linked to game theory and they include, decision theory, general equilibrium theory and mechanism design theory. Decision theory is a game theory of a single player against nature that focuses on preferences and the formation of beliefs (Fernandez Bierman 1998). The theory is used to demonstrate how best to acquire information before making a decision. Equilibrium theory is a branch of game theory that deals with trade and production and mostly with where there are relatively large number of individual consumers and producers (Fudenberg Tirole 1991). It is widely used in the macroeconomic analysis of broad based economic policies like monetary and fiscal policies, stock markets analysis, interest and exchange rates studies. Mechanism design theory is built on game theory but have special focus on the consequences of different types of rules (strategies). Example of a game theory is price game used by companies in a duopolistic market to increase their market share. In a duopoly market, two firms control the market and they use factors like prices, quality products and services, promotions, branding and promotion to compete over the market share (Samuelson 2008). When market share of one company increases, the other company’s share decreases. Firms in sectors that sells homogeneous products (e. g. energy sector), uses pricing strategy to win increase their market share. Taking example of two oil companies in a duopolistic market in current oil price surge, the companies are faced with problem of adjusting their prices upwards since this will adversely affect the demand of their oil products and thus reduce their revenues. Increase in crude oil prices has been experienced in the world, and oil and petroleum companies have to increase their retail prices upwards to realize earnings from their venture. Companies also have objective of increasing the volume of their sales, by increasing the market share of their products. Since petroleum companies trades homogeneous products, the main marketing tool to increase their market share is price. For two companies in a duopoly market, if one company increases its prices, and other maintains or even reduces, the former loses market share to the latter. Both companies face the following possibilities from their moves; reduction of market share of their products and hence their future revenues and profit or reduction in their profit margin or loss and hence shrink of their financial performance and growth in the future. Therefore each of the firms is faced with dilemma of which move to take in this situation of sharp increase in their raw materials. The two firms have the following strategic problem; to ensure profitability of their companies amid high cost of their sales, and pressure to maintain their prices at competitive price over their rivals in order to increase demand of their products. These are conflicting goals that management of each company must resolve by making strategic price decisions. Pricing strategies for the two firms are either to increase the price that would results to increase in revenue and retain its market share, reduce price which results to increase in market share of its products or maintain the price (Ibid 2008). Each company want to maximize its utility in the pricing moves i. e. to select a move that will see its market share maintained or increased and also ensure profitability of the company. Each strategy that the companies may take have implications on the other i. e. move by one firm affects the other firm. Example, in case of one firm decreasing its prices, this will affects negatively market share of the other as the demand of the former company’s product increases. Therefore, each company is expected to take choice that will result to its favor. Since the two firms are competing for success in their business, there is no cooperation expected while making this very important pricing choice. However, both firm being the only supplier in the market, they can cooperate and set their price mutually in a way that will ensure that no company will lose out to the other. Such arrangements are common in oligopolistic markets, where producers when faced by price pressure mutually agree to set their prices at the same level that will maintain the market share levels. In this game, each player (company) prefers to increase its market share over the other over maintaining the current market share. Therefore, they are taking conflicting moves to win over the other. The information about the available strategic choices is available to both firms. Both firms also know the current market share of their products and prices of the rival group. Each company has information about the strengths of the other company and knows how much they can support low prices in the price wars. They also know that the cost of crude oil has increased in the world market and that price was the tool to increase their revenues and growth. The only information both companies do not have is which choice their rival make and when. Companies will not make price changes at the same time; therefore the company that will make price changes after the other will have advantage over the other as it has prior information that is very important in making the pricing decisions. This game is an extensive game and the moves are in a sequence order. Therefore, timing of their moves is very important as it will give the second company advantage to make a well informed move. Using a hypothetical case, we take example of one company making first move and then the other follows. Using the game tool we can get the possible outcomes and solutions in an economic situation like ours. The payoffs assigned to each possible result indicate situations where a company can benefit (high payoffs) or lose out to the other competing company (low payoffs). Using a hypothetical example of oil companies BP Inc and Shell Plc as companies that operates in a monopolistic market, we can examine outcomes of pricing moves made by the two companies. The game can be used to give solutions to the price problem in a tight monopolisic market. The pricing game is based on the following assumptions: both BP Inc and Shell Plc are rational entities and in their moves their objectives are to increase their market share. Both firms make a sequential move on