# Game Theory Explaining The Behavior Of Firms In Oligopolistic Settings

It can be said that game theory is a philosophy regarding strategies. More specifically, it provides abstract models for hypothetical interactions between a number of parties. These models present the various possible interactions between the parties involved and their respective outcomes, offering interesting insights about different social scenarios. These observations are then used to formulate stratagems. As such, game theory is widely used by numerous social sciences like Politics and Economics and has many real-life applications. This essay will look into the prisoners’ dilemma, an example of game theory, and how it explains the behavior of firms in oligopolistic settings.

In spite of what the name may imply, game theory does not revolve around simple activities intended for entertainment. Rather, it studies the interactions that take place between rational, practical decision makers, whom it refers to as players. By employing mathematical tools, game theory constructs simplified theoretical models representing the many possible ways two or more parties may interact with one another. These mathematical models assume that the players will either choose cooperation or conflict solely based on their desire to maximize their individual utilities- that is, rationality. Game theory includes many games like the prisoners’ dilemma, the Chicken, and the Stag Hunt game that are categorized based on their properties. For example, some are sequential games while others are simultaneous games. The theory is widely applied in the various fields of social sciences; most notably, economics and politics. Academics and politicians use game theory to summarize the possible interactions between players in a given scenario and then come up with the best possible strategy(s).

A typical game theory game that is often utilized and has many applications is the prisoners’ dilemma. It is a simultaneous, non-zero sum game which conventionally consists of two players (econ book). A player’s chosen action is made without actual knowledge of the other player’s choice. However, the probable behavior of the player is taken into consideration. Moreover, the total gains and losses of the players do not equal zero since both can gain something. The prisoners’ dilemma has a simple structure. Consider the hypothetical case of two players, A and B, whom were arrested by the police for robbing a jewelry shop in Edinburgh. Also note that both players are not as concerned about the wellbeing of each other as they are about their own. The police lack solid evidence and can only jail them for 2 years. They decide to interrogate each suspect separately in order to secure a testimony, and offers both of them the same proposal: if you confess and your partner remains silent, you will not be charged while your partner gets imprisoned for 10 years, but if you remain silent and he confesses, you will be jailed for 10 years while he goes free. In addition, the police is willing to provide a reduced sentence of 4 years if both confess.

The prisoners’ dilemma highlights the difficulty of maintaining cooperation in scenarios involving rational, self-interested players. Price-setting in an oligopolistic environment is one scenario.

An Oligopoly is a market consisting primarily of a small number of rival firms. These firms own the majority of the market share and exercise dominance over it. Other firms may operate in an oligopoly; however, their negligible market share means that they are not seen as competition. Oligopolies are unique due to the interdependence of its firms. A firm’s behavior is closely linked to that of its rivals. Its strategies are formulated based on its competition’s likely actions. This is similar to the situation of players A and B. Hence, the prisoners’ dilemma provides an explanation for the functionings of such firms. Price-setting in United Kingdom’s coffee shop market which is oligopolized by Starbucks, Costa Coffee, and café Nero does well to illustrate this. In order to construct a hypothetical model, it is first important to set some restrictions, for the sake of simplicity.

First, the model will only take into account the case of two players, Starbucks and Costa Coffee, who are rational, utility-maximizers Second, it will assume that acts of ‘cheating’ are prohibited. Third, the players’ decisions are made simultaneously without knowledge of each other’s actual action(s); they have a limited access to information. Both firms have the choice of either increasing their prices or lowering them. If Starbucks chooses to increase its prices but Costa Coffee defects and decides decrease its prices, the former will only earn 2 million in profits; the latter will earn 8 million and vice versa. If both firms decide to lower their prices, they will earn 4 million each. This highlights the model’s dominant strategy, reducing the prices, and its Nash equilibrium of (L, L). On the other hand, by cooperating and increasing their prices, both firms will actually be able to earn an overall better outcome of 6 million, and this is what actually has happened. Over the last few years, both firms’ prices have increased by approximately 0. 325p. It is apparent that the prisoners’ dilemma showcases the interdependence of firms in an oligopolistic market and provides interesting insights into their functionings regarding price-setting. By utilizing it, we can describe the behavior of firms within oligopolies; however, it is not perfect.

The prisoners’ dilemma, and game theory in general, ignores many aspects of reality. It is important to understand that it is merely a theory upon which hypothetical models are constructed. These models, similar to the ones above, are simplified versions of social scenarios between two or more parties. Many facets of these scenarios are left out. One important example is rationality. The prisoners’ dilemma assumes that the players are practical, self-interested decision-makers pursuing selfish goals. In the case of many, this is not true. Instead of defecting, both Starbucks and Costa Coffee cooperated and raised their prices. In reality, neither followed the game’s Nash equilibrium of (L, L) and its dominant strategy as was shown; a clear violation of the theory. It not just rationality that poses a problem. Outside the two dimensional world of the theory, factors such as government interference will also affect price-setting. Price ceiling and price floor policies may restrict the firms and force them to behave differently. These left out factors can greatly impact the choices of decision-makers.

## References

1. Dastidar, K. G. , 2017. Oligopoly, Auctions and Market Quality, Tokyo: Springer Japan: Imprint: Springer.
2. Friedman, J. (1983) “Introduction and overview,” in Oligopoly Theory. Cambridge: Cambridge University Press (Cambridge Surveys of Economic Literature), pp. 1–18. doi: 10. 1017/CBO9780511571893. 002.
3. Jameson, K. (2014). Game Theory and its Applications. [ebook] Sr. Seraphim Gibbons Undergraduate Symposium. Available at: https://sophia. stkate. edu/undergraduate_research_symposium/2014/natural_sciences/30?utm_source=sophia. stkate. edu%2Fundergraduate_research_symposium%2F2014%2Fnatural_sciences%2F30&utm_medium=PDF&utm_campaign=PDFCoverPages [Accessed 16 Feb. 2019].
4. Murphy, A. (2019). Cost of coffee up 20 per cent - but beans fall to cheapest in seven years. [online] The Sun. Available at: https://www. thesun. co. uk/money/7212192/cost-of-high-street-coffee-rockets-20-per-cent-despite-beans-falling-to-cheapest-price-in-seven-years/ [Accessed 16 Feb. 2019].
5. Myerson, R. B. , 1991. Game theory: analysis of conflict, Cambridge, Mass. ; London: Harvard University Press.
6. Osborne, M. J. and Rubinstein, A. , 1994. A course in game theory. MIT press.
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10 December 2020

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