Application of Game Theory in Various Aspects of Human Life

Game Theory

The earliest conceptualization of game theory is by Cournot in 1838 where the analysis sought to clarify choices and actions taken in a duopolistic market[footnoteRef:1]. Over the years, exploration of the game theory incorporates market equilibrium entailing economic social and political decisions. As a concept, Game theory lays down the structure that through analysis, facilitates an understanding of the strategic choices agents adopt[footnoteRef:2]. Game theory is a concept that entails formal study of cooperation, conflict and actions taken up by several interdependent agents[footnoteRef:3]. [1: Rasmusen, and Eric. Games and Information: An Introduction to Game Theory, 3rd Ed. . Oxford: Blackwell, 2001] [2: Gibbons, and Robert. Game Theory for Applied Economists. Princeton, NJ.: Princeton University Press, 1992. Gibbons, and Robert. Game Theory for Applied Economists. Princeton, NJ.: Princeton University Press, 1992.] [3: Milgate, M. (2008). "Palgrave's Dictionary of Political Economy" the New Palgrave: A Dictionary of Economics. New York: New Palgrave]

As a decision making tool, game theory involves the application of mathematical concepts to analyze strategic choices and problems. This process of making decisions allows the conceptualization of individual players' strategic options with consideration of their responses and preferences [footnoteRef:4]. This paper presents an elaborate discussion on game theory, its evolution over time and related contemporary economic applications of game theory. [4: Nasar, & Sylvia. (2000). A Beautiful Mind: A Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994. New York: Simon and Schuster.]

Historical Evolution of Game Theory

In 1838, Antoine Cournot explored the characteristics and behavior of players in a duopolistic market[footnoteRef:5]. Cournot's analysis gave birth to game theory where his study shows the rational choices duopolistic market players take up. Following Cournot's analysis, Emile Borel a mathematician suggesting a formal game theory, made advancements on the theory in 1921. John von Neumann a mathematician followed in 1928 with a theory of parlor games. The establishment of game theory as field of its own took place following a publication by von Neumann and the economist Oskar Morgenstern on Theory of Games and Economic Behavior[footnoteRef:6]. [5: Dixit, Avinash, K., & Nalebuff, B.J. (1998). Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life. New York: Norton] [6: Gibbons, & Robert. (1992). Game Theory for Applied Economists. Princeton, NJ.: Princeton University Press.]

A demonstration that finite games always have equilibrium by John Nash in 1950 followed. The demonstration exhibits that agents in interactive decision games achieve optimality by allowing choice the opponents. Following growing interest in game theory in the 1950s and 60s, game theory has found application in extensive fields including politics, war, economics, psychology and sociology[footnoteRef:7]. [7: Rasmusen, & Eric. (2001). Games and Information: An Introduction to Game Theory, 3rd ed. . Oxford: Blackwell.]

Game theory has also established link with biology and evolution. A level profile application of game theory has resulted in the 20 and 21 century. This is the case since; it is considered a cardinal measure to achieve practicality in policy formulation, resource allocation and competitive nature of man. Popularity of Game theory was also influenced by the award of Economic Nobel Prize to John Harsanyi, Nash and Reinhard Selten the main proponents of the Theory[footnoteRef:8]. [8: Myerson, & Roger, B. (1995). Game Theory: Analysis of Conflict. Cambridge Massachusetts: Harvard University Press.]

To date, the major applications of game theory include political science sociology, economics, psychology, evolutionary biology, strategic and tactical military problems. Most recently, game theory has been applied in computer science, mathematics, accounting, statistics, ethics, epistemology and philosophy. Game theory cuts across all boundaries as far as rational decision making between players is needed.

Game theory presents a well-developed methodology applying interactions to determine the methodology that lead to the desired outcome. Opposed to other theories and approaches that use rather complicated and far-fetched measures, game theory applies well-known principles connected to any interaction situation. This aspect supports its application across a broad range of fields.

Application of Game Theory

Cooperative and non-cooperative game theory

The application of game theory can formally through coalition where a payoff to a group is determined by the cooperation level within the group members. Game theory facilitates the formation of bonds among the players and groups to form coalitions and have a majority vote base. This type of game is seen mostly in political parties and among member of the legislatures. Members of different group engage explicitly in forming coalitions to move and pass a motion. Although a particular party or group in the legislature has the bigger numbers, negotiations and open negotiations form a coalition [footnoteRef:9]. [9: Fudenberg, Drew, & Jean, T. (1991). Game Theory. Cambridge, MA: MIT Press.]