pricing that take extensive form (Fudenberg Tirole 1991). Shell Plc makes their decision after the BP Inc makes their pricing move. There is perfect market information symmetry (all company has all market information). Other factors that affect influence market share of the companies are constant. Strategies employed are price increment, price reduction or maintaining the price level. Payoffs (utility functions) for the moves are assigned as: Company that increases its market share over the other gets 5, company that losses its market share to the other gets -5. The payoffs represent the companies gain or loss in market share. The range for payoff is from -5 to 5, with both the lowest and the highest value representing the highest gain and the highest loss. The medium values represent an outcome of moderate change in the market share of the companies. The game can be represented in a tree diagram as follows: BP Inc P^ Pv PÂ ¦ Shell P^ Pv PÂ ¦ P^ Pv PÂ ¦ P^ Pv PÂ ¦ (0, 0) (-5, 5) (-2, 4) (5, -5) (3, 3) (4, 2) (4, 0) (2, 4) (2, 2) If BP Inc increases its prices ( P^) due to increased world crude oil prices, and shell Plc increases (P^) too the outcome will be (0, 0) i. e. their market share would not change but their sales may reduce due to decreased demand. If Shell Plc reduces (Pv) the prices after BP Inc has increased its prices, the pay offs are (-5, 5) i. e. BP Inc will loss its market share at a rate that is same as one Shell Plc will increase its market share. In the scenario that BP Inc will raise its prices and Shell maintains its prices (PÂ ¦), the payoffs are (-2, 4) i. e. market share for BP will reduce (Pv) but at low rate compared to Shell increment rate will be. On the other hand, if BP Inc reduces its prices first and then Shell raises its prices, the outcome will be (5, -5) i. e. market share for BP will increase at a rate that’s same as the one Shell Plc will lose its share. If both firms reduces their prices, the payoff is going to be (3, 3) i. e. their market share will not change but their sales will be better (higher revenue than if prices are higher). However, if BP reduces its prices but Shell maintains its price, the pay off will be (4, 2) i. e. BP’s market share will increase comparatively higher than Shell’s. In the last scenario, in case BP maintains its price level but Shell Plc increases its price the outcome payoff will be (4, 0) i. e. BP’s share will increase over Shell’s at relatively higher rate. But if BP maintains its prices and Shell reduces its prices, the pay off will be (2, 4) i. e. Shell Plc will increase its market share at a higher rate than BP Inc. In the last possible scenario, if both BP and Shell maintains their prices, the payoff will be (2, 2) i. e. there is not going to be changes in the market share, though both firms will have higher sales than if they raise their prices. The game theory provides the solution that the second (shell) should take a move to reduce its price, if BP increases as it will greatly increase its market share. Also it can get increased market share and profit if it maintains its prices, after BP increases its prices. To the company that makes the first move, the best solution is to maintain the price level as it will have higher payoffs without risking the move by the Shell. These options are the only one that will increase their market share and profitable growth. The price game theory can be used to understand economic changes in duopolistic markets. The game can be used in making strategic pricing and marketing decisions. The approach is important to economic theorists in describing the economic rationale that relates to commodity prices, demand and supply dynamics (Guala 2005). Despite the usefulness of game theory, there are some challenges to this theory. The assumptions on which the theory is based sometimes do not hold (Fernandez Bierman 1998). Game theorist assumption that players always act in a way to directly maximize their utility sometimes is violated by human behaviors i. e. in practice, human behavior often deviates from this model. This is because of the following factors that need to be considered; irrationality, new models of deliberation, and different motives (). In real life some people tend to respond irrationally in a situation where they are ideally expected to respond rationally. Also different people are motivated by different things and thus tend to respond differently in the same situation. To this end some theorists take game theory as tool for suggesting how people should respond but not as a tool to predict human behaviors and that game theory is used to explain strategic reasoning rather than strategic behaviors. Other limitations of the theory are based on the assumptions that prices changes are the only factors that will affect the demand of the oil products and consequently the market share. In real life there are rational factors that affect the market share of a product or a company. Quality of products and services, brand strength, promotions and other marketing strategies influences the demand of a product and its market share. Companies may also be motivated by other factors other than increasing market share when making pricing decisions. The theory also does not assign specific values to specify to what percentage a company gain or lose the market share. Since it’s an economic analysis it should give outcomes that can be easily understood and that make economic sense. However, the theory is very important in giving the general description of how individuals are expected to respond given a certain economic conditions. In the economic field the theory has been instrumental in explaining behaviors of firms and individuals’ producers and consumers. The theory is also very important in understanding how strategic decisions relate. Reference: Camerer, C. (2003). Behavioral Game Theory: Experiments in Strategic Interaction. Princeton: Princeton University Press Fernandez, L F. ; Bierman, H S. (1998), Game Theory with Economic Applications, Addison-Wesley Fudenberg, D. , and Tirole, J. (1991). Game Theory. Cambridge, MA: MIT Press Guala, F. (2005). The Methodology of Experimental Economics. Cambridge: Cambridge University Press Samuelson, L. (2005). Economic Theory and Experimental Economics. Journal of Economic Literature 43:65-107.

