Game Theory: Application & Analysis, Term Paper Example

Introduction

Game theory has long been a concept in which was used to analyze several problems in order of obtaining a viable solution. Game theory utilizes itself to applications and perspectives, which do no question the expectations underlying existing institutions or structures in society. Game theory’s selective usefulness concepts are largely reflected in the actual applications and uses of the theory. While mostly used in Economics, game theory concept are used cohesively with real world problems and applications. Game theory has been researched to proved that it can be applied in several non-scientific influences, intellectual, social, economic, and political. More importantly as Brian Martin shares, “there are also studies which show that scientific knowledge (often that produced under the influences of such non-scientific factors) can selectively lend itself to certain practical or ideological uses.” (Martin, 1978) Game theory is a formative tool that is used in several diverse fields in which they are several individual agents. More fundamentally, the approach to victory in game theory is in process of decision-making, which is guided by the deduction of the strategy of the opponents, and the correct and corresponding strategy. This paper will not only provide the fundamental applications in which game theory has been known to be applied to, but also in real world applications in which many would not think it can be applied. Divided into two parts, this paper explains the elements of game theory, as well as the type of games, and then will explore how relevant it is to real world situations.

Game Theory Part I

Game theory is a formal study of cooperation and conflict. The concepts of game theory apply to the independent actions of several agents, in which they can be firms, group, or individuals. Game theory concepts offer a language to comprehend strategic scenarios, as well as analyze, and formulate structure. Game theory’s object is the game which is provides a model of interactive situation in which consists of multiple players. The concept of game theory how strategic situations deal with people’s behavior. The actions of one player influence the well-being of the other player. Game theory arises from competitive scenario analysis, in which tells the players how to behave within the game to provide the best results.

The Elements of Game Theory

In breaking down the elements of game theory in a brief review. Game theory is adequately defined as, “Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents.” (Ross, 2014)

• Rules of the game: What can the players do? Where do the players move and when>
• Players: different types of individuals that make the decisions
• Information: What is known when decisions are made?
• Chance: if any probability over chance events?
• Payoffs: The player’s outcomes compared to their preferences.
• Outcomes: What is produce from the various combinations of actions?

Game theory has been known exclusively to logical and mathematical framework. Game theory stretches back as far as ancient Greece, with Plato and Socrates describing the Battle of Delium. (Ross, 2014) In providing an example that mirrors that of battle in which game theory has been applied, we can look at the battlefield. Consider a trooper at the front, holding up with his friends to shock a foe assault. It may jump out at him that if the guard is liable to be fruitful, then it is not extremely plausible that his own particular individual commitment will be fundamental. However, in the event that he stays, he runs the danger of being executed or injured evidently for no point. Then again, if the adversary is going to win the fight, then his shots of death or damage are higher still and now unmistakably to in any case will be overpowered. In light of this thinking, little doubt remains that the officer is in an ideal situation fleeing paying little respect to who is going to win the fight. Apparently, if the majority of the troopers reason thusly as they all evidently ought to, since they’re all in indistinguishable circumstances then this will positively achieve the result in which the fight is lost. Obviously, this point, since it has struck us as examiners, can jump out at the troopers as well. Does this provide for them a purpose behind staying at their posts? Simply the opposite: the more prominent the troopers’ apprehension that the fight will be lost, the more noteworthy their impetus to get themselves out of hurt’s way.

Furthermore, the more prominent the officers’ conviction that the fight will be won, without the need for any specific singular’s commitments, the less reason they need to stay and battle. On the off chance that each one officer envisions this kind of thinking from the others, all will rapidly reason themselves into a frenzy, and their stunned leader will have a defeat staring him in the face before the foe has discharged a shot. Game theory has been used throughout time in which analyst use the concept to apply to situations in which they confront situations, in which their best action is dependent on the assumptions of how the other player will be have, and the other player’s best action is dependent on the assumptions of the former player.

