Economic Applications of Game Theory

This article focuses on the economic applications of game theory. The foundation for the basis of game theory is introduced followed by examples of some simple games. The concept of Two-Person Zero-Sum Games is evaluated. There is also a discussion on how social norms influence behaviors when playing games. One particular game, the exclusion game, is highlighted.

Keywords: Bona fide player; Combinatorics; Exclusion Game; Game Theory; Lausanne Theory; Norms; Robinson Crusoe Economy; Social Exchange Economy; Zero-Sum Games

Economic Applications of Game Theory

Overview

Economically speaking, people have choices, wants and needs. The ultimate goal of economic action is to satisfy one's desires. While it is expected that individuals will act in a rational way in order to be in compliance with social norms, the process is complicated due to external factors such as prices, production, gains and expenses. Additionally, individual behavior is dictated by choice, or free will. The act of making a rational decision regarding choices involves what is referred to as social exchange economy.

Social Exchange Economy Models

A social exchange economy can be described in terms of three models, which are:

• Robinson Crusoe Economy

This type of economy focuses on how the economic well being of a single person is influenced by a single will. The person in this model must decide how to satisfy a need to obtain commodities that will provide maximum satisfaction. For example, Crusoe is given information that describes his desires and commodities. His goal is to select a combination of choices that will give him maximum satisfaction. The key to this model is that Crusoe controls all of the variables that influence the decision. Once Crusoe enters into a social exchange economy, he loses some of his autonomy. He no longer has control over all of the variables as he seeks to enter into an exchange relationship with another person.

• Free Competition

In contrast to the Robinson Crusoe model, free competition is a theory that emphasizes the notion that there are many people involved in a social exchange economy. In addition, these individuals are aware that their choices have an effect on the decision making process of others. The participants in this process believe that as more people enter into the equation, the influence of each person becomes a mute point. Free competition encourages diversity and variety while discouraging seller involvement in monopolies, duopolies, and oligopolies.

• Lausanne Theory

This theory values individual planning as well as an interrelated network of individual plans. One can assume that this theory takes the best of the Crusoe model as well as the free competition philosophy. In essence, each individual develops an individual plan and utilizes it to interact with the masses and obtain maximum satisfaction.

As one looks at the individual and collective behaviors of a group, the focus centers around how one obtains maximum satisfaction, which could be referred to as the game.

Individuals play the game, which is governed by a set of rules. Each player has the choice of making a move, which ultimately has consequences. In many cases, the players participate in two types of procedures; direct and inverted signaling.

Game Theory

Game theory came to prominence in 1944 when von Neumann and Morgentern published a book entitled, "Theory of Games and Economic Behavior." The second edition was published in 1947. One of the reasons for the book's popularity was its focus on decision- making involving more than one decision maker. World War II activities led many scholars to seek opportunities to model decision situations. At the time, the military was a large proponent of game theory.

Game Theory can be viewed as a mechanism for resolving conflicts of interest (Thomas, 1984). Conflicts of interest evolve as a result of disagreement between people. According to Thomas (1984), game theory:

  • Is a way to resolve these types of conflicts;
  • Describes types of results that may occur;
  • Suggests the best solution to the game and how the players should respond;
  • Suggests which players will work together to resolve problems (p. 15).

Some of the key assumptions for a game include:

  • There are at least two participants who are referred to a players;
  • Players make moves, which are decisions made by the players;
  • Players receive a payoff at the end of the game; and
  • Players develop strategies in order to win the game.

Players are constantly developing strategies throughout the game. The goal is to anticipate moves to make, which will lead to ultimate victory. Players seek to gain the greatest payoff in order to win. Payoff can be explained in terms of two concepts — zero sum and non-zero sum games. Zero sum occurs when the payoff for all players is zero regardless of the strategy. In this scenario, there is always a winner and a loser. Poker is an example of this strategy. On the other hand, games that do not have a clear distribution of wins and losses are considered non-zero sum games.

Game Theory & Economics

How is game theory applied to economic decision making and forecasting? Firstly, forecasting involves the ability to predict future behavior based on historical evidence. For example, forecasting models are applied to problems that need to be resolved on a number of levels (i.e. managerial strategic plan, operational decisions). A manager may want to review sales from previous years in order to predict what the sales will be for a certain product line in the future. There is a review of consumer trends to predict future spending habits. Game theory allows the manager to speculate what the different alternatives will be as he seeks to make the decision that will yield the greatest sales.

Shefrin (2002) has argued that "traditional game theory assumes that players are fully rational in respect to preferences (expected utility), judgments, and strategic choices" (p. 375). Scholars have supported the concept of rational choice theory to support this notion. The concept of rational choice theory is significant in microeconomics. In the model, the assumption is that individuals will make choices based on favorable conditions, preferences and constraints.

When making a choice, one can assume that all parties will make decisions based on amount of return. Each player studies all of the possible choices and determines the return for each. The alternative with the optimum "win" should be selected in order for this process to yield great economic outcome.