Physics of Springboard Diving :: Sport Swimming Swim Diving Diver Physics

The Hurdle Before a diver jumps off of a springboard, he does a sort of hop-skip step called a hurdle. After doing a few steps, the diver leaps up into the air with his arms raised. When he lands back down on the tip of the board, he swings his arms down past his legs and then up, leaping into the air and off of the board. The purpose of this hurdle is as follows: A diver cannot simply stand on the end of board, step off, and expect to have the power to go up or the momentum to rotate his body in any direction. What the hurdle does, is first to allow the diver to use the diving board as a slingshot, and second get as much energy as possible out of the "slingshot". This is achieved when the diver takes the first leap into the air with his arms raised. When he comes back down on the board, his own mass falling onto the board will apply a certain force. An additional force is added as the arms swing down at the same time with a greater acceleration, applying more force. At the bottom of the diving board's oscillation, all of the now stored potential energy is released. The diver swings his arms upward and begins to release his pressure on the board. The board pushes the diver up and into the air with a huge force. This force now can be used by the diver not only to go up, but to rotate and therefore perform various dives. The Dives and Application To do a front dive a diver pushes his hips upward just slightly as he leaves the board. After he had begun to go up into the air, he throws his arms downward just enough to make is upper torso rotate around his hips. At the peak of the dive, the diver tightens his stomach muscles and pulls his legs up towards the sky, leaving his body in a perfect upside-down position to enter the water head-first. In order to perform a front dive with a somersault, it requires a full flip of the body and therefore it takes a quicker rotation to cover such an angular distance. The diver takes off from the diving board with the same hip motion and arm swing as for a forward dive, but throws the arms further and makes a smaller "ball" in the air. Physics of Springboard Diving :: Sport Swimming Swim Diving Diver Physics The Hurdle Before a diver jumps off of a springboard, he does a sort of hop-skip step called a hurdle. After doing a few steps, the diver leaps up into the air with his arms raised. When he lands back down on the tip of the board, he swings his arms down past his legs and then up, leaping into the air and off of the board. The purpose of this hurdle is as follows: A diver cannot simply stand on the end of board, step off, and expect to have the power to go up or the momentum to rotate his body in any direction. What the hurdle does, is first to allow the diver to use the diving board as a slingshot, and second get as much energy as possible out of the "slingshot". This is achieved when the diver takes the first leap into the air with his arms raised. When he comes back down on the board, his own mass falling onto the board will apply a certain force. An additional force is added as the arms swing down at the same time with a greater acceleration, applying more force. At the bottom of the diving board's oscillation, all of the now stored potential energy is released. The diver swings his arms upward and begins to release his pressure on the board. The board pushes the diver up and into the air with a huge force. This force now can be used by the diver not only to go up, but to rotate and therefore perform various dives. The Dives and Application To do a front dive a diver pushes his hips upward just slightly as he leaves the board. After he had begun to go up into the air, he throws his arms downward just enough to make is upper torso rotate around his hips. At the peak of the dive, the diver tightens his stomach muscles and pulls his legs up towards the sky, leaving his body in a perfect upside-down position to enter the water head-first. In order to perform a front dive with a somersault, it requires a full flip of the body and therefore it takes a quicker rotation to cover such an angular distance. The diver takes off from the diving board with the same hip motion and arm swing as for a forward dive, but throws the arms further and makes a smaller "ball" in the air.

