Game theory evolution and contemporary economic applications

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.

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.]

Compliance inspection and certification

Game theory finds application in the now evolving field of compliances and licenses of software packages. Considering the benefits likely to result to the consumer purchase and use of the software, the buyer has an incentive to violate the restrictions relating to use of the product. On the side of the vendor, the vendor needs to ascertain that the consumer abides with the regulations.

In this type of gain, Nash equilibrium is where both player chose a strategy that is preferred and maximizes the gains is not feasible[footnoteRef:20]. Considering that undertaking inspection is a hustle for the vender and failure to inspect leads to losses, then the vender has no maxi min option. Alternatively, the buyer has higher yield benefits if they cheat and an avenue to change their strategy given the option taken by the vender. [20: Ibid ]

In this form of game, probability randomized inspection is advised for the case of the vendor. This measure works to reduce the consumer's certainty of the vendor's possible action. This results to the mixed equilibrium strategy. As a measure to come up with maximum benefit, to the vendor as well as reduce the costs incurred if inspection would be carried out always. In this perspective, Game theory is seen to give an option where a challenge exists in determining the preferred action.

Zero-Sum Games

This is the case where the players face the challenge of making a decision completely unaware of the strategic choices the by the opponent. This type of game has a constant sum and the players strategically may choose to randomize their action as this yield better chance for higher payoffs. Ideal practical examples of a zero sum game include "rock-paper scissors," Poker chess and checkers[footnoteRef:21]. Zero-sum game can be applied in modeling the computer science concept strategy of "demonic" non-determinism. This rides on the assumption that worst possible outcome is likely to occur when ordering of events is not specific. One can take nature as an opponent antagonistic enough to randomly yield to favorable and unfavorable possible outcome. This allows an individual to conceptualize the worst case likely to result and use it as a benchmark for alternate decisions[footnoteRef:22]. [21: Myerson, & Roger, B. (1995). Game Theory: Analysis of Conflict. Cambridge Massachusetts: Harvard University Press.] [22: Ibid ]

Similar to the Zero-sum game is the randomization in the algorithms theory by Rao. This theorem defines the power of random algorithms. Zero-sum games and randomized algorithms facilitate analysis of online problems. In this case, algorithm receive input on data at a time and give decision based on the input given. This facilitates decision making on scheduling among other without necessarily waiting for the entire input. The use of algorithm facilitates optimal decision making on matters that are difficult to ascertain with minimal information. Procession of massive data and its analysis is facilitate also through algorithm

Conclusion

Game theory serves to make simple the idea of thinking through the interactions to come up with optimal decisions and actions. Additionally game theory serves to accommodate rational decision and resolve a great deal of conflict situation. The application of Game theory has over the years contributed to exploration of market equilibrium and player's decision targeting a broad spectrum of aspects. These aspects include social, economic and political perspectives. In these aspects, game theory contributes to decision evaluations and assessments of the optimal positions for operations.