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Game Theory in Modern Economies

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GameTheory in Modern Economies

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GameTheory in Modern Economies

Thegame theory involves mathematical analysis of strategic reasons inorder to solve a problem. The game theory has been applied ineconomics by economists such as John Nash, Oskar Morgenstern and JohnNeumann (Leonard 2010, p. 293). It has been applied in studyingcompetition in the modern markets, uncertain planning, advertisingand more. In studying the competition in the markets, lots ofanalysis of perfectly competitive markets, monopolies and oligopolieshave been done. The game theory comes in when deciding on the bestprices for a product. Economists need to find out what theircompetitors might do if they set certain prices for theircommodities.

Thegame theories, which are used includes the zero-sum games, corporategames and non-corporate games. The “Prisoners Dilemma,” developedin 1940s and 1950s is a famous game used to describe the moderneconomies (Turocy 2001, p. 17). The question is, how well do themodern economists utilize the mathematic techniques behind these gametheories in analyzing markets?

Applicationof Game Theory in analyzing markets

Inthe nineteenth century, most economists focused on the oligopolisticmarkets. Oligopolies form part of imperfect markets, which refers tomarket situations whereby there are few firms that have a substantialcommand on the market prices (Vives 2001, p. 231). Today, mostoligopolistic firms are involved in price making rather than pricetaking and, therefore, most economists apply the game theory inmaking prices in order to retain markets and maximize profits. Themodern economists have developed the game theory in order to studythe behavior of the oligopolies in the current market (Kolokolʹt︠s︡ovand Malafeev 2010, p. 189).

Apple,Huawei and Samsung are some of the big companies that control theelectronics industry and mostly the mobile phones. In this case,therefore, Apple has two major players in the market. Beforereleasing a new product, Apple must decide on the most appropriateprice by considering the possible responses from its competitors ifthe product was released. In their decision making, Apple strategicmanagers ought to apply the game theory in making the price. It isextremely important for Apple set the most appropriate price in orderto retain its market.

However,the game theory only predicts and explains the possible thecompanies’ behaviors. Economists make uncertain decisions becausethey do not know what will happen in the future. Mathematicalanalysis of the decisions gives multiple outcomes that are likely tohappen (Myerson 1999, p. 45). For example, critical analysis of thedecision made by Apple would reveal that, its competitors woulddesign cheaper products or counteractive high quality products ofsimilar prices. In summary, the game theory enables the study ofcompetition existing between a coalition of firms and other firms.Additionally, a game theorist can study market situations where manyfirms compete individually (Peters 2008, p. 67).

Thegame theory is well explained by two players in the so called“zero-sum game.” In this game, when one player wins the otherplayer must lose (Turocy 2001, p. 17). The zero-sum game can,therefore, be referred in understanding the nature and outcomes oftwo oligopoly firms’ competition. Another game theory involvesmultiple players. The game is referred to as “positive-sum games,”where all participants can gain due to the gains resulting from tradeamong people. Economists explain individual’s behavior in makingdecisions (Chwe 2001, p. 45).

Mathematicalanalysis behind the game theory

Inthis section, the simple games are described and their application indecision making. Each player moves once and all the moves happensimultaneously. The game will then be analyzed in a Normal Formtable. Then, the most important part of the games involves discussingthe reasoning behind the players’ moves (Chwe 2001, p. 46). Nashequilibrium will also be discussed.

Considerthat two players are playing the rock-scissors-paper in order to winone dollar. The game is an example of a zero-sum game where the totalnumber of the payoffs of all the players amounts to zero for everysingle outcome. The payoff can be referred to as the value thatreveals a player’s level of satisfaction after getting the outcome.In this game, the players are rational in that they make the moves tomaximize their own utility (Corbae, Stinchcombe and Zeman 2009, p.243).

Thefollowing table shows the payoff (utility) matrix for the zero-sumgame.

