Within economics, game theory occupied a rather isolated niche in the 1960s and 1970s. It was pursued by people who were known specifically as game theorists and who did almost nothing but game theory, while other economists had little idea what game theory was. Game theory is now a standard tool in economics. Contributions to game theory are made by economists across the spectrum of fields and interests, and economists regularly combine work in game theory with work in other areas.
Game theory is a theoretical framework for conceiving social situations among competing players. In some respects, game theory is the science of strategy, or at least the optimal decision-making of independent and competing actors in a strategic setting. Game theory tries to understand the strategic actions of two or more "players" in a given situation containing set rules and outcomes. Any time we have a situation with two or more players that involves known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes.
Nash equilibrium
Nash equilibrium is a concept in game theory where the game reaches an optimal outcome. This is a state that gives individual players no incentive to deviate from their initial strategy. The players know their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player. Nash equilibrium was discovered by American mathematician, John Nash. He was awarded the Nobel Prize in Economics in 1994 for his contributions to the development of game theory.
Example
Imagine two competing companies: Company A and Company B. Both companies want to determine whether they should launch a new advertising campaign for their products.
If both companies start advertising, each company will attract 100 new customers. If only one company decides to advertise, it will attract 200 new customers, while the other company will not attract any new customers. If both companies decide not to advertise, neither company will engage new customers. The payoff table is below:
Company A should advertise its products because the strategy provides a better payoff than the option of not advertising. The same situation exists for Company B. Thus, the scenario when both companies advertise their products is a Nash equilibrium.
Prisoners dilemma
The Prisoner's Dilemma is the most well-known example of game theory. Consider the example of two criminals arrested for a crime. Prosecutors have no hard evidence to convict them. However, to gain a confession, officials remove the prisoners from their solitary cells and question each one in separate chambers. Neither prisoner has the means to communicate with the other.
If both confess, they will each receive a five-year prison sentence.
If Prisoner A confesses, but Prisoner B does not, Prisoner A will get one year and Prisoner B will get eight years.
If Prisoner B confesses, but Prisoner A does not, Prisoner A will get eight years, and Prisoner B will get one year.
If neither confesses, each will serve two years in prison.
The most favorable strategy is to not confess. However, neither is aware of the other's strategy and, without certainty that one will not confess, both will likely confess and receive a five-year prison sentence. The Nash equilibrium suggests that in a prisoner's dilemma, both players will make the move that is best for them individually but worse for them collectively.
Here are a few ways in which ideas drawn from the Prisoner's Dilemma can be applied to economic analysis:
Oligopoly competition: The Prisoner's Dilemma can be used to model oligopoly competition, where a small number of firms dominate in a market. In this context, each firm has an incentive to maximize its profits, but if all firms do so, it can lead to a suboptimal outcome for the industry as a whole. The Prisoner's Dilemma provides a framework for understanding how firms can coordinate their actions perhaps through tacit collusion to achieve a better outcome.
Public goods provision: The provision of public goods, such as clean air or national defense, is often subject to the free-rider problem, where individuals have an incentive to enjoy the benefits of the public good without contributing to its provision. The Prisoner's Dilemma provides a framework for understanding how individuals can be incentivized to contribute to the provision of public goods.
Environmental policy: The Prisoner's Dilemma can be used to model situations where individuals or firms are polluting a common resource, such as air or water. Each individual or firm has an incentive to pollute in order to maximize its own profits, but if all individuals or firms do so, it can lead to a suboptimal outcome for everyone. The Prisoner's Dilemma provides a framework for understanding how environmental policy can be designed to incentivize individuals or firms to reduce pollution.
Works Cited
Comments