Types of Game of Theory Dilemmas

Game theory ca be broken down further in order to demonstrate the strategy of equilibrium for two-person and zero sum games. In using both the simultaneous and sequential types of games, Nash’s equilibrium, the Prison’s dilemma, and the dominant strategy are depicted primarily. There are several types of games played in the concept of game theory. The two primary ways in which represent game theory are extensive form and normal (strategic) form. Strategic form is shown primarily by a matrix or grid. Within this game, the players each have a choice to not compromise or to compromise. On the left hand side of the matrix/grid they first player is given the two choices. Across the top, the second player is given the two choices. When the first and the second player choose the same choice, then it is represented in the grid in which their choices intersect, in which is depicted in the integers. If one does not compromise then it was written as negative and positive integer. The player that chooses not to compromise will get a better result and will do better. The game is symmetrical in what the other player does not do, will get a different result. If both players choose not to compromise then they receive an integer of (-10, -10) in which they both lose, as they both do not choose to back down. This provides further analysis and solution for finding equilibrium.

In looking at the extensive form of game theory, it is depicted as a labeled picture, or played on trees, that much resemble a decision tree. Time sequencing of moves are used in formalizing the extensive form. For the choice of the player, each node or vertex is used. Listed on the vertex is the each player, and the lines of the tree represent the player’s possible actions, and at the bottom of the tree show the payoffs. This is seen primarily as a way in which sequential games are represented in which the choices made by the players at different times. Additionally this the type of games in which several decisions can be made by each player. A cooperative or coalitional game is a description that is high-level that specifies each coalition or group’s potential payoff, that members can obtain by cooperation. This can be viewed as a political example in which primarily two parties divide members of the government. Each party has their own strengths and weaknesses, however if they are cooperative in their behavior through the process of consensus decision making, they can enforce their parties influence.

Game theory is used strategically in trying to find equilibrium. In looking at game theory and equilibrium, we can look to economics that discusses the money market. “Under the appropriate conditions on preferences and production, it has been provided that a price system that clears the market will exist, provided that each individual acts as an independent maximizer.” (Shubik, 1968) These can be seen as phenomenon in which sees the invisible hand that creates a competitive market or equilibrium. The number of people in the market or game, the maximum output is the largest. Now looking at how game theory is used in Nash’s Equilibrium, it can be viewed in which the solution consists of two or more players. The players each assume to know the other player’s equilibrium strategies, and by using their own strategy unilaterally have nothing to gain.

In game theory there can be more than one Nash Equilibrium, it is used primarily to examine the outcome of several decision makes strategic interaction. According to analysts, “A pure strategy in this repeated game is a plan that prescribes which action is to be taken at each stage, contingent on every possible history of the game to that point.” (Campbell, Miller 2007) It offers a way of prediction the actions of several institutions or people that make a decision at the same time. The decisions of others provides the outcomes. Used in a real world example, Donny and Betty are in Nash Equilibrium if Donny makes the best decision, taking into account the decision of Betty. Betty will make the best decision she can in account of the decision of Donny. This strategy of game theory has been used in analyzing armed races, wars, and used in the prisoner’s dilemma.

The prisoner’s dilemma, an example of both the game theory and Nash Equilibrium, the two criminals are arrested and separately interrogated. Each criminal has a choice to refuse to talk or to confess. For the suspects, the police do not have any substantial evidence, so they try to one to confess. If they both choose to confess, they will receive minor sentences for up to one month of jail time. However, if they both refuse to take then they will carry a longer sentence for up to six months. Another choice is that one confesses, and the other doesn’t, the one that confess gets to be released, while the one that didn’t has to do about nine months of jail time. The police then tell the suspects these terms, if looking at a game theory point of view, no matter the choice that is made the other suspect is better off if they do not talk. The conclusion is that both choose to not talk and spend half a year in jail, rather than confess to the crime. The prisoner’s dilemma can be seen in philosophically view as a culmination of pursuit of self-interest and rationality. Looking to Betrand Russell, he states, “Reason has a perfectly clear and precise meaning. It signifies the choice of the right means to an end that you wish to achieve.” (Stanford, 1999) Prisoner’s dilemma can be seen as a prime reason in which people will not collude or cooperate even if it serves their best interests; it is commonly used in real world applications for law enforcement.

