Nash Equilibrium and Game Theory - Essay Example

?Nash equilibrium and game theory By: ID Email Address Location Exercutive summary This paper gives the relevance and the applications of the concepts of game theory to the real world. The concept of game theory that the paper would focus on is the Nash equilibrium. Nash equilibrium has several application in the real world, especially in the economic world. Therefore, the paper would relate the applications of the game theory in real world economic scenarios. When relating the ideas, there will be limitations and advantage of relying on the answer for decision making. On e would be able to find out the importance and demerit of using Nash equilibrium in the real world. Introduction Game theory refers to the study of the techniques of decision making. The study gives calculated methods of giving a strategic decision in an economic issue. It puts related disciplines of philosophy, mathematics and psychology in making strategic decision making. Since its invention in 1944 by John von Neumann and Oskar Morgenstern, it has undergone severall improvement and applications. The Nash equilibrium is a concept in game theory that gives solutions to games that involves more than one player. In Nash equilibrium, every player makes the best decision considering that the opponent would make their own best decision too. Jon Nash realized that one has no capabilities to tell and predict others’ decisions by only viewing one case. Isolation prevents proper analysis of decisions. In addition, every player knows that there is nothing to gain by changing their strategy. Therefore, the only option left for a player is to get know what one player would do by considering the others’ decisions in the process. Game theory uses the concepts of Nash equilibrium when making an analysis of strategic interaction that occurs between the decision makers. Throughout history, Nash’s equilibrium concept has been useful with practical application in times of war and arms races. Some of the practical applications of Nash equilibrium include; mitigation of members in conflict by use of repeated interactions, determining the point in which people of different preferences may agree to cooperate, occurrence of currency crises, the flow of traffic on busy roads, setting up regulatory regulations and during soccer when kicking penalties (Myerson 2013, p56). In Nash equilibrium, everybody gets involved in a game the moment their fate is a point where the decision depends on the other person playing the game. The game does not have all the practical conditions that exist in the real world. Some of the unrealistic assumption that the game assumes are as follows; the concepts operate in the assumption that the players possess powerful computing techniques, through which, they analyze every situation giving no chance to any faults. Human beings operate under situations that may involve a lot of unforeseen situations. Thus, humans are prone to making incorrect decisions during the period. In addition, the concepts call for radical decisions that raise a lot of questions (Zhao 2007, p89). Another unrealistic nature is that it gives either the optimum or a value at equilibrium. It does not give a true value. In pratically, the scenarios are true and would require two choices giving true results. That is; the results of the prisoner’s dilemma are not as optimum as the theory tends to show. In some of the cases, the concept could be unreliable and misleading the practical user. However, such cases are limited since the Nash equilibrium has registered many instances of positive feedback. Nash equilibrium sets up a base in which other theories and practical scenarios can base their applications for success in the real world (Zhao 2007, p77). Conditions that exist in the real world seem to be more complicated that in examples. For example, if an event that two competing companies set their market price at say, $10, one company would attempt to set a slightly lower price to increase its sales, as long as the other competing company remains to sell at $10. The companies would play the same game until they reach a point where they do not change their prices any more. If at this point, their prices are the same, they would have reached a Nash equilibrium. However, in the practical perspective, it would be hard for one company to be sure of a conclusion that a change in the product’s market price would result to a positive change in total profits. In addition, when making practical decisions, other conditions such as the market could have more than two competing companies, the market could be at an overlapping position, and the competing products could be similar and not identical (Srinivasan 2010, p12). The prisoners’s dilemma is a practical application of Nash equilibrium. The example uses the concepts to explain the reasons why prisoners would not cooperate even if it would be to their advantage. In the example, the two prisoners had an opportunity to either betray one another or cooperate between them to see them get a lesser charge than before. However, the prisoners are self-interested and would, therefore, go for a decision that would only benefit themselves. In the end the prisoners opt to betray each other due to lack of trust. This model is important in assessing human cooperative