Player 2

Player 1

Rock

Scissors

Paper

Rock

0

1

-1

Scissors

-1

0

1

Paper

1

0

0

Table1

Thefirst left hand top corner cell says, “0” that stands for “0,0,” In this case, both player 1 and 2 has a payoff of 0. The secondcell says “1,” which represents “1,-1,” Player 2 gets apayoff of 1 that is paid by player 1, who gets a payoff of -1. Thenthe game is solved mathematically to give satisfactory answers. TheNash equilibrium in the game refers to the decisions made by eachplayer, which cannot be changed by either player in order to get ahigher payoff (Corbae, Stinchcombe and Zeman 2009, p. 245).

Interpretationof the Normal form table

Considertwo companies Samsung and Apple are competing on sale of a product.The competition is similar to the zero-sum game where one companywill gain the market whereas the other must lose. Although the gameis not applicable in real life, it has been used to explore thenature of imperfect markets (Watson 2013, p. 67).

Ina situation where the market is controlled by a monopoly economistsfind it easy to apply the game theory since the single firm is thesole “price maker.” In this case, economists reveal thatconsumers have no control over the market since the monopoly candecide on any price. The game theory studies the responses made by amonopoly after realizing that there are upcoming firms that mightreduce its control over the market. Following the new release of aproduct from a competitor, a monopoly will lower its prices for thesame, but, differentiated product. Such an action is essentiallymeant to counteract with the potential competitor who might reducethe monopoly’s market (Watson 2013, p. 67).

Thegame theory also explores the decisions made by firms in perfectlycompetitive markets. Each firm in these markets has no control overthe market. Firms care about the market conditions, but, not thecompetitors as in the case of oligopolies. In other words, each firmis a “price taker” from the market, which is determined by theforces of demand and supply (Watson 2013, p. 69).

Applicationof game theory in Advertising (Petrosi︠a︡nand Mazalov 2007, p. 378)

Asstated earlier, in application of the game theory in economics theremust be players, strategies put in place and preparation of payoffmatrix. The Nash Equilibrium applies where each player/firm choosesits strategy given the strategy by the other player/firm. Inadvertising, a strategy is leading if it is always the best(Petrosi︠a︡n and Mazalov 2007, p. 378).

CompanyA are competing with Company B in advertising their products. Theirpayoff matrix is represented in the table below. Payoff valuesrepresent the level of satisfaction each company will get afterdeciding to advertise or otherwise. Each company is rational inmaking choices, that is, the choices made deliver maximum utility(payoff). In other words, no company would opt to make choices thatare of low payoffs (Chwe 2001, p. 47)

Scenario 1

Company A

Company B

Advertise

Do not Advertise

Advertise

(4,3)

(5,1)

Do not Advertise

(2,5)

(3,2)

Table2

Theoptimal strategy for company A if Company B chooses to advertise isalso to advertise. This is because if it chooses to advertise thepayoff will be 4 and if does not advertise the payroll is 2.

CompanyA should advertise even when company B decides not to advertise.Advertising is the optimal strategy because A has a payoff of 5 if itchooses to advertise. Otherwise, if A chooses not to advertise thepayoff is 3. Therefore, Company A should adopt the dominant strategyto advertise regardless of Company B actions.

Scenario2

Company A

Company B

Advertise

Do not Advertise

Advertise

(4,3)

(5,1)

Do not Advertise

(2,5)

(3,2)

Table3

Theoptimal strategy for company B is to advertise if Company A decidesto advertise. This is because Company B choice to advertise gives ita payoff of 3, if otherwise it gets a payoff of 1. When Company Achooses not to advertise, Company B should advertise. The optimalstrategy to advertise is favorable since it will get a payoff of 5 ifit chooses to advertise and if otherwise it would get a payoff of 2.

Thedominant strategy for Company B is to advertise regardless of theactions of Company A. The Nash Equilibrium for both companies is toadvertise since the both companies’ dominant strategies are toadvertise (Myerson 1999, p. 47). The form of advertising is common inmonopolistic competition where there is product differentiation. Thefirms are usually involved in advertisements of their products. Forexample, the restaurants and soap companies rely much onadvertisement. As illustrated, before a firm decides to advertise itmust consider the competitors (Petrosi︠a︡n and Mazalov 2007, p.383).