In looking at rationality and self-interest, the tragedy of commons is used in showing the application of game theory. Multiple players are involved in a situation in another dilemma. In which they consult their own self-interests and act independently to deplete a limited number of shared resources, even when it does not serve the long-term interests. This can also been seen as Kant detailed, “in each according to their needs”. In which a group of neighboring farmers want to increase their number of sheep on their land. If the sheep were to increase substantially, then the land will be quickly depleted and would not be able to support the increased number of sheep. The tragedy of commons much like the prison’s dilemma shows a lack of cooperation, and failed collusion. The tragedy of commons is mostly use in studying traffic congestion, advertising competition among oligopolists, over-study, and bell curves. Minimally the examples of Nash Equilibrium, Prisoner’s Dilemma, and Tragedy of Commons, the failure of coordination can be examined in daylight saving times, choices in restaurant, driving on the left side of the road, in history during the mass revolution in Eastern Europe, the economics of QWERTY, the Stock market speculative bubblies, and market crashes.

Game of Theory Part 2

Utility can also be seen as behaviorists, in which show more of the player’s behavior, and how it influences the game. Utility is the represents the player’s motivations. They are commonly used when there is more than just a monetary value in the choices. It is measure of the total amount of each outcome, in which reflects the player’s behaviors towards the strategy of the game. In determining the function of the utility, using the utility approach the optimal decision can be made. Utility is multiplied correspond by each probability of the alternative decision. The alternative decision with the expected highest utility is chosen. Utility is not used in measuring the psychological motivations of the players, but instead, “utility is merely a measure of relative behavioural dispositions given certain consistency assumptions about relations between preferences and choices.” (Ross, 2014) In looking at real world examples, can be viewed in economics are closely in stores. Such as the owner purchases a loaf of raisin bread at $5 a case, and is able to turn a profit but selling them at $10 a loaf. There is a great risk in stocking the bread, as it easily perishable. After the first day, the bread does not have the same value. The owner of the store must make the alterative choice according to the expected utility in which she buys additional amounts of bread in order keep up with the demand and increase the profits.

Game theory is applied to different sectors of the society besides economics. Ross (2014) shares that, “Gintis (2000, 2009) feels justified in stating, “game theory is a universal language for the unification of the behavioral sciences.”(Ross, 2014) In looking at the work of several political theorist, many believe that game theory works exclusively in the realm of rationality. While rationality is required, there are several dilemmas such as Prisoner’s and Tragedy of Commons in which rationality breaks down. In looking at the works of Rousseau and Hobbe’s, without some manifestation of outer demand on individuals’ behaviors, disorder would result. Cooperation among individuals would be inconceivable since individuals act just to amplify singular welfare and not the welfare of society overall. In all actuality, there will exist altruists (possibly a large number of them) who compel their ventures toward oneself for the benefit of other people.

In any case, if even one self-intrigued individual exists, he/she will misuse the altruists’ imperatives, benefitting from both his/her nonattendance of requirement and the altruist’s unselfish conduct. Thus, Hobbes accepts that it is mentally unnatural for altruists to exist. On the off chance, that only one barely self-intrigued individual exists no altruist can survive unless he/she gets to be barely self-intrigued as well. “In such an environment, known as a State of Nature, Hobbes contends that an individual must dependably be suspicious that an alternate will assault keeping in mind the end goal to amplify his/her own speculation toward oneself.” (Standford, 1999) Accordingly, in place for an individual to amplify his best advantage, he must assault the other individual before that other individual can assault. Hobbes accepted that the “Hobbesian Dilemma” brings about a State of Nature in light of the fact that profound quality is a shaky authority of social cooperation. As per Hobbes, a stable implementer can just exist if not one individual can veer off from the secured manage by which the rest hold fast to. Since the cooperation among individuals is naturally essential, a stable master must exist. Hobbes accepts that the best manifestation of social authorization is the presence of an almighty sovereign.

