Game Theory

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What is 'Game Theory'

Game theory is a framework for hypothetical 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. The key pioneers of game theory were mathematicians John von Neumann and John Nash, as well as economist Oskar Morgenstern.

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1. Nash Equilibrium

2. Tit For Tat

3. Mechanism Design Theory

4. John Harsanyi

BREAKING DOWN 'Game Theory'

The focus of game theory is the game, which serves as a model of an interactive situation among rational players.  The key to game theory is that one player's payoff is contingent on the strategy implemented by the other player.  The game identifies the players' identities, preferences, and available strategies and how these strategies affect the outcome. Depending on the model, various other requirements or assumptions may be necessary.
Game theory has a wide range of applications, including psychology, evolutionary biology, war, politics, economics, and business. Despite its many advances, game theory is still a young and developing science.

Impact on Economics and Business

Game theory brought about a revolution in economics by addressing crucial problems in prior mathematical economic models. For instance, neoclassical economics struggled to understand entrepreneurial anticipation and could not handle imperfect competition. Game theory turned attention away from steady-state equilibrium toward the market process.
In business, game theory is beneficial for modeling competing behaviors between economic agents.  Businesses often have several strategic choices that affect their ability to realize economic gain.  For example, businesses may face dilemmas such as whether to retire existing products or develop new ones, lower prices relative to the competition, or employ new marketing strategies.  Economists often use game theory to understand oligopoly firm behavior.  It helps to predict likely outcomes when firms engage in certain behaviors, such as price-fixing and collusion.

Types of Game Theory

Although there are many types (e.g. symmetric/asymmetric, simultaneous/sequential, et al.) of game theories, cooperative and noncooperative game theories are the most common.  Cooperative game theory deals with how coalitions, or cooperative groups, interact when only the payoffs are known.  It is a game between coalitions of players rather than between individuals, and it questions how groups form and how they allocate the payoff among players.  Noncooperative game theory deals with how rational economic agents deal with each other to achieve their own goals.  The most common noncooperative game is the strategic game, in which only the available strategies and the outcomes that result from a combination of choices are listed.  A simplistic example of a real-world noncooperative game is Rock-Paper-Scissors.

Classic Game Theory Example

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 each other.  Officials present 4

1. If both confess, they will each receive a 5-year prison sentence.  
2. If prisoner 1 confesses but prisoner 2 does not, prisoner 1 will get 3 years and prisoner 2 will get 9 years. 
3. If prisoner 2 confesses but prisoner 1 does not, prisoner 1 will get 10 years and prisoner 2 will get 2 years. 
4. If neither confesses, each will serve 2 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 5-year prison sentence.