Analysisof the Cartels and price competitions

Thegame theory is applied in exploring the formation of cartels, whichis rampant in the modern economies. The most appropriate game in thiscase is the “Prisoners Dilemma.” The Prisoners Dilemma is a formof a corporate game where players form coalitions in order to competewith others (Turocy 2001, p. 17).

PrisonersDilemma

Twocriminals were arrested after they were suspected that they engagedin armed robbery. The police separated them immediately. If therewere proven guilty, they would serve 10 years in jail. However, theycannot be convicted since the evidence available is not enough. Eachsuspect is asked to confess and get released. However, each suspectis given condition that, one will be released after he confesses andhis partner does not confess. If he does not confess his partnerconfesses, he will be jailed for 10 years. If both confess they willbe jailed for 5 years (Landsburg 2011, p. 321).

Thepayoff matrix table is as follows:

Suspect N

Confess

Confess

Suspect M

Confess

(5,5)

(0,10)

Do not Confess

(10,0)

(1,1)

Table4

Notethat the Payoff Matrix values are negative since the suspects do notdecide on the length jail terms. After analysis of the payoffmatrices, the dominant strategy for both suspects is to confess (2,2). It forms the Nash Equilibrium (Landsburg 2011, p. 323).

Applicationin Price Competition (Landsburg 2011, p. 321)

Company N

Low Price

High Price

Company M

Low price

(4,4)

(10,2)

High Price

(2,10)

(6,6)

Table5

Applyingthe analysis of payoff matrices in the “Prisoners Dilemma,” pricecompetition among firms in perfect competition results to thedominant strategy, which is a low price (2, 2).

Applicationin Cartels (Neumann and Weigand 2013, p. 56)

Company Y

Cheat

Do not Cheat

Company X

Cheat

(4,4)

(10,2)

Do not Cheat

(2,10)

(6,6)

Table6

Applicationof the “Prisoners Dilemma” in analyzing cartels, the dominantstrategy identified is cheating (2, 2). After, company X and companyY agrees to set a certain price, each company in turn engages incheating in order to dominate the market (Neumann and Weigand 2013,p. 56).

ReferenceList

Chwe,M. S.-Y., Rationalritual: Culture, coordination, and common knowledge,Princeton, NJ: Princeton University Press, 2001.

Corbae,D., Stinchcombe, M., &amp Zeman, J., Anintroduction to mathematical analysis for economic theory andeconometrics,Princeton: Princeton University Press 2009.

Kolokolʹt︠s︡ov,V. N., &amp Malafeev, O., Understandinggame theory: Introduction to the analysis of many agent systems withcompetition and cooperation,Singapore: World Scientific, 2010.

Landsburg,S. E., Pricetheory and applications.Australia: South-Western/Cengage Learning. 2011.

Leonard,R. VonNeumann, Morgenstern, and the creation of game theory: From chess tosocial science, 1900—1960,New York: Cambridge University Press, 2010.

Myerson,R.B.: Nash equilibrium and the history of economic theory. Journal ofEconomic Literature 37,1999,1067–1082

Neumann,M., &amp Weigand, Theinternational handbook of competition,Cambridge: Cambridge University Press, 2013.

Peters,H. J. M. (2008). Gametheory: A multi-leveled approach.Berlin: Springer.

Petrosi︠a︡n,L. A., &amp Mazalov, V. V.. Gametheory and applications, volume 11,New York: Nova Science Publishers, 2007.

TurocyT. L., Stengel B., GameTheory, London,Academic Press, 2001.

Vives,X., Oligopolypricing: Old ideas and new tools,Cambridge, Mass. [u.a.: MIT Press, 2001.

Watson,J., Strategy:An introduction to game theory,Mason, OH: South-Western Cengage Learning, 2013.