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# Key Assumptions of Game Theory

## Executive Summary

## Introduction

## Body

### Reality of Assumptions

### Predictions of the Model & its Accuracy

### Normative conclusions

### Improvements to the model

### Practical Implications

## Conclusion

## References

- Subject:
**Science** - Category:
**Math** - Topic:
**Game Theory** - Pages 5
- Words: 2444
- Published: 16 December 2021
- Downloads: 28

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Game theory is a mathematical technique used to interpret the behaviour of interdependent decision makers who use strategic behaviour. It assumes that players are rational and that payoff matrices are predetermined and known to everyone. Most of these assumptions do not hold true in real life. Managers may be motivated by other factors when making strategic decisions like growth and revenue maximization or their corporate social responsibility. Additionally, it is hard to achieve complete information in real life which is when all players within the game are aware of the payoffs when they switch strategies.

One such game is based on the Prisoner’s Dilemma and it predicts that 2 oligopolistic firms who use strategic behaviour will always end up worse off due to their incentive to collude and then cheat. This has been historically accurate as seen through the U.S. Market for Automobiles in the 1950’s. Another such game is the Cournot Duopoly model which predicts that a duopoly produces more favourable market outcomes compared to a monopoly. It does this by having firms compete based on changes in quantities since ‘increasing prices would result in a decrease in market share’ (Ferguson, n.d.). This model is not easily testable, however its conclusions are considered accurate by economists.

This model can be improved by acknowledging the key information differences between players in order to make it more accurate. The model can also be improved by acknowledging that there can be multiple ideal equilibria or Nash equilibria for the player. This model has several implications for our understanding of oligopolistic firms. It explains why firms avoid non-price competition, why prices are considered to be rigid and why they face the incentive to collude. It can also be used to analyse how other large entities like governments from around the world work together for issues like international trade.

In this report, we will be having an in depth look into an economic model known as the game theory. This theory analyses your opponent’s reactions in order to help you make a decision to give you the most favourable result. Decisions taken by other players in the game can change the outcome for all the individuals involved and thus, can affect the outcome of the player. There are two different types of game theory, non-cooperative and cooperative. An example of non-cooperative game theory is the Nash Equilibrium, where no player has an incentive to change strategy, even if they know all the choices of their opponent (MBA Crystal Ball, n.d.). We will explore multiple examples of the Nash Equilibrium known as the Prisoner’s Dilemma and the Cournot Approach, and its implications for the study of economics.

Cooperative game theory is where players form groups and compete against other groups. This can be likened to cartels such as OPEC as this organisation works together to keep the supply of oil low between member states and therefore keep the price high to maximise profit. In this report we will discuss the fundamental elements of this theory and it’s real life applications as well as it’s flaws.

The key assumption of the game theory is that all players are rational in the sense that they all ‘strive to maximise their payoffs within the game’ (Economics Discussion, 2019). While this assumption may make the model confined in the real world, it is crucial to justify why players make the decisions they do. The next assumption is that there exists a ‘finite number of competitors and a set number of predetermined outcomes’ (Ferguson, n.d.). It is important that all of the outcomes can be foreseen before the game has begun. Players will try their best to maximise their win and will only make concessions when that increases their risk of winning. Lastly, all the players can adopt multiple strategies and everyone is aware of the different rules of the game

The assumption that all players act rationally does not hold in real life as individuals could make decisions based on impulse or emotions. For instance, an individual could reject investing in a football team that is more likely to win a competition and essentially give the best return at a lower risk in exchange for a team who they have supported since childhood. In cases of oligopolistic firms, managers may choose to overlook profit maximisation and instead base their decisions on other factors like growth maximisation, revenues and corporate social responsibility.

Next, the assumption that all outcomes can be foreseen before the game has begun is not realistic for multiple reasons. Firstly, in real life, unexpected events can always occur which would change the outcomes to the game. Secondly, ‘most firms will not have enough knowledge of their own payoffs, let alone those of their competitors’, hence, in cases like this, managers cannot make strategic decisions (Osak, 2010). Additionally, it is hard to achieve complete information in real life which is where ‘each player is aware of its opponent’s payoffs’ (Kovach, Gibson & Lamont, 2015). One player might have more information than another, so they may be in a more favourable position to make a strategic decision compared to its opponent.