Catholic Church’s responses to Nazi antisemitism

Antisemitism refers to hatred or prejudice towards the Jews. The Nazi antisemitism started in 1933 and ended in 1945 marking a period of persecution and murder of Jews in Europe by the Nazis in Germany under Hitler's ruling regime (Poliakov, 8). Background information. Hatred against the Jews was prevalent in the modern era especially in the 19th and 20th century. This led to the origin of the word antisemitism which refers to the pogroms, violence and riots propelled by governments against the Jews (Falk, 10). Pogroms and violence against the Jews were initially instigated by false beliefs that the Jews were using blood from Christian children for their religious rituals. In the 19th century, the prejudice against the Jews intensified with the formation of antisemitic political parties in Germany, Austria and France. This marked the beginning of an international conspiracy against the Jews with the component of nationalism which treated Jews as disloyal and illegal citizens. In the late 19th century, a political party named as Voelkisch movement which comprised mainly of German philosophers promoted the notion that Jews were not a part of the Germandom. Eugenic theories based on racial anthropology helped to support this notion and from this pseudoscientific ideas, the Nazi party was founded in 1919. The Nazi party which was headed by Adolf Hitler helped to promote theories of racism and hatred towards the Jews which called for their removal out of Germany. In 1933, the Nazi party was elected to power and it immediately ordered for economic boycotts against the Jews with the introduction of anti-Jewish laws. In the beginning of 1935, the anti-Jewish laws called for a total separation between the Jews and the rest of the citizens thereby legalizing a hierarchy based purely on racism. In November 1938, antisemitic groups embarked on a mission to destroyed synagogues and business establishments owned by the Jews in Germany and Austria in what is now known as the Kristallnacht. This marked the beginning of an era of destruction and mass killing for the Jews. This period is known as Nazi antisemitism and it led to a holocaust which killed millions of Jews and destroyed many more (Learner, 128-134). The catholic church has in the past faced many rows over claims that it supported Hitler and the Nazis in the racial discrimination against the Jews (Doyle, 120). However, the Roman catholic has strongly denied these claims and in fact, it highly opposed such acts of hatred against the Jews. Though the church has admitted of having failed to do its best to end the war, it has evidently affirmed its opposing stand against Hitler's regime and acts of antisemitism. This paper seeks to establish the response of the catholic church towards the Nazi antisemitism. Biblical views on antisemitism. The bible and particularly the New Testament has been singled out as having strong hostility and antagonism towards the Jews. The Gospel of John has many antisemitic phrases and episodes which refer to the Jews in a derogatory way. In John 8: 37-40 is one such phrase where Jesus was speaking to the Pharisees of how the Jews were planning to persecute Him since they did not believe in what He spoke to them about God. The book of 1 Thessalonian 2:13-15 speaks of how Churches in Judea were suffering under the hands of those people people who persecuted Jesus. It also talks about how such acts by the Jews were displeasing to God and Christians. The New Testament also adds that while on trial, a Jewish guard struck Jesus on the face for uttering ill words against the Jewish high priest (John 18: 20). Moreover, the death of Jesus preceded by brutal mockery (Matt 27: 24-39) has been entirely blamed on the Jews who mocked and persecuted Him in life and on the cross. Some theology scholars have speculated that the unnamed people who mocked Jesus while on the cross were actually Jews and they have added that though Romans were the lead executors of the prosecution and crucification of Jesus, the Jews also played a great role in the events which led to His death. The chronological events which led to the death of Jesus as stated in the New Testament led to the anti-Judaism perception held by most Christians. After the death of Jesus, the New Testament indicates that the Jewish leaders living in Jerusalem became hostile towards the followers of Jesus forcing them to stop preaching the gospel or die. Stephen who was on of the Jesus disciples was stoned to death by the Jews for going against the Jewish laws and preaching the gospel of Jesus Christ. In Acts 7: 51-58 just before his persecution, Stephen spoke to the Jews in an antisemitic way referring to them as â€Å"stiff necked, uncircumcised and opposers of the Holy Spirit. † All this instances show how the New Testament which was primarily written by the Jews who became Jesus followers contains many antisemitic passages which led to an anti-Judaism perception in the early Christian churches. The Roman Catholic Church which is one of the early churches had also had the anti-Judaism belief which has led to its association with antisemitic acts in the Nazi antisemitism. Catholic church and Nazi antisemitism. Throughout the 19th and the 20th century, the Roman Catholic Church still held on strongly to many antisemitic beliefs and the notion that the Jews led to the death of Jesus as indicated in the New Testament despite efforts to distinguish between anti-Judaism and racially instigated antisemitism. However in the early 20th century, the Catholic church made a clear distinction between good and bad antisemitism to all its followers. According to Kertzer (pp. 2-25), the bad type of antisemitism was unchristian as it advocated for hatred and racial bias against the Jews due to their background while the good type of antisemitism only served to criticize the Jewish conspiracies which sought to control all sectors of the economy in Germany for selfish wealth accumulation. At this time, many catholic bishops wrote articles criticizing such acts but when