Game theory (Business)

Situations arise all the time prompting individuals to consider whether their own choices or collaborative actions will yield greater payouts. Game theory provides a rich framework for studying interactive decision-making processes. Most decisions, whether collective or individual, usually lead to actions, but games require two or more players acting and reacting in a strategic manner. In our dual roles as employees and as customers, we often exhibit certain behaviors in the marketplace that correspond with those roles and the structures of markets in which we conduct our transactions. Competition and free enterprise are ingrained ideals that favor low prices and wide varieties of consumer goods and services all the while inciting producers to use scarce resources as efficiently and effectively as possible. Digging a little deeper behind the competitive market scene, however, we may find producers who are competitive in appearance but who really have the capacity to charge high prices, maintain market shares, and devise arrangements that empower them to behave as if they were monopolists. A market structure in which a few sellers behave likewise while providing goods or service characterizes an oligopoly. A key feature common amongst oligopolies is their interdependence and their perpetual search for prices. This essay improves the reader's ability to ponder and to answer the question: How do producers know when the price is right?

Imagine a class meeting in which the economics' professor devises an exercise for students to bid on and receive $20.00 in cash. It could be more depending on what college you attend, but the actual dollar amount and the auction rules are insignificant in relation to the learning outcome potential. Like any auction, the highest bidder gets the goods fair and square without any strings, though some bidders are more lucky and/or strategic than others. In this instance, the goods are two $10.00 bills and the professor divides the class at random into two groups of bidders with one sent to visit a nearby empty classroom. For various reasons pending disclosure, your own bid and potential payout will likely differ depending on which group you belong to. One group consists of classmates who have the privilege of discussing their bids with other members of their group. The other group consists of classmates who must remain quiet as they determine their individual bids. It is entirely appropriate to speculate at this point about which individuals or group would receive the bill and the strategies that lead to that outcome.

As a players' board is in sight, the basic rules and payouts set forth by game theory are beginning to emerge. They are relevant to our exploration of varied market pricing strategies. The purpose of game theory may be explanatory, predictive, or prescriptive in nature. Whatever purpose fits a given scenario, this essay aims to help the reader answer the following set of questions.

• How does a group of buyers and sellers act in a market environment?
• How should they act?
• Do their independent or interdependent actions prepare them to develop the best response as they move toward convergence at an equilibrium point?

In contemplating the answers to these questions, readers should keep in mind that traditional economics and its bias for competition centers squarely on the actions of individual decision makers who contemplate prices found in the marketplace. However, recent developments in the field of economics give greater attention to the influences on market price originating through the collective, sometimes very strategic, interactions between and among sellers. Those interactions generate a number of implications for consumers. From a consumer perspective, competition is indeed an ideal economic condition that brings the greatest amount of benefit to the greatest number. Consumers want to pay a low price for a variety of goods or services available in large quantities. Usually, consumers get their way as sellers of those items want to retain them and/or to gain patronage through strategies centered largely on competitive prices.

Sometimes sellers will go as far as engaging in price wars; a situation which favors consumers the most. In contrast, sellers prefer to receive the highest price possible and to maintain their market shares. Some sellers may realize cooperation is better for them than competition. The range of cooperative actions available to sellers includes options that may be illegal. Consider the simplified example in which there are only two sellers of an item. It is illegal in the United States for these two sellers to devise a formal agreement that sets, or fixes, the price of a good or service at a specific amount. Certainly, this kind of strategy especially when it goes undetected would alleviate their concerns over retentions of customers and market share. One step removed from formality is the case in which one of the firms publicly announces its plan to raise prices all the while leaving it to the discretion of the other firms to ignore the increase or to follow suit. Some firms stand to realize gains by following suit, but perhaps they will gain more by ignoring the price leader's strategy. In essence, the choices made between these two firms depend on how well they can play the pricing game and how well they understand game theory, market structures, and microeconomics.

The Profit Payout & Economic Theory: Prices & Markets as Game Pieces

Assumptions for Understanding Microeconomics

Microeconomics deals with producer and consumer behaviors in the marketplace and it focuses on the structures of the markets in which suppliers operate. Due in part to the deliberate omission of graphs from this essay, the author encourages readers to consult any economics textbook including those by Arnold (2005), Guell (2007), or McConnell & Brue (2008) whether they do so as they read this essay or afterwards. Aside from the early introduction of graphing techniques and interpretations of basic relationships, students in undergraduate microeconomics courses usually begin their studies by learning a set of assumptions.