The assumption that players will only make concessions when that increases their risk of winning holds true in real life. The TV game show “Golden Balls” is an example of this where in the final round the players have the option to split or steal the money. In a lot of cases, contestants are happy to share the prize as they would feel bad about themselves if they screw the other player over and take all the cash (Investopedia, 2019). Lastly, the assumption that players would be capable of adopting multiple strategies and change their prices in response to their competitors may be harder to accomplish in real life. This could be due to any legislation within the industry like price ceilings that may inhibit firms from raising their prices above a certain point.

- Prisoner’s Dilemma

The model is concerned with predicting the outcome of a game in which players are affected by the decisions of its opponents. One such example of this is the Prisoner’s Dilemma. This model predicts that ‘two rational decision makers who attempt to make themselves better off by using strategic behaviour always end up becoming worse off’(Tragakes, 2015).

Initially, both firms adopt a low price strategy where they earn profits of $20 million. They eventually realise that by colluding and adopting a high price strategy together, they can earn profits of $50 million. However, each firm now faces a dilemma: the incentive to cheat the agreement and enter a low price strategy in order to capture their opponent’s market share and increase profits to $70 million. Each firm also thinks that if they do not do it first, then their opponent will beat them to it. They both cut their prices, and profits reduce back to $20 million.

The game theory predicts that two firms who use strategic behaviour will always end up worse off due to their incentive to cheat, therefore it concludes that price competition between oligopolistic firms should be strongly avoided (Tragakes, 2015). This model also reveals the strategic interdependence that exists between oligopolies and their conflicting incentives to cheat or collude. Unfortunately, this prediction is not easily testable due to the inherent shortcomings of the game theory discussed previously. However, there have been cases which indicate that the conclusions of the Prisoner’s Dilemma have been accurate. In the 1950’s, GM, Ford and Chrysler dominated the U.S. Market for automobiles and colluded with one another when they introduced their own versions of small cars. During the 70’s, Chrysler continually introduced sustained increases in the price of its small cars which were meant to be followed by GM and Ford. However, in an attempt to capture some of Chrysler’s market share, GM increased their prices by a smaller margin than Chrysler. They were successful until Chrysler reduced their price to its original one. This shows how the conflicting incentives to cheat and collude due to the strategic interdependence between oligopolistic firms will always leave them worse off.

- Cournot Duopoly Model

The Cournot Duopoly Model also uses game theory to predict that firms have within a duopoly market structure are more beneficial to society compared to monopolies as they produce greater quantities at lower prices. Suppose within an industry, there exist two firms who produce a homogenous product, who act strategically, do not collude and are completely rational. If any of these firms wants to increase their profit, they can do so by increasing prices. However, increasing profitability through higher prices results in a loss of market share which is why ‘Cournot’s approach attempts to maximise both market share and profits by defining optimum prices’ (Ferguson, n.d.). This price would be accepted by both firms, making it a Nash Equilibrium. Since this approach assumes that firms compete through changes in quantities, it predicts that this market structure is better able to produce socially optimal quantities of the good compared to monopolies.

While this model is not easily testable, its predictions are considered to be accurate because it is generally agreed upon by economists that from society’s point of view, monopolies the worst market structure. However, in real life, monopolies are either illegal or regulated by the government, so they may produce market outcomes more favourable than that of firms within a duopoly.

The word normative means to follow a set of rules in the context of your behaviour. The model does generate a few normative conclusions. The player should follow the option which is most likely to give them the better outcome, even if this means getting a lower reward but at a lower risk. Furthermore, by forming groups and conducting cooperative game theory, you should have a better chance of gaining a good result as you will be turning potential enemies into allies.

Improving the game theory would allow it to transcend some of the challenges it currently faces. By doing this, it can achieve or produce conclusions that would be more useful to different stakeholders within society. The game theory is used to answer how individuals behave in strategic situations when ‘opponents know very little about one another’ (Kovach, Gibson & Lamont, 2015). While many oligopolistic firms may fit this notion as they attempt to shield information from their rivals, this assumption may not always hold in the real life. In such cases, the game theory model becomes less accurate in ‘providing solutions for complex real-world conflicts as information differences exist between key players’ (Kovach, Gibson & Lamont, 2015). Hence, a way to improve the game theory would be to develop different game models for each player, in order to take into account ‘the differences in each player’s information, beliefs and understandings of the game’ (Kovach, Gibson & Lamont, 2015).