In order to take advantage of all economic tools, one may elect to create a simulation by role-playing. Role-playing can be argued as a more plausible way of forecasting given its outcomes. "Role-playing outcomes emerge from the actual interaction of real human beings, whereas, game theoretic outcomes emerge from the theoretical interaction of idealized human beings" (p. 382). There may be times when a player cannot theoretically conceive what the possible outcomes could be given the limitations of the environment. However, if the players engage in a role-playing scenario, each can use external factors and the environment to visualize what potential outcomes could be.

Application

Two-Person Zero-Sum Games

A Two-Point Zero-Sum game involves two players; one player wins and one player loses. According to Rapoport (1966), the following occurs in this type of scenario:

  • The game begins by one or more of the players making a choice among a number of specified alternatives. For example, in the game of Tic-Tac-Toe, the first player has a choice of eight boxes to make a mark of "X" or "O."
  • After the choice associated with the first move is made, a certain situation occurs. This situation determines who is to make the next choice and what alternatives are open to the player. Once the player places a "X" or "O" in a box, the next player will make a mark.
  • The choices made by the players may or may not become known. In the game of Tic-Tac-Toe, the choices are known.
  • If a game is described in terms of successive moves, there is a termination rule. Each choice made by a player determines a certain situation. When such a situation occurs, the game is ended. The game ends when one player has placed three of his marks in a row. A win can occur as soon as the fifth move takes place.
  • Every play of a game ends in a certain situation. Each of these situations determines a payoff to each bona fide player (p. 18-21).

Another way to describe a two-person zero-sum game is in terms the process of the game. One can list all of the possible sequences of moves that a player can make and what the payoff is at the end of the sequence. A tree graph is a way that this information can be documented. When creating the graph, one can list multiple move points, which represent at what point a move must be made. A move is considered a decision made by one of the players or a chance event. All possible moves that can be made are represented by lines that are drawn to the designated point on the tree graph (Thomas, 1984).

Viewpoint

Role of Norms in Game Theory

Some may consider norms to be the basis for human behavior. For example, it has been said that a norm can dictate an individual's behavior. Theft is consider to be an illegal act. Therefore, the norm is that one does not steal if he/she does not want to go to jail. A person who steals understands that it is an illegal act against the rules of society. Researchers in this area have determined that:

  • An individual's behavior is a reflection of society's norms;
  • Social order is a result of norms encouraging cooperation and pro-social behavior (Arrow, 1974; Elster, 1989).

There are social researchers, who believe that norms effect behavior as a result of their influence on a person's motivation (Elster, 1989; Gintis, 2003; Becker, 1996). For example, if an individual's motivation is to win at all costs, this particular individual may consider cheating (a behavior) even if it is against society's norm of appropriate behavior. The individual has insulated himself against feeling any type of remorse for acting in a deviant manner because the motivation to win at all costs has superceded the need to be in compliance with society.

Given this scenario, it is not surprising that "self-interest and opportunism have recently become the target of criticism by behavioral economics theorists, who urge the introduction of a more complex account of the motivations of economic agents" (Sacconi & Faillo, 2005, p. 57). Sacconi and Faillo (2005) conducted a study to determine at what point players who have contributed to the choice of a norm actually comply with the norm, especially when the norm does not align with the motivation of the players. In essence, under what conditions will a player desert the characteristics of a person adhering to the self-interest based model?

The study was based on an experiment called the Exclusion Game. The participants were asked to choose how to play the game once they had agreed to play according specific rules. The experiment was conducted at the Computable and Experimental Economics Laboratory of the University of Trento. There was a total of 150 participants. Fifteen participants were active in each session, and there was a total of 10 sessions.

The participants were divided into groups of three individuals. Two of the participants were active players and one player did not have an active role. This one player, the "dummy player", had to rely on the decisions of the active players and his/her rewards were determined by the decisions made by the active players. The three choices were to ask for half of the money, ask for one third of the money or ask for one fourth of the money. The agreement was that if both of the players asked for half of the money, the dummy player would not receive anything. However, if both active players asked for one third of the money, the pot would be split equally among the three players.

Saconi and Faillo (2005) found that:

  • About 85% of the players chose the second principle at least once in the first phase.
  • Considering the players in phase one who chose the second principle at least once, and in phase two chose the first principle (approximately 60% of the players), those who expected that the other active players would select the first principle agreed to support this decision
  • Choosing a principle induced a change in the behavior of a significant number of the players (p. 103).

Conclusion

As one looks at the individual and collective behaviors of a group, the focus centers around how one obtains maximum satisfaction; or, how one plays the game. Within such games, each player as the choice of making a move, which ultimately has consequences.

Game theory came to prominence in 1944 when von Neumann and Morgentern published a book entitled, "Theory of Games and Economic Behavior." The second edition was published in 1947. One of the reasons for the book's popularity was its focus on decision-making involving more than one decision maker. World War II activities led many scholars to seek opportunities to model decision situations. At the time, the military was a large proponent of game theory.