• First and foremost, is the ceteris paribus (translation means all else is held constant) assumption.
• The second assumption is that consumers and producers behave as rational agents who have access to full, perfect information relevant to their decisions.
• Another assumption is those agents engage in transactions through which no individual or group brings an inordinate amount of influence to an exchange decision.

Exchanges of items between consumers and producers occur in a market. On the consumer or demand side, students learn very early in their coursework that an inverse relationship exists between price and quantity in accordance with the Law of Demand. Relatively speaking, smaller amounts are in demand at higher prices and vice versa. The specific amounts that consumers are willing and able to purchase at given prices are critical sources of information. The demand curve, or line -- taken here and elsewhere as interchangeable descriptors -- is the graphic construction of those price and quantity combinations. Prices generally reflect an implicit agreement between sellers and buyers who exchange goods and services as they interact in the marketplace. On the producer or supply side, students also learn early in their course work that a positive relationship exists according to the Law of Supply.

Soon afterwards they learn that the price at which producers are willing and able to sell their goods and services is only one constraint. Those prices also take into account the variety of costs that firms incur in their production of goods and services. Total costs are the sum of fixed and variable costs. Fixed costs are those that exist even without any production. Furthermore, they are constant as they do not vary with the scale of production. Some examples of fixed costs include monthly installments paid on machinery, buildings, and land. Variable costs are those that vary with production. Some examples of variable costs include wages, materials, and supplies.

The allocation of costs across larger scales of production results in a variety of cost curve shapes. Graphs depicting these functions show cost on the vertical axis and quantity on the horizontal axis. Average total cost and average variable cost form important U-shaped curves. Their calculation involves dividing them by the production quantity. The lowest points on those curves are significant; at those points is where the marginal cost curve, which is J-shaped, intersects them. Marginal cost is the change in total costs that arise from producing one additional unit.

Firms produce and sell items and they receive a price for each one sold. Total revenue is the mathematical product of price times the quantity sold at each price. Marginal revenue is the change in total revenue that arises from selling one additional unit. Price is equal to marginal revenue in perfectly competitive market structures and it is greater than marginal revenue for imperfectly competitive market structures. Though graphs can become quite confusing with each addition of a line or curve, keep in mind that the marginal revenue line is horizontal in perfectly competitive market structures and it is downward sloping in the other structures.

A key relationship exists where marginal revenue equals marginal cost and where these two curves intersect. The intersection determines the profit-maximizing amount of output. Most, if not all, firms attempt to set production to that amount as they pursue profit-maximizing behaviors. Now, let's bring prices back into the analysis for a short discussion of the rules of production. These rules help gauge whether a firm may continue its operation as a competitive viable entity.

Rules of Production

To comply with the first of two rules, firms must produce at the profit maximizing output, again where marginal revenue equals marginal cost. The second rule is firms must receive a price that is equal to or greater than average variable cost. Why? Their sales must cover, at the least, average variable costs and contribute something toward average fixed costs. In other words, they must cover their variable inputs, labor costs for instance, and make payments on their plants and machinery. Moreover, they must operate at or above the shut-down point, which is where the marginal cost curve intersects the average variable cost curve and at the latter's lowest point.

Depending on the market structures in which they operate, some firms can influence the market price and others merely accept the market price for their outputs. Market structure reflects whether a firm makes the market price or it takes the market price. Structures at the extreme ends of a continuum refer to the relative presence or the absence of competition in a market for a specific output or item. The book ends of that continuum are perfect competition and imperfect competition. In addition to whether firms are price makers or price takers, market structure descriptors often include the number of sellers and buyers, the ease with which firms can enter or exit a market, and the volume of advertising for a product.

One example of a highly competitive market structure is agriculture. In this instance, there are numerous buyers and sellers of an agricultural product such as corn. Grain farmers usually take the price dictated by the market. Almost anyone can obtain enough resources to grow corn. Few variations in corn exist so there is very little need to advertise. In contrast, the production of soft drinks serves as an example of a noncompetitive market structure. In this instance, there are numerous buyers but only a few sellers dominate the market. Pepsi and Coca-Cola are two firms that often come to mind with reference to soft drinks. Consequently, these firms make the market price and remarkably little difference exists between the prices of their cola or other beverages. Furthermore, no other producers can obtain the cola recipes and other resources required for developing and producing the beverages.