Cooperation and rationality in game theory is dependent on the information received. In particularly sequential games, information is fundamental for all players to be aware of the previous moves made by other players. Simultaneous games; players do not have “perfect information”; instead it is viewed as “imperfect” information. Games such as mancala, go, and chess shows game theory and perfect information, and how players are able to play the game. Game theory is applied throughout different fields of society including in the fields of biology and evolution, in which game theory tries to answer the question of what sets species apart. It can be viewed in looking human behavior, and how they respond to certain situations. “Game theory is a multiplayer decision theory where the choices of each player affect the payoffs to other players, and the players take this into account in their choice behavior. “(UMass, n.d) Game theory covers the procedural and conceptual tools for examining the payoffs, the informational structure, the rules of the game, the characteristics of the players, and social interaction. The social dilemmas presents real world behavior of individuals that includes the propensity to cooperate, and inequality aversion. In which the in order to reduce their own payoff, the one individuals will increase the equality of the entire group. This can be seen in the support widespread for charities and social welfare programs.

A break down in game theory and human behavior can be seen in sociopaths, in which their behaviors are seen as self-regarding agents in which the traits of professional killers, recreational cannibals, and sexual predators serve their own self-interest. The economic framework of game theory, also serves to discuss the subject of morality and interpersonal relations as, people that at as self-regarding agents have low morality, or none. They are mainly guided by hostility, instead of empathy and self-regard.  According to UMass (n.d), “We can just as well build models of honesty, promise keeping, regret, strong reciprocity, vindictiveness, status seeking, shame, guilt, and addiction as of choosing a bundle of consumption goods subject to a budget constraint.”(UMass, n.d). Game theory, can be used by people in salary negotiations , relationships, as demonstrated, and in several other aspects such as sociology, ethics, and laws. While it is largely used outside of the realm of business and economics, it is not as fruitful in other fields in which the outcomes can be bias, or leave no rational actions.

Game theory permits individuals to think about the interactions and behaviors of rational and selfish individuals. Game theory offers individuals the array of which the invisible hand can control. This can be easily understood in market failures in which theoretical contexts are used in games such as Coordination, and the Prisoner’s Dilemma. Game theory is largely focused on egocentric and selfish individuals that demonstrate the traits of sociopaths. In other dilemmas and games in which the parties are groups used cooperative behavior to make the best decision, allocentric perspective is commonly used. This spawns support for charitable and social programs, used commonly in the government by political parties. Game theory is an interactive and strategic decision making model in which details the behaviors of mainly rational individuals. Using the mathematical framework it has been used throughout history as a way of incorporating the fields of evolutionary biology, psychology, philosophy, logic, and many more. Modern game theory applications are used in looking at the relations of behaviors of individuals, as well as common real world problems, such as technology, international politics, wars, etc. While there is not much flexibility in game theory in defining untidy that doesn’t respond to emotion, game theory usually depicts the rational behavior of individuals towards cooperation. Game theory is essential in society, and in depicting the behaviors of the function of society.

References

Applications of Game Theory. (n.d). Stanford. Retrieved from http://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/applications.html

Campbell, W. Keith, Miller, Joshua D. (2007). Nash Equilibrium. International Encyclopedia of the Social Sciences, 2^nd Edition. Retrieved from http://www.columbia.edu/~rs328/NashEquilibrium.pdf

Game Theory and Human Behavior. Bounds of Reason. UMass. Retrieved from http://www.umass.edu/preferen/Class%20Material/Bounds%20of%20Reason/BOR%20Game%20Theory%20and%20Human%20Behavior.pdf

Martin, Brian. (1978). The Selective Usefulness of Game Theory. Social Studies of Sciences, Vol. 8. Retrieved from https://www.uow.edu.au/~bmartin/pubs/78sss.html

Ross, Dan. (2014). Game Theory. Stanford Encyclopedia of Philosophy. Retrieved from http://plato.stanford.edu/entries/game-theory/

Shubik, Martin. (1968). Game Theory: Economic Applications. Cowles Foundation Paper. International Encyclopedia of the Social Sciences. Retrieved from http://cowles.econ.yale.edu/P/cp/p02b/p0280.pdf