behavior. In addition, it would be useful when dealing with situations in real world that involves two entities with a potential of gaining more from cooperating and to suffer otherwise, but instead find it difficult to go through, because of personal reasons (Srinivasan 2010, p08). The dilemma presented shows a notion that humans would tend to carry out selfish moves in times of desperation. However, selfish moves are not the best moves to balance the odds in a business environment. Sometimes cooperation between competing companies would land each company a better deal than the one where by one loses. In economics, the prisoner’s dilemma is practical during advertising products. When competing firms advertise at the same time, it cancels out automatically. This is because, one firm’s maximum advertisement, depends on the other firm’s intensity. In practical scenario, the companies would benefit more when each agrees to advertise below the equilibrium level. Tit for that strategy is one of the game theory concepts that is valuable in real life scenarios. Practicaly, one using this strategy would cooperate in the beginning and then follow the opponet’s previous move. The strategy is rather risky as it tends to rely on judgements made on the opponent. A slight mistake when making the decisions would lead to complete turn of events leading to bad results.Despite this; tit for that has grown popular in real life application. Common use of the strategy is when peers bitTorrent to increase their downloading speed. During the search of a cooperating peer, the system in the ap would allow a previously uncooperating peers to have another opportunity to cooperate. In the second world war, this strategy ensured the end of the war. Since one side expected the other to retaliate in the same war, the strategy brought a change in the war events, in terms of retaliation. Economically, this strategy is quite useful in the market during intense completion between two firms (Myerson 2013, p14). The concepts of Wardrop’s principles are very similar to the concepts of Nash equilibrium. Therefore, the principles are an application of the Nash equilibrium in the real world. The difference is that the transportation networks makes the analysis more complicated and difficult. The first principle uses the concepts to show that all road users would ensure that they follow the ir best route to any destination. As such the principle states that the number of times a vehicle would follow in a journey, would be equivalent or slightly below the number of journey times that a single car would use when following the unused routes to the same destination. The second principle shows that each road user cooperatively behave to ensure that he follows best routes to the destination. Practically this concept could be used to control he flow of traffic and designing of roads to easen flow (Carmona 2013, p39). The auction theory is an economics concepts that embrace Nash equilibrium concepts. The auction model would show strategies that the players employ during the game. In the real world, the players are buyers and sellers in a market place. The bids that the players make would represent the buyer’s value or the seller’s cost. The profits that the players would get represents the resulting profits made by each player. Practically, this concept would be useful in auction business. Such concepts would ensure that the company realizes desired profits out of the business (Daskalakis 2008, p18). Conclusion As stated above, the Nash equilibrium as a concept in game theory has a variety of applications in the real world. Major applications are in the economics field. In economics field, te players would represent the forces of supply and demand that tend to outplay one another to achieve their maximum potential. The concepts have application in areas that involves two or more players. In addition, the complexity of the application would depend on the number of the players in the practical environment. That is; as the number of participants increase, computing becomes complicated making analysis difficult. The same is true for the reverse scenario. The Nash equilibrium may not perform as predicted during a practical scenario. This is because the theory has a number of assumptions that would only operate in a computer environment and fail terribly in the real world. In such cases, the player should make a decision while having such scenarios on mind. Areas in economics that uses the concept extensively is in marketing and dealing with competition. In marketing, companies would try to dominate the market by advertising their products. As explained earlier, the Nash equilibrium would balance the odds and put each company at the same level in the market, limiting foul play. Balancing the forces of demand and supply is a major illustration of Nash equilibrium. Bibliography Carmona, Guilherme. Existence and Stability of Nash Equilibrium. Chicago: World Scientific, 2013. Daskalakis; Konstantinos. The Complexity of Nash Equilibria. New York: ProQuest, 2008. Myerson, Roger B. Game Theory: Analysis of Conflict. New York: Harvard University Press, 2013. Srinivasan, Dipti. Innovations in Multi-Agent Systems and Application – 1. Chicago: Springer, 2010. Zhao, Jinye. Recent Applications of Nash Equilibria. New York: ProQuest, 2007. Read More