Through the negotiations, persons with common interests band their votes to push for a common agenda. In the political scenario of adopting and coming up with policies, this has been the norm and has been facilitated by game theory. The different individuals and groups assess the composition of different groups and assess the probable measures they would take to push their agendas. This assessment allows for a holistic understanding of the ideals with the various groups their preferences measures necessary to achieve these ideals[footnoteRef:10]. [10: Binmore, K. (1997). Fun and Games: A Text on Game Theory. Lexington, Massachusetts D.C. Heath.]

Cooperative games facilitate negotiations among players with different ventures to reach an agreement and reduce friction. Cooperative game theory has been widely used in international relations, war and national politics. Using a proposal by Nash, game theory has gained wide acceptance in the bargaining for power in the political arena.

Parties with differing views and opinion can give offers and counter offers in negotiations with each party seeking to safeguard their preferences. In the negotiations, the results are the middle ground where both parties feel their preferences are met to the optimal given the existing differences[footnoteRef:11]. In these types of negotiations, the focus is mainly the outcome where both parties emerge as winners. [11: Harsanyi, J.C. (1982). Solutions for some bargaining games under the Harsanyi -- Selten solution theory I: Theoretical preliminaries; II: Analysis of specific games. Mathematical Social, 3, 179 -- 191; 259 -- 179.]

Different from the cooperative game theory is the non-cooperative game theory. The interactions in this type of scenario focus mainly on, the strategic choices players prefer and the time the take up their choices. The players take up choices in complete regard of their own interests, and their best choice of action is one that outwits their competitors.

In the non-cooperative model of game theory, cooperation may also arise when a player considers it in their best interest to approach opponent players. The cooperation in this model of the non-cooperative game theory follows from the players appreciations that it is the only rational choice. Implying that should they approach the other players, they will attain and optimize their outcome[footnoteRef:12]. [12: Gibbons, & Robert. (1992). Game Theory for Applied Economists. Princeton, NJ.: Princeton University Press.]

In the game theory whether or not there is cooperation the player are seen to pick the most rational choice. This choice yields the most outcomes related to their preferences considering effects of their opponent's actions. Game theory in this perspective gives an analysis of the interplay of actions and facilitates prediction of opponent's actions and their effects.

Game Theory and Quality of Choice

The simplest form of game theory is seen in the Prisoner's Dilemma game theory between two players. The interactions seen in this interplay lead to the conclusion that no rational player would be willing to take up the dominant strategy. This is because it is associated with lower returns considering the other persons choice[footnoteRef:13]. [13: Harsanyi, J.C., & Selten, R. (1987). A General Theory of Equilibrium Selection in Games. Cambridge, Mass: MIT Press.]

In the case for quality in service provision and the choices consumers' face, it is seen that the dominant strategy among the players will be avoided. The dominant strategy is easily avoided in the interactions of choices between the supplier and consumer. Assuming that the supplier of inter-service is faced with the decision to provide low quality and high quality service. The supplier is faced with a choice to embrace the high quality service that has fixed cost independent of whether or not a contract is signed. The customer has the choice to take low or high quality service. However, the customer is not aware of how low the service is and it is not verifiable through the contract. The two players are faced with the choice of whether or not to pay and to provide the service[footnoteRef:14]. [14: Ibid]

Considering the cost associated with the high quality service the supplier will prefer low quality service. On the other hand, the customer will always prefer to high quality. Since the dominant strategy for the supplier is to provide low quality service and the of the consumer is to buy high quality service, the result will be no contract will be signed

Different to the above examples of game theory, many game interaction do not have a dominant strategy[footnoteRef:15]. The absence of a dominant strategy allows for the existence of a point where each player takes up a strategy that maximizes his or her outcome given the other player's options. This is what is known as the Nash equilibrium. At this point, the players take up their own individual choices and cannot improve their outcome given that the prevailing circumstances. Satisfaction of the Nash equilibrium follows from rational choices by players and the expectation that opponent players will follow the same route. [15: Rasmusen, & Eric. (2001). Games and Information: An Introduction to Game Theory, 3rd ed. . Oxford: Blackwell.]