Competition may occur between them on the basis of price or by virtue of advertising. The latter creates an image in the mind of a buyer regarding product quality and appeal. Soft drink manufacturers attempt to differentiate their products through massive expenditures on advertising and marketing. Many consumers fail to detect any difference between the colas when participating in taste tests and wearing a blindfold, while others can detect differences readily demonstrating their tastes, preferences, and brand loyalties. Many economists view the amount of product differentiation or advertising expenditures as a method that generates an appearance of intense competition though it may really be absent between two dominant firms. Delineation of market power requires an examination of the proportion of total market sales accounted for by some number of the largest firms.

Two common measures of market power include the concentration ratio and the Herfindahl Index (HI). Calculating the concentration ratio for the four largest firms (the CR4) involves dividing the dollar amount of their sales by the dollar amount of total market sales. For example, the CR4 in the beer market is approximately 90 meaning that the four largest firms manufacture and sell 90 percent of the market's beer. Farthest from perfect competition on the market structure continuum is a monopoly (one seller), which is the sole supplier of an item for the entire market. For a monopolist, the CR1 would be 100 percent, which is the maximum for a concentration ratio. Calculating the HI involves squaring the market share of each firm in the market and adding them together; it would be the highest at 10,000 in the case of a monopolist. A step or two down along the market structure continuum from a monopoly is a duopoly (two sellers) and an oligopoly (few sellers). The next section contains theories about oligopolistic pricing and output strategies.

Applications

A key commonality across oligopolies is their perpetual search for firm prices in relation to market prices. Readers may find the following question useful as this essay unfolds: How do they know when the price is indeed right? These search processes frequently resemble games in which each player pursues strategy that is interactive, collusive, or reactive in nature at one time or another.

The main objectives of the game are to set a high price, maximize a market share, and earn a profit while anticipating the other player's moves. Player interactions involve varying degrees of cooperation and usually lead to a set of joint outcomes. Three perspectives provide players with a method by which they can assess their chances for success.

Kinked demand theory and price leadership theory assert that firms set or change their prices in relation to what other firms are doing. Cartel theory asserts that firms, which are formal members of a relatively small group, agree in advance regarding the price and/or the output of their goods and services. The size of the group varies according to whether its origin is artificial or natural. Using these and other descriptors, this section presents each theory in the same order as their introduction above.

Three Perspectives on Playing a Game of Setting the Price

Kinked Demand Curve Perspective

The smallest group of oligopolists is a duopoly, which contains two firms. Each firm faces a demand curve. In the simplest case, these two demand curves have different slopes and one curve is likely to be steeper than the other. Furthermore, at the market level of aggregation, one graph is useful for displaying the two firm's demand curves and their intersection at a meaningful point. Moreover, derivation of the market demand curve results from connecting the segment of the steeper curve that is above the intersection to the segment of the flatter curve that is below the intersection. That connection forms the kinked demand curve and it reflects an assumption critical to kinked demand curve theory.

The underlying assumption is that a firm will follow the price decrease initiated by another firm, but it will ignore a price increase. Consistent with the characteristics of most downward sloping demand curves, readers should keep in mind that consumers are more sensitive to price changes when prices are above the kink and less sensitive to those below the kink. By extension, price hikes for one firm will generate revenue declines while the firm charging a stable price will experience more sales and revenues. As a depiction of these consequences, a kinked demand curve contains an upper segment and a lower segment, but the marginal revenue for the market contains three segments.

Like the kinked demand curve, the marginal revenue curve is steeper in the upper segment than in the lower segment. Furthermore, in the area directly below the kink in the demand curve, the marginal revenue line is vertical in the section between its upper and lower extremities. This vertical section of the marginal revenue curve reflects important information. It conveys a range of prices in which the profit maximizing quantity remains constant. This facet is unique to duopolistic or oligopolistic market structures. Considering that market prices increase less frequently than do production costs, as a result of a firm's reluctance to raise prices and its sensitivity to the actions of rival firms, there is a lot of uncertainty and fluctuations in profit levels.

There is also uncertainty about the validity of kinked demand curve theory. Arnold (2005, p. 542) cites some criticisms. On the theoretical side, further clarification is needed with respect to how an initial market price is set and why it occurs at the kink. On the empirical side of matters, economist George Stigler is widely cited for his studies and the lack of evidence supporting the notion that firms are reluctant to raise prices. Additional scholarly work is needed to refine kinked demand curve theory, which has its roots in the 1930s originating through the work of economist Paul Sweezy. There is more evidence, however, suggesting support for the second of these three theoretical perspectives on oligopoly.

