GAME THEORY AND IT’s APPLICATIONS

Solution:

Introduction

Game theory is considered to be a theoretical framework, allowing the conception of social situations through a number of competing players. As opined by Aumann (2019), it is often considered to be a science of strategies, where decision-making processes of independent as well as competing actors take place in a strategic environment or setting. The emphasis of game theory lies on the game itself, where the game is considered as an interactive model of rational players. The major aspect of the game theory is that the payoff of one player is contingent on the strategies which have been implemented by another player. The game thus undertakes identification of the identities of the players, their preferences, the strategies available to them and the impact of these strategies. In practical life, game theory finds a number of applications in different sectors which include biology, economics, psychology and business. Modelling a real life environment through game theory has allowed better comprehension of understanding the perspectives and potential actions of people (Samuelson, 2016). In this particular report, an insight would be provided into the importance of game theory and its application in a real-world situation.

Game Theory in real life

Importance of Game theory in real life

Game theory highlights how decisions are taken using the theory and the different factors affecting such processes. Although most of the terms are scientific and provide a model to understand the concepts better, game theory finds importance in real life issues and practical circumstances. One can use game theory almost anywhere. The process of creating a model using game theory principles allows better opportunities for people to understand different perspectives and provides potential for critical thinking processes (Bonau, 2017). In game theory, one not only has to consider their own options and choices but also think about the potential choices which the interacting factors would make. Thus the person has to critically analyse before making a decision. Game theory finds its use in simple tasks such as choosing which shop to buy from to difficult and complicated tasks in business environments.

Tobacco company advertising and game theory:

Background and factors to be considered:

Tobacco industry currently faces a ban on advertising its products in the UK. In 1965, a ban was implemented on advertisement of tobacco on the Television through the Television Act of 1964. In 2003, further ban on advertisement of tobacco was witnessed through the Advertising and Promotion Act of 2002 which prohibited the companies from using press and billboards to directly advertise their tobacco products (Hiilamo and Glantz, 2017). Further ban on indirectly promoting the sale of tobacco was implemented which prohibited sponsorship advertisement for sporting brands.

However, it is important to note that although the measures were taken to ensure low sales of tobacco and reduction of its consumption, the sales did not decrease. A report from 2018 further shows that the total turnover for retail sales from tobacco was 12.6 billion pounds (Statista, 2020). Although, one might consider that lack of advertising would hamper  the sales of the product, it is seen that the lack of advertising from all brands makes it a more competitive and flourishing market.  In this particular case, a model for the game would be created to understand how the companies would have fared had no bans been implemented by the government. It would provide a clearer insight into the potential outcomes and the optimum solution.

Players for the game: Players are decision makers in the game (Marden and Shamma, 2018). In this particular scenario, the players include the tobacco companies. For simplicity, we would be using two tobacco companies operating in the UK market. These would be denoted by company A and company B.

Pay Off: Pay-out refers to the pay-out received by the player from a particular result. Payoff in this case would be the greater market share owing to advertising methods. Advertising and promotion of a product in the market leads to greater visibility of the product and higher chances for the people to avail the said product or service. This would subsequently lead to a greater market share.

Strategy: Strategy in the game refers to the actions a player would take in the game. In this particular case, the strategies would either be to invest in advertising or to not invest in the advertising measures.

Assumptions: Before undertaking measures of game theory, a number of assumptions are often made to make the decision processes easier. Here, we assume that there exists two companies, company A and company B, who sell tobacco products in the UK market.

Modelling the game before the TV ban:

Before the government had banned advertisements of tobacco products, the brands were free to spend money or choose not to. In this case the following scenarios could be witnessed.

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Figure 1: Payoff Matrix for the companies

(Source: Created by author)

Case 1: Both brands spend equal amounts on advertisement.

Outcome: In this case, since both brands spend any money on advertisements, both the brands would gain equal amounts of, say 3 million pounds.

Case 2: Company A invests but Company B does not.

Outcome: Company A gets a greater share in the market of 5 million while B gets 2 million.

Case 3: Company B invests but Company A does not

Outcome: Company B gets a greater share of 5 million while A gets 2 Million.

Case 4: Neither company advertises.

Outcome: Both gain an equal amount of 4 million pounds.

Prisoner’s Dilemma in this case:

As opined by Robèrt and Broman (2017), prisoner’s dilemma is often referred to as a paradox in the process of analysis of decisions where two individuals or entities tend to act in their own interests and not produce any optimal outcome. From this particular case study, we find that the most optimal outcome for the companies would be the fourth case where neither company spend on advertising and gain 4 million. This amount is higher than the scenario where the other party invests since the gain is above 2 million. The rational option for the brands should be to not spend. However, the dilemma arises when one company starts scrutinizing and doubting. Company A may become wary of company B investing in the market which would lead to their losing of market share and profits.

Nash Equilibrium in this case:

Nash equilibrium is an important concept of game theory in which the optimal result of the game is one where there exists no incentive to deviate from an initial plan (Heusel et al.  2017).  The particular theory is extremely important as it allows players in the game to determine their best payoff for the situation, considering not only their decisions but also of the other party involved. In this case, although both the companies are aware that the optimal outcome for them would be to not invest and gain equal amounts. The uncertainty and self-interest to gain more would lead a company to invest, although it would lead to the other party to lose their share in the market.