Considering the internet service example given above, the interactions with the game can be altered by inclusion of a clause where the consumer can opt-out of the service contract. This clause safeguards the interest for the consumer to receive a high quality service as the producer is given an incentive to do so. The resultant game interaction is such that the consumer will take up high quality service since it has the highest payoff. Similarly, the service provider will take up provision of high quality service since it is in their best interests give the opt-out clause included.

The resulting interactions yield two equilibrium position. The first position is where both player maximize their gain by not buying (consumer) and provide low quality service (service provider). The other equilibrium is the Nash equilibrium where preference is to buy and provide high quality service. This equilibrium provides a high pay to the players in the game and therefore, it is a preferred option. It is in the best interest for the players to make no alterations on their choice. In the Nash equilibrium, the player seeks to maximize their gain and is the ideal situation in utility maximization. The Nash equilibrium is attained from the elimination of the dominant strategy that adds to the choices a unique strategy combination. The unique strategy combination is thus the Nash equilibrium.

Selection of equilibrium

In game theory, situations arise where there is more than one equilibrium. This situation calls for a guide to facilitate players through the interactions and help them to pick the most reasonable equilibrium. This will be the position whose utility is highest and meets the preference of the players. Game theory works to assess the equilibrium positions that are convincing and more plausible. Recent attempts of game theorist try to refine the equilibrium and heighten them as plausible and of high utility[footnoteRef:16]. [16: Harsanyi, J.C., & Selten, R. (1987). A General Theory of Equilibrium Selection in Games. Cambridge, Mass: MIT Press.]

Consider two firms that provide communication services to consumers as well as interact between themselves. If these firms have the choice between two strategies high and low bandwidth equipment, their best option for will be derived from the ability to interpret the other player's preferences. The situations the firms face indicate that, low bandwidth connection works equally well similar to high bandwidth connection. So if firm one has low bandwidth. Switching to high bandwidth is only preferable if firm two has high bandwidth. It is notable that switching to high bandwidth while the other firm has low bandwidth will mean incurring unnecessary costs.

In this type of situation, the option for low bandwidth has an inferior payoff compared to the payoff derived from high bandwidth. However high bandwidth has a higher payoff despite the high cost that to some extent is deemed unnecessary. Low bandwidth options is seen to avail a better worst-case gain in the presence or absence of rationality considering all other options available to the other player, in this it is seen that the player will take up low bandwidth option as one that maximizes the minimum attainable payoff. This option makes investment in low bandwidth a safer choice. This is so with the expectation that the other player will apply similar reasoning as opposed to going for high bandwidth. The realized equilibrium is one the will maximize the minimum attainable payoff.

Evolutionary games

The more practical application of game theory follows from the appreciation that in any economic, political or social scenario there are more than two players. This complicates the rational decision-making process since each of the players in the game can easily opt for any of the strategies given their respective preference and measures of utility. The game dynamic is given by a display of the fact that a specific ratio of the players opts for each of the strategy. Subsequent interplays though increase in the number of players or change in decision by existing players will be dictated by the measures of the better average gains. This will evaluation and changes will eventually contribute to elimination of some strategies and shift to a long-term surviving strategy. This shift yields the long-term equilibrium[footnoteRef:17]. [17: Rasmusen, & Eric. (2001). Games and Information: An Introduction to Game Theory, 3rd ed. . Oxford: Blackwell.]

Initially a smaller proportion of the population, embrace high quality bandwidth compared to those with low quality bandwidth. This is the case owing the simplistic assessment and preference of maximizing a minimum by the players. Combination of the proportion of individuals with high quality bandwidth with the payoff yield a higher average payoff compared to the low quality bandwidth. New entrants in to the game will look at the average payoff of the different strategies and opt for the strategies with the higher average[footnoteRef:18]. [18: Ibid ]

Existing players in the game will also make similar calculations whet they intent to replace their equipment. Subsequent interaction in the game will lead to a shift to a new equilibrium considering the average advantage. This makes the high quality bandwidth strategy a preferred strategy in future compared to the low quality strategy. However, a shift to the high payoff strategy in the future is pegged upon there being a large enough fraction at the start. If the initial proportion of users in not large enough to attract new entrants, the long-term option will remain as the low quality bandwidth. This interaction declares that long-term sustainability of a strategy is dependent upon the initial combination of the particular option. Those strategies with high initial average will remain the more preferred strategy[footnoteRef:19]. [19: Myerson, & Roger, B. (1995). Game Theory: Analysis of Conflict. Cambridge Massachusetts: Harvard University Press.]