Game Theory can be viewed as a mechanism for resolving conflicts of interest (Thomas, 1984). Conflicts of interest evolve as a result of disagreement between people. According to Thomas (1984), game theory:

  • Is a way to resolve these types of conflicts;
  • Describes types of results that may occur;
  • Suggests the best solution to the game and how the players should respond;
  • Suggests which players will work together to resolve problems (p. 15).

Some of the key assumptions for a game include:

  • There are at least two participants who are referred to a players;
  • Players make moves, which are decisions made by the players;
  • Players receive a payoff at the end of the game; and
  • Players develop strategies in order to win the game.

Researchers in this area have determined that: An individual's behavior is a reflection of society's norms; and, social order is a result of norms encouraging cooperation and pro-social behavior (Arrow, 1974; Elster, 1989). However, there are social researchers, who believe that norms effect behavior as a result of their influence on a person's motivation (Elster, 1989; Gintis, 2003; Becker, 1996). For example, if an individual's motivation is to win at all costs, this particular individual may consider cheating (a behavior) even if it is against society's norm of proper behavior. The individual has insulated himself against feeling any type of remorse for acting in a deviant manner because the motivation to win at all costs has superseded the need to be in compliance with society.

Terms & Concepts

Bona Fide Player: A player who makes choices and receives payoffs.

Exclusion Game: — Game that provided players two alternatives. One alternative rewarded all of the players equal benefits, whereas, the other alternative only rewarded the active players.

Game Theory: — A mechanism for resolving conflicts of interest.

Lausanne Theory: — A theory that values individual planning as well as connecting individual plans so that they are interrelated.

Norms: Rules that dictate behavior.

Robinson Crusoe Economy: A type of economy focusing on how the economic well being a single person is influenced by a single will.

Social Exchange Economy: A theory that suggests that human behavior is rewards received as a result of what is important to the players.

Zero-Sum Games: A game where there are two players and the payoff for all players is zero regardless of the strategy.

Bibliography

Arrom, K. (1974). The limits of organization. New York: Norton & Company.

Becker, G. (1996). Accounting for tastes. Cambridge, MA: Harvard University Press.

Brink, R., Katsev, I., & Laan, G. (2011). A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure. International Journal of Game Theory, 40, 591-616. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=63577473&site=ehost-live

Elster, J. (1989). Social norms and economic theory. Journal of Economic Perspectives, 3, 99-117.

Gintis, H. (2003). The hitchhiker's guide to altruism: Gene-culture coevolution, and the internalization of norms. Journal of Theoretical Biology, 220, 407-418.

Owen, G. (2013). Applications of game theory to economics. International Game Theory Review, 15, -1. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=89438288&site=ehost-live

Qin, C. (2013). Contests, managerial incentives, stock price manipulation, and advance selling strategies: introduction. Pacific Economic Review, 18, 162-163. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=87549828&site=ehost-live

Rapoport, A. (1966). Two-person game theory: The essential ideas. Ann Arbor, MI: The University of Michigan Press.

Richardson, B. (2006). Game theory: History and applications. Retrieved March 1, 2009, from education.uncc.edu/cmste/summer/2006%20History%20of%20Mathematics/ Ben.doc

Sacconi, L., & Faillo, M. (2007). Norm compliance: The contribution of behavioral economics theories, Discussion Paper. Department of Economics, University of Trento.

Sacconi, L., & Faillo, M. (2005). Conformity and reciprocity in the Exclusion Game: An experimental investigation, Discussion Paper. Department of Economics, University of Trento.

Shefrin, H. (2002). Behavioral decision making, forecasting, game theory, and role playing. International Journal of Forecasting, 18, 375-382.

Thomas, L.(1984).Game theory and applications. New York: Ellis Horwood Limited.

Suggested Reading

Dogan, G. & Assen, M.V. (2009). Testing models of pure exchange. Journal of Mathematical Sociology, 33, 97-128. Retrieved April 1, 2009, from EBSCO Online Database Academic Search Complete. http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=37208253&site=ehost-live

Ferreira, N., Kar, J. & Trigeorgis, L. (2009). Option games. Harvard Business Review, 87, 101-107. Retrieved April 1, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=36589943&site=ehost-live

Finkelstein, N., Facey, B.A. & Finkelstein, J. (2009). Game theory and the Competition Act: Winners and losers in Canadian merger review. World Competition: Law & Economics Review, 32, 113-133. Retrieved April 1, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=37151383&site=ehost-live

Guastello, S.J. (2009). Evolutionary game theory and leadership. American Psychologist, 64, 53-54. Retrieved April 1, 2009, from EBSCO Online Database Academic Search Complete. http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=36129817&site=ehost-live

Essay by Marie Gould

Marie Gould is an Associate Professor and the Faculty Chair of the Business Administration Department at Peirce College in Philadelphia, Pennsylvania. She teaches in the areas of management, entrepreneurship, and international business. Although Ms. Gould has spent her career in both academia and corporate, she enjoys helping people learn new things — whether it's by teaching, developing or mentoring.