Price Leadership Perspective

Price leadership theory assumes that one firm dominates an industry. It determines market price as most, if not all, other firms follow suit. In contrast to kinked demand theory that assumes firms will ignore price increases and follow price decreases, this theory suggests that other firms will follow the leader's price changes regardless of the direction. Frequently, the dominant firm communicates openly about its movements in price to other firms in the industry.

Arnold (2005, p. 544) provides the following list of firms and industries where one can find open application of price leadership: R. J. Reynolds, tobacco; General Motors, automobiles; Kellogg, breakfast cereals; and, Goodyear Tire and Rubber, tires. Perhaps it would be easy for readers to expand that list using their own personal experiences, especially those instances in which the result was a price war.

Consumers favor low prices and gain much from a price war. In contrast, some problems may arise from a producer's perspective when following the leader in the practice of price reductions. Firms need to realize exactly how far they can reduce prices or they will soon find themselves at the shutdown point and facing a severe economic loss. In addition, they need to know that the dominant firm sets its price at its own profit-maximizing output level, which is probably different across most of the other firms comprising the industry or market. The dominant firm also calculates how much demand resides in the market while taking into account how much demand the other firms can satisfy at the prevailing price.

In order to understand how the dominant firm is mechanically strategic in its behavior, consider the current prevailing price that all the other firms charge is the price set earlier by the dominant firm. In other words, all the other firms are effectively price takers and bear a close resemblance to firms that operate in a perfectly competitive market structure. Accordingly, they will each supply an amount where price equates to marginal cost as long as the price is above their average variable costs or their shutdown point. The dominant firm can estimate quite precisely how much the other firms will supply to the market at various prices by summing the quantities of each individual firm that correspond with price and marginal cost; it knows the supply schedules for all the price-taking firms. In addition, the dominant firm knows the market demand schedule. It uses the information on demand and supply to eventually choose what price it will invoke next.

The amount that the dominant firm will supply approximates the difference between the market demand and the supply made available by the price-taking firms. In essence, the dominant firm begins to delineate its own demand schedule by setting quantity demanded to zero at the existing or prevailing price. Because it already knows its own marginal cost and marginal revenue functions, it will be able to find the price and quantity price where its marginal costs equal its marginal revenues. The next step involves determining its demand curve by sketching a line between the profit maximizing quantity and the zero demand quantity. Now it can estimate exactly how much it will provide at the next market price by examining the points where it intersects the market supply and demand curves. In essence, it will provide the amount that is equal to the shortage created by the next market price; for those readers who have interest in a brief articulation and graphical presentation of this entire process, the author of this essay refers them to Arnold's (2005) Economics textbook (see page 543). The next section presents the last of three theories of oligopoly and prepares the reader for an introduction to game theory.

Cartel Perspective

Cartel theory assumes that all firms unite in order to operate as one in the industry. That unification or collusion strikes a close resemblance to a monopoly. In general, a cartel is a group of oligopolists that band together in order to realize the benefits that typically accrue to a monopoly. Specifically, a cartel is an organization of firms that reduce output and increase prices in an effort to increase collective profits. One example of a cartel that is widely known around the globe is OPEC, which is an acronym for Organization of the Petroleum Exporting Countries. Its headquarters are in Vienna, Austria.

Legislation prohibits various types of cartels in some places including the United States. An array of problems arises in forming cartels and in maintaining them. Beginning from the moment of a cartel's formation, incentives exist for member firms to cheat on official declaratives regarding output and prices. Cheating occurs for several reasons and may come naturally whenever there is committee work and group exercises. Cartels require teamwork and some members of the team are more active and do more work than other members.

It is difficult to achieve consensus at times and some members are unwilling to abide by resultant policies. A free rider problem arises when the cartel agrees to restrict output and to raise prices. Member firms may sell more than their share at the elevated high price resulting in profits that are greater than those achievable through compliance. Higher profits in turn generate additional interest in joining the cartel and barriers to entry may be weak or nonexistent. By way of review, collective pricing and output strategies entail applications of alternative perspectives along with overt or covert approaches.

A Real or an Unreal Deal: Game Theory & a Prisoner's Dilemma

The nature of the game is finding a strategy that generates a mutually acceptable payout. Interdependence is a common theme in economic perspectives on market structure and games. Over time, the behavior of each player depends on and determines the behaviors of other players. Frequently, the techniques involve analyzing behaviors of decision makers who attempt optimization by playing games or using strategies, engaging in interactive processes, and anticipating the moves of other players.