Advertisement ban and optimal solution

Upon analysis of the entire scenario, the ban on the tobacco advertisement provides an optimal solution. The ban prevents all the companies from investing in advertising their products and hence provides the post optimal solution. In this case, the power to decide and the tendency of either of the companies to invest and follow through Nash equilibrium is taken away. The decision is already made by the government. The rising sales and lack of decline in the tobacco market is owed to a number of assumptions, the most important one of which is that a consumer is more likely to keep continuing their consumption processes even if there is a lack of advertising. On the other hand, lack of advertising helps the tobacco companies. Lack of advertisements also ensures equal opportunities for the companies to gain larger profits, through lack of competition.

Game theory and decision making

Game theory is considered to be one of the most powerful tools used for predicting the different outcomes of a number of interacting entities or firms. In such instances, the action of one entity would directly affect the payoff of the different other players participating. Considering the fact that each firm acts as a part of a complicated and complex web of a number of interactions, the decisions taken by any one firm would impact multiple firms and entities interacting with this firm or which exists within that firm. Every decision maker acts as a player for the game. According to Webster (2018), in business, firms have to take into account all the potential options and choices and payoff of the other entities. This is done while also taking into account that the other firms would also be creating strategies and making a decision on the said firm. Thus game theory allows businesses to create an optimal solution and base their decisions accordingly.

Game theory also finds wide applications in numerous political affairs. As opined by Kwok (2017), these political affairs include those of war strategy, international politics, social choice theory, war bargaining, political economy and strategic voting. When in the hands of politicians and diplomats, game theory becomes an effective tool providing the scope to analyse different instances of conflicts taking place between states, individuals, companies and political parties. One of the major assumptions of the theory lies in the rationality of the players and actors, along with the choices of strategies. This theory is considered to be an important tool when conducting research on issues such as terrorism. This is because it allows capturing of the interaction between the terrorist organizations and the subjects attacked, when independent steps help in separate analysis.

An important theory which analyzes the behaviours of humans is the decision theory. It focuses and emphasizes on the identification of the best suited option or decision for the decision maker (Okasha, 2016). This theory focuses on the rationality in decisions, where parameters such as preferences and beliefs are also taken into account while analysing an outcome. Game theory and decision theory are related closely. Both the theories together analyze the interdependent problems between the strategic and rational agents during decision making (Frahm, 2019). What distinguishes the two theories is that decision theory tends to treat the outcomes as moves of nature and exogenous events while game theory takes into account the uncertainties of other agents and their potential behaviours.

Conclusion

As opined by Sun and Sun (2018), game theory is often considered as the study of different mathematical models of interactions which are strategic, among rational makers of decision.. In this particular report, an insight was provided into the application of game theory into a practical and real life circumstance. The chosen circumstance included two tobacco brands and how the ban on their advertisements actually enabled the brands to reach an optimum solution, preventing them from undergoing prisoner’s dilemma. The four scenarios are presented for the two brands where the optimum solution is reached when neither of the parties invest. However, the ban on advertisement makes the decision making processes easier. In the day to day lives, a number of similar instances could be observed where game theory plays a major role.

Although considered to be complicated, game theory finds its use in simple circumstances as well as complex mathematical problems (Seaberg, Devin and Zhuang, 2017). Through the practical example of Tobacco companies, an insight into Nash equilibrium is also provided which further draws attention towards how people tend to work for their own self interests. This particular aspect deters a person or an entity to make the optimum solution, instead aim for their own gains. When implemented in different scenarios, the game theory provides different insights. Use of the different tools allows better scope for critical thinking and analysis. This is one of the major reasons why the theory finds its relevance in different sectors and continues to become popular in science.

Reference List

Aumann, R.J., (2019). Lectures on game theory. CRC Press.

Bonau, S., (2017). A case for behavioural game theory. Journal of Game Theory, 6(1), pp.7-14.

Frahm, G., (2019). Rational choice and strategic conflict: The subjectivistic approach to game and decision theory. Walter de Gruyter GmbH & Co KG.

Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B. and Hochreiter, S., (2017). Gans trained by a two time-scale update rule converge to a local nash equilibrium. arXiv preprint arXiv:1706.08500.

Hiilamo, H. and Glantz, S., (2017). FCTC followed by accelerated implementation of tobacco advertising bans. Tobacco control, 26(4), pp.428-433.

Kwok, K.H., (2017). When Education Meets Politics in Taiwan: A Game Theory Perspective (1994–2016). Springer.

Marden, J.R. and Shamma, J.S., (2018). Game theory and control. Annual Review of Control, Robotics, and Autonomous Systems, 1, pp.105-134.

Okasha, S., (2016). On the interpretation of decision theory. Economics and Philosophy, 32(3), p.409.

Robèrt, K.H. and Broman, G., (2017). Prisoners’ dilemma misleads business and policy making. Journal of Cleaner Production, 140, pp.10-16.

Samuelson, L., (2016). Game theory in economics and beyond. Journal of Economic Perspectives, 30(4), pp.107-30.

Seaberg, D., Devine, L. and Zhuang, J., (2017). A review of game theory applications in natural disaster management research. Natural Hazards, 89(3), pp.1461-1483.

Statista.com (2020), Turnover From Retail Sale Of Tobacco In The United Kingdom (UK) From 2008 To 2018. [online] Available at: https://www.statista.com/statistics/309142/tobacco-retail-sales-turnover-united-kingdom-uk/ [Accessed on 4th June 2021]

Sun, S. and Sun, S., (2018). Management Game Theory. Springer.

Webster, T.J., (2018). Introduction to game theory in business and economics. Routledge.

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