accused of being antisemitic, the bishops argued that they were strongly against any acts of hatred o r destruction plotted against the Jews. The church's response to Nazi antisemitism. Catholic church and the Christian community as a whole strongly despised the Nazi antisemitism. Kain in his popular book entitled Europe: Versailles to War-saw explains that the Nazis acts towards the Jews greatly offended Christians and led to protests by German army chaplains to Hitler in 1937 warning him of a future war in Germany due to his ungodly acts. The opposition by the catholic church response towards the Nazi antisemitism was quite straight-forward and emphatic. Catholic clergy was one of the first people who stood firmly to declare opposition towards the Nazis despite threats of persecution. Several Christians also stood firmly to oppose the Nazi antisemitism. For instance, Stauffenberg who was a devout catholic plotted Hitler's assassination in 1944 to depict his strong faith and opposition against the Jews' persecutions and killings. Stauffenberg was later killed by the Nazis after the attempts to assassinate Hitler failed. The catholic church believes on the Christian view of man made in the image and likeness of God and for this reason, every human being deserves enormous dignity regardless of race, state or background. According to Macrobio a professor at the Regina Pontifical University, Pope Pius XIII who was the leader of the Roman Catholic Church during the period of Nazi antisemitism was strongly opposed to the antisemitism and eugenic theories imposed against the Jews. A decree released by the Holy office in December 1940 by the Pope clearly condemned the killings and the racial laws put forward by Hitler and the Nazi party against the Jews. The decree stated that such killings were wrong and ungodly since they went against the natural law and all the divine precepts as defined by the Holy Bible. Throughout the war, Pius XII kept on pleading privately for a stop on the continued killings on behalf of the Jews and even after the war, he still condemned the Nazi antisemitism. In 1946 when speaking to a group of delegates in Palestine, the Pope affirmed the Church's stand on its opposition towards the persecutions carried out by Hitler and the Nazis against the Jews with no apologies. Why the church opposed Nazi antisemitism and eugenic theories. Eugenic theories are aimed at imposing discrimination to a certain group of people. For the catholic church, all men are equal in the eyes of God since humanity is not defined by neither external capabilities such as beauty nor internal characteristics such as knowledge. Every one be it a saint or a sinner is believed to be a son of God and only the father can judge whom to punish for their sins and whom to bless. Due to this fact, its wrong for the church to support the eugenic theories and antisemitic acts which seem to favor some individuals or racial groups over others. The catholic church further believes that discrimination of any kind is ungodly and unlawful regardless of whether it occurs in form of verbal racism or holocaust as in the case of the Nazi antisemitism as long as it threatens man's dignity and the church has an ultimate responsibility to oppose it by all means. Conclusion. The Pope's reactions towards the holocaust were quite complex but one clear indication is that the catholic church was against these antisemitism acts and it strongly condemned them (Schoenberg, 2). At times the Pope acted privately with attempts to help the Jews in their escapes out of Germany and he succeeded but on most occasions, the church just chose to remain quiet on issues surrounding the war with the aim of appealing neutral. The reason which might have led to continued silence by the Pope and the catholic church during the holocaust has been attributed to fear of Nazi reprisals, the notion that public speech would have had no significant effect on the war or the feeling that such speeches were likely to harm the Jews more. However, sources have shown that though the church did not directly support Nazi antisemitism, catholic anti-Judaism played a great role in fostering this hatred against the Jews. The false assumptions that most of the Nazis who participated in the killings and destruction of the Jews were Christians are unfounded and have no empirical evidence to support them. In conclusion, it can be said that the catholic church was strongly against the Nazi antisemitism but just like all other positions of power, there is still more that the church could have done to stop this war against the Jews.

This Community Base Spiral Texture Wall Was Design By Tara...

Our Lives Yesterday and Today This community base spiral texture wall was design by (Tara Cady Sartorius, 2006) and sponsored by the Central Alabama Community Foundation. The spiral texture title is a wonderful piece of work that represents the expressions of more than 700 artists containing more than 1000 textured titles using different kinds of material. I find this art to be abstract art, because this art stresses elements of composition, rather than a subject. This body of work was designed with undefined proportions and great balance. This piece of art has artistic element of color, line, shape, form, and texture. The spiral was added to give tone and balance to the art and provide a smooth separation of colors. These are some of thing that immediately drawls the viewer to the bodywork. The work is a colorful representation of the past as well as the future showing all aspects of life. There was no detail information on this collage of title work other than the name, but it spoke to me and I had to share th is with the class. If you didn’t know anything about art, this work would get your attention and show you the past and take you forward into today. The complimentary colors used in this display has a smooth earthly tone, but as you view the artwork it has a very pleasant, comforting feel as you view the mellow soft colors displayed in this design. This type of work has vivid elements, it really get your