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Game of Theory

Topic: Game theory
by Simon, 2019 Cohort

Complex problems which involve numerous stakeholders and perspectives can lead to often tedious and difficult positions of decision making. These problems may range from the individual level to complicated modelling of businesses and human behaviour. Game theory, developed by John von Neumann, is a form of problem solving which incorporates decision making and mathematical modelling to explain possible outcomes of scenarios whilst considering all perspectives and options and the consequences of these actions. With this method of prediction, it is possible to explore a range of conclusions and provide insight, even to the extent of prescribing what decision should be made in complex situations.

Game theory includes various ‘game’ types, which include cooperation, symmetry, zero-sum and a combination of types to achieve more complex modelling. Poker is an example of a zero-sum game as one player wins however much the others lose. However, an assumption that game theory is based on is that all players involved behave rationally which is not usually the realistic outcome. The concept of game theory relies on how people should play games based on rationally predicting the behaviour of others and logical assumptions.

A well-known example of game theory is the Prisoner’s Dilemma. This problem takes the assumption of the rationality of all players and explains why not cooperating is the decision they should make despite not leading to the best possible outcome. Two prisoners are being interrogated with no means of communicating with each other. Each prisoner is given the opportunity to betray the other or cooperate by remaining silent and depending on their choice changes the sentence they must serve. Betraying the partner in crime is the rational decision since it provides a greater reward and less risk. Decision making such as this can be described by game theory and applied to much more complex issues which can be interpreted can provide reasonable solutions.

Irrational decision making can lead to drastically altering the predicted equilibrium. The behaviour of the irrational player may seem to imply that they are not maximising their level of success compared to rational players, although this is not always the case. Consider an auction for an iPhone, where each bidder’s valuation for the iPhone is between $0 and $200. The rational player would bet $0 whereas the irrational one would bid $200, leading to them ‘winning’ the bet. The rational player knows this and decides not to bet as they decide its not worth it, again leading to the victory of the irrational player.

Despite the roots of game theory being procured from mathematical modelling it is now used in a wide-spread of disciplines including computer science, economics, politics, war, biology, psychology and is apparent throughout the social sciences in dissecting complex issues. The application of game theory has become integrated into these disciplines to an extent where it is essential in understanding the complex nature of relative issues and to the advancement of these fields. It may seem that the mathematics behind the theory would not be comprehended by the less mathematically advanced individual. But this is not so, a clear account of game theory can be provided through metaphor and the intricacies explained.

Explore this topic further#

  • Wikipedia page{.link-ext target=”_blank”}
  • Prisoner’s dilemma{.link-ext target=”_blank” } as a classic example of Game Theory
  • Why do competitors open their stores next to one another? Jac de Haan on TED-ed (4 mins) a great introduction to Hotelling’s Law{.link-ext target=”_blank” }, explaining why similar shops set up next to one another YouTube{.link-ext target=”_blank”}
  • Hendricks, V., Hansen, P. and Aumann, R. (2007). Game theory. [Copenhagen]: Automatic Press VIP.
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Complex problems which involve numerous stakeholders and perspectives can lead to often tedious and difficult positions of decision making. These problems may range from the individual level to complicated modelling of businesses and human behaviour. Game theory, developed by John von Neumann, is a form of problem solving which incorporates decision making and mathematical modelling to explain possible outcomes of scenarios whilst considering all perspectives and options and the consequences of these actions. With this method of prediction, it is possible to explore a range of conclusions and provide insight, even to the extent of prescribing what decision should be made in complex situations.

Game theory includes various ‘game’ types, which include cooperation, symmetry, zero-sum and a combination of types to achieve more complex modelling. Poker is an example of a zero-sum game as one player wins however much the others lose. However, an assumption that game theory is based on is that all players involved behave rationally which is not usually the realistic outcome. The concept of game theory relies on how people should play games based on rationally predicting the behaviour of others and logical assumptions.

A well-known example of game theory is the Prisoner’s Dilemma. This problem takes the assumption of the rationality of all players and explains why not cooperating is the decision they should make despite not leading to the best possible outcome. Two prisoners are being interrogated with no means of communicating with each other. Each prisoner is given the opportunity to betray the other or cooperate by remaining silent and depending on their choice changes the sentence they must serve. Betraying the partner in crime is the rational decision since it provides a greater reward and less risk. Decision making such as this can be described by game theory and applied to much more complex issues which can be interpreted can provide reasonable solutions.

Irrational decision making can lead to drastically altering the predicted equilibrium. The behaviour of the irrational player may seem to imply that they are not maximising their level of success compared to rational players, although this is not always the case. Consider an auction for an iPhone, where each bidder’s valuation for the iPhone is between $0 and $200. The rational player would bet $0 whereas the irrational one would bid $200, leading to them ‘winning’ the bet. The rational player knows this and decides not to bet as they decide its not worth it, again leading to the victory of the irrational player.

Despite the roots of game theory being procured from mathematical modelling it is now used in a wide-spread of disciplines including computer science, economics, politics, war, biology, psychology and is apparent throughout the social sciences in dissecting complex issues. The application of game theory has become integrated into these disciplines to an extent where it is essential in understanding the complex nature of relative issues and to the advancement of these fields. It may seem that the mathematics behind the theory would not be comprehended by the less mathematically advanced individual. But this is not so, a clear account of game theory can be provided through metaphor and the intricacies explained.

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