Prisoner's dilemma effectively portrays the relevance of game theory to economics. Most textbooks present the scenario using two captives to illustrate their situations, choices, and possible outcomes. The scenario demonstrates that the exercise of individual level rationality has obvious implications for group level outcomes. As their separation is immediate at the time of capture, the severity of punishment or sentence depends on whether one, both, or neither of the captives provide details about their pre-capture activities or make a confession.

The outcome for each individual ranges from gaining a full release to receiving a maximum penalty. A two-by-two matrix best illustrates and summarizes the strategic choice of whether to confess to the authorities and the possible payouts that correspond with each of their decisions; each payout has 25 percent chance of success.

The best case scenario appears in the lower right cell of this matrix: Each prisoner chose to withhold confession and the payout is a full release. Some key assumptions in this analogy are that the authorities are missing any compelling evidence; the case prosecution is just and reasonable; and one or both of the prisoners probably committed a questionable act but did not anticipate capture. Perhaps they agreed in advance on their post-capture strategy. Payoff maximization is possible through collusive and strategic behaviors whether they originate in advance or unfold otherwise.

Consider the case in which there is an allowance for talking among players in one group, but not in the other group. The highest bidder in each group wins the bill though one group may employ a strategy remarkably different from the other group. Recall the auction of $20.00 cash by an economics instructor, as mentioned in the opening paragraph of this essay. From a theoretical viewpoint, we would expect the group without talking privileges to tender high bids and therefore receive a net gain lower than the group of talkers due, in large part, to the competition among classmates for the $10.00 bill. We would also expect the talking empowered group to develop a collusive agreement that calls for each classmate in the group to tender a bid of one cent, for example, except for one member of that group who tenders a bid double that amount. Moreover, the group of talkers may agree to share the proceeds equally with those in his or her group. From a reality viewpoint, the story unfolds as follows: One student, who perhaps read the text ahead before class and maintains a high grade point average, attempted to convince her four group members to tender one cent bids and then she would joyfully give $2.00 to each from the winnings. One can certainly imagine all the potential winners this single application of game theory may produce among those taking a course in economic principles.

That is only one example of a simple application of game theory, but there are plenty of other more complex applications available to readers who hold an interest in bolstering their understanding. Coverage of those extensions and applications are beyond the scope of this essay especially as we draw closer towards its conclusion. Consequently, the author uses the remaining pages of this essay to briefly summarize some key applications and extensions of game theory components. For a highly effective introduction to the topic, textbook author Arnold (2005) provides a section outlining various game theory applications such as grades and partying, the arms race, speed limit laws, and the fear of guilt as compliance mechanism.

Development of Game Theory

The development of game theory is interesting in itself to those with or without keen analytical or mathematical skills. Many economists believe that game theory originated during the 1920s from the work of John von Neumann and through his collaborations with Oskar Morgenstern. The earliest versions of game theory portrayed strategies as being largely static in nature. For instance, one player devises a tactic and follows through with a preset course of action thereby missing opportunities to learn from feedback concerning the latest actions of opponents. Furthermore, those and later versions made references to: A zero sum game in which one player's loss is another player's gain in which there will be a win-loss outcome; a non-zero sum game in which each gain depends on behavior of others in which there will be a win-win outcome.

Game theory utilizes algorithms and emphasize the dynamic nature of the strategic pursuits of all parties. Dixit and Skeath (2004) point out games may consist of moves that are sequential, simultaneous, or a mixture of both. In addition, games may incorporate: One play or repeated plays; the same set of opponents or a different set; full and equal information or the lack thereof; fixed rules or flexible rules; and, cooperative agreements without regard to their enforceability. Taking into consideration all those angles, a strategy equilibrium is said to occur when one party's strategy is the best response to the other party's strategy. A brilliant trio consisting of Reinhard Selton, John Harysanyi, and John Nash won a Nobel prize in 1994 for their development of game theory and strategy equilibriums; the latter of which is the most famous. In short, they expanded the notion that players engage in a game cycle that contains action, feedback, and reaction phases all the while anticipating the next move of another player as they formulate moves of their own. Additional value accrues to a set of players when it chooses a mixture of moves at random thereby diminishing opponent capacities for prediction.

Conclusion

In conclusion, game theory attempts to simplify reality and it presents analytic models much like other models of economic theory. These two perspectives are convergent when we view economics more in terms of strategic cooperative behavior and less in terms of idealistic competitive behaviors. Hopefully, this essay produced a much broader and deeper foundation of understanding the complexities of pricing strategies and cooperative efforts of sellers. Perhaps it will also motivate readers to explore and to expand knowledge on the cooperative behaviors of buyers.

