Game Theory Essay

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Game theory is the application of applied mathematics and evolutionary theory to understanding people’s strategies in maximizing benefits. Game theory began as a system for understanding card games with its first practical application to economics in the early 20th century. Several human behavioral sciences (psychology, sociology, and anthropology) use game theory to understand why individuals may be in conflict or cooperation given specific situations.

The two main representations of game theory are normal, which is sometimes referred to as strategic, and extensive form games. In the normal form game, each player has two strategies-cooperate or defect. If player one defects and player two cooperates, the defecting player’s payoff (reward) is higher (e.g., $6) than the player who cooperates (e.g., $0). If both player one and two cooperate, they receive an equal payoff (e.g., $3). If both player one and two defect, they receive an equal payoff (e.g., $0). The players do not know what the others’ actions will be before they make their own choice, thereby limiting their ability to cooperate by prior agreement with each other. Each play does not connect to the next.

The extensive form game is structurally similar to a normal form game, but instead tracks player choices over time, thereby enabling the assessment of more complex decision-making strategies. Extensive form games also enable players to make decisions based upon what choice the other player has made. For example, if one player decides to cooperate, the second player may then decide to cooperate (both players’ payoff is $3) or defect (player two’s payoff is $6 and player one’s, $0). In addition, if both defect, they both receive no payoff. Since players make decisions based on previous choices, extensive form games make use of diagrams, often tree diagrams, to represent the order and outcomes of choices over time.

There are several variations of the normal and extensive form games. In a symmetric game variation, the payoffs are the same for both players. In an asymmetric game variation, the payoffs are different for each player and the strategy for each player to do well in the game is different. A game may be zero sum, in that the result of the game always equals zero because when one player has a positive payoff, the other takes a negative payoff. To explore the impact of games on decision making, one may also change the length of the game, number of players, and strategies available to the players.

In environmental anthropology, game theory has been widely used in studies of the Tragedy of the Commons. Robert Axelrod applied the normal form game-the prisoner’s dilemma-to the Tragedy of the Commons. Axelrod and others are concerned with the problem of explaining why and how cooperation evolved without central authority. By being able to explain the evolution of cooperation, it can be determined how much, and in what capacity, cooperation may avert the Tragedy of the Commons. With this knowledge, viable solutions relying on realistic expectations of cooperation should result in conservation of common resources.

As important as explaining the evolution of cooperation is to commons management, what is essential is an understanding of how to maintain cooperation in a community, because only through such understanding can a program succeed. The stability of a cooperative strategy, as understood within a prisoner’s dilemma game, depends on the ability of a dominant strategy to resist invasion by a free-riding strategy.

Bibliography:

  1. Robert Axelrod, The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration (Princeton University Press, 1997);
  2. Robert Axelrod, The Evolution of Cooperation (BasicBooks, 1984);
  3. Drew Fudenberg and Jean Tirole, Game Theory (MIT Press, 1991);
  4. John Maynard Smith, Evolution and the Theory of Games (Cambridge University Press, 1982).

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