Another shortcoming of the game theory is that it assumes that players act strategically and always consider the competitors’ response to their actions. However, not every manager thinks in this mindset which ultimately invalidates its conclusions. Additionally, this model can only be effective when managers make sense of the expected positive and negative payoffs of their actions. In reality, this is difficult because ‘most firms will not have enough knowledge of their own payoffs, let alone those of their competitors’ (Osak, 2010). Unfortunately, these challenges are inherent to the nature of the model and there remains no way to improve it. This means there remains an increasing need ‘for empirical tests of these theories’, which are frankly impossible due to its highly simplified assumptions (Reinganum, 1984).

The game theory significantly impacts our understandings of oligopolistic firms, ‘given that each firm functions as part of a complex web of interactions’, where a business decision taken by one firm can severely affect the profits of another (Osak, 2010). Hence, this model allows firms to formulate an optimal strategy in order to reach a desirable outcome based on a pre-calculated payoff matrix. It also provides significant insights into the behaviour of firms in terms of their incentives to collude and cheat. This can be useful when studying the operations of cartels like OPEC and other forms of tacit collusion between oligopolistic firms.

This model can also be useful for the ways that government make decisions relating to international trade. For instance, countries who would want to achieve allocative efficiency within the market for common access resources like fish may cooperate to introduce a cap and trade scheme. However, these countries now face a dilemma. If Country A joins then they can only catch a set quantity of fish whereas if they remain independent, they are free to catch as many fish as they want. At the same time, Country A believe that other countries will not join the agreement, allowing them to catch a higher quantity of fish within that area. This demonstrates how game theory can be used by governments when making decisions related to international trade and cooperation.

The game theory looks over the behavioural decision making of individuals in situations where they are against an opponent. Many assumptions have to be made and these are not always present in the real world. The Nash Equilibrium has shown strategic behaviour between competitors will always end up worse off due to their incentive to cheat by collusion and have a win-win situation between themselves. The Cournot Duopoly model shows that competitors can maximise their market share and profits by finding the optimum prices. The game theory could be used to describe many real world situations. However, the model is not perfect and has room for improvement. It considers players to always act strategically and think of their competitors response, which is not always the case.

- Abbott, P., & Panu K. S. Kallio. (1996). Implications of Game Theory for International Agricultural Trade. American Journal of Agricultural Economics, 78(3), 738-744. doi:10.2307/1243297
- Economics Discussion. (2019). Game Theory: Assumptions and Structure of Game Theory. [online] Available at: http://www.economicsdiscussion.net/game-theory /game-theory-assumptions-and-structure-of-game-theory/3797 [Accessed 1 Dec. 2019].
- Ferguson, T. S. (n.d.). Game Theory. Retrieved from https://www.math.ucla.edu/~tom/ Game_Theory/bimat.pdf.
- Gallego, L. (n.d.). Oligopoly I: Cournot duopoly. Retrieved from https://policonomics.com /lp -oligopoly-cournot-duopoly-model/.
- Investopedia. (2019). Prisoner’s Dilemma Definition. [online] Available at: https://www.investopedia.com/terms/p/prisoners-dilemma.asp [Accessed 1 Dec. 2019].
- Kovach, Nicholas S., G., S., A., Lamont, & B., G. (2015, August 19). Hypergame Theory: A Model for Conflict, Misperception, and Deception. Retrieved from https://www.hindawi.com/journals/gt/2015/570639/.
- MBA Crystal Ball. (n.d.). Introduction to Game Theory in Economics | MBA Crystal Ball. [online] Available at: https://www.mbacrystalball.com/blog/economics/game-theory/ [Accessed 29 Nov. 2019].
- Osak, M. (2010, July 24). Using Game Theory to Improve Strategic Decision Making. Retrieved from https://business.financialpost.com /executive /using-game-theory-to-improve-strategic-decision-making.
- Reinganum, J. (1984). Practical Implications of Game Theoretic Models of R&D. The American Economic Review, 74(2), 61-66. Retrieved from www.jstor.org/stable/1816331
- Singh, P. (2019, September 30). Oligopoly and Its Most Famous Examples. Retrieved from https://www.luckscout.com/oligopoly/

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