Terms & Concepts

Ceteris Paribus: Latin meaning "all else is held constant."

Concentration Ratio: A metric that estimates the concentration of market power among a small number of firms.

Demand: The amount of a good or service an individual consumer or a group of consumers wants at a given price.

Demand Schedule: The actual quantities that consumers are willing and able to purchase at various prices.

Equilibrium: The price and quantity associated with the intersection of the demand and supply curve reflecting alignments among consumers and producers on an item's price and quantity.

Equilibrium Price: The price at which demand and supply curves intersect reflecting an agreement among consumers and producers.

Equilibrium Quantity: The quantity at which demand and supply curves intersect reflecting an agreement among consumers and producers.

Free Rider Problem: Arises whenever anyone who receives a benefit does not incur a cost.

Law of Demand: Specifies the inverse or negative relationship that exists between an item's demand quantity and its price; quantity and price move in opposite directions.

Law of Supply: Specifies the direct or positive relationship that exists between an item's demand quantity and its price; quantity and price move in same direction.

Marginal Revenue: The contribution to total revenue from the sale of one additional item.

Market: A virtual space where consumers and producers interact while exchanging a specific item in accordance with their demand and supply schedules.

Monopoly: The firm that is the sole supplier of a good or service within a market, which can determine output level and price and prevent entry of new suppliers.

Output: The quantity of items or services produced by a firm or group of firms in a market.

Perfect Competition: The condition of a market in which several buyers and sellers exist, but none of them can influence price though entry and exit are easy to accomplish.

Price: The amount of money that is required to obtain an item.

Price Fixing: The act of conspiring with competitors to establish prices alleviating competition and preserving market share.

Producers: Firms that supply or provide goods or services desired by consumers.

Quantity Demanded: The amount of goods or services that consumers desire at given prices.

Quantity Supplied: The amount of goods or services that suppliers are willing and able to produce at given prices.

Revenue: The proceeds from the sale of an item; the mathematical product of quantity of item sold times the price of item.

Supply: The amount of a good or service an individual producer or a group of producers will provide at a given price.

Supply Schedule: The actual quantities that producers are willing and able to purchase at various prices.

Variable Costs: Costs for production or output that vary according to activity level.

Bibliography

Arnold, Roger A. (2005). Economics(7th ed.) Mason, OH: Thomson South-Western.

Dixit, A. & Skeath, S. (2004). Games of strategy (2nd ed.). New York: W. W. Norton & Co.

Guell, R. C. (2007). Issues in economics today(3rd ed.). Boston, MA: McGraw-Hill Irwin.

McConnell, C. R. & Brue, S. L. (2008). Economics(17th ed.). Boston, MA: McGraw-Hill Irwin.

Navidi, H., Bashiri, M., & Messi Bidgoli, M. (2012). A heuristic approach on the facility layout problem based on game theory. International Journal of Production Research, 50(6), 1512-1527. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=75125696&site=ehost-live

Owen, G. (2013). Applications of game theory to economics. International Game Theory Review, 15(3), -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

Pearce, D. W. (Ed.). (1992). The MIT dictionary of modern economics.Cambridge, MA: MIT Press.

Von Neumann, J. & Morgenstern, O. (1947). Theory of games and economic behavior (2nd ed.). Princeton, NJ: Princeton University Press.

Yung-Sung, C., & Han-Jen, N. (2013). Advertising expenditure and price as joint indicators of product quality perceptions: a perspective from game theory. International Management Review, 9(1), 78-86. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=86721067&site=ehost-live

Suggested Reading

A Beautiful Mind. http://www.abeautifulmind.com/

Anderlini, L., & Lagunoff, R. (2005). Communication in dynastic repeated games: 'Whitewashes' and 'coverups'. Economic Theory, 26(2), 265-299. Retrieved September 25, 2007, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=15286140&site=ehost-live

Berger, U. (2006). A generalized model of best response adaptation. International Game Theory Review, 8(1), 45-66. Retrieved September 25, 2007, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/loginaspx?direct=true&db=buh&AN=20298490&site=ehost-live

John Nash's Autobiography http://www.nobel.se/economics/laureates/1994/nash-autobio.html

Nash, John. (2001). The essential John Nash. Edited by Sylvia Nasar and Harold W. Kuhn. Princeton, NJ: Princeton University Press.

Streich, P., & Levy, J. (2007). Time horizons, discounting, and intertemporal choice. Journal of Conflict Resolution, 51(2), 199-226. Retrieved September 25, 2007, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=24615298&site=ehost-live