Indifference Curve, Oligopoly & Game Theory

Introduction:
Microeconomics aims to cover every aspects of our economic life. This report will discuss, evaluate and assess the usefulness and limitations of microeconomic theories in reaching that aim. Microeconomics is “The study of choices that individuals make and the way these choices will interact in given markets” (Parkin et al. 2012, p.2) or put more simply, microeconomics is the allocation of scarce resources. There are a number of objectives of microeconomics, the foremost being; Equity, Efficiency, Growth and Stability. This report will examine the commonly used theories of; Indifference analysis, Game Theory and the market structure of Oligopoly; analysing the benefits and drawbacks and how they are applied in the real world.
Indifference Curve Analysis:
To answer questions about individual decision making indifference curve analysis is applied. Before looking at this model it is necessary to assume that the individual satisfies the four axioms of rational preference formulated by Savage (1954). These are; completeness, more is better, transitivity and convexity. Sugden (1991 p.761) describes these as “Preferences over acts, where acts are made up of consequences.”

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A rational consumer will of course spend their money on the mix of products that give them most pleasure (Read 2007, p.45). However this will vary for each consumer, because each consumer will have different preferences. The consumer is constrained financially by their exogenous income to only be able to purchase bundles of goods X and Y on or below their budget line. This line does not always have to be straight, and in everyday applications it often is not. This is true with perfect compliments such as right and left shoes, the budget constraint will be stepped because a consumer will not gain much “util” (benefit) from having significantly more right shoes than left. An indifference curve is a graph showing a combination of two different goods that give the consumer equal satisfaction. There are four main properties of an indifference curve; it is ubiquitous, downward sloping, cannot cross and cannot become less steep. The marginal rate of substitution is the rate at which the consumer is willing to exchange one bundle, for another along the indifference curve (this is equal to the value of the slope). Diminishing marginal rate of substitution explains why the line is curved as seen in figure 1 (Perloff, 2012). The consumer will take any allocation of resources along each indifference curve (I1, I2, I3). Their utility is optimal where the indifference curve meets the budget constraint. It can be observed that I2 is tangent to the budget constraint at point ‘e’ therefore that is the rational and optimal choice, although I1 does also intersect part of the budget constraint (points ‘a’ and ‘c’), the equilibrium of goods will be less desirable. Therefore that leaves I2 as the rational choice. However indifference curve analysis does not take into account the consumers preference to save instead of spend. This could cause point ‘d’ to be the most desirable option.
An application of Indifference curve analysis is the use of the Edgeworth box; TheEdgeworth boxis a traditional visualization of the benefits potentially available from trade. When both parties have utilised the benefit that they can receive this is called Pareto optimality. If two consumers (A and B) have fixed amounts of two products (X and Y) they must find a way to trade these goods that benefits both of them without making the other worse off. This can be solved by using their preference maps to construct an Edgeworth box diagram.
Figure 2 (Perloff, 2012) shows the indifference curves of the two consumers (Jane and Denise) are tangent at a number of points. If the consumers originally plan on commencing trade at point ‘e’ this will give Jane 30W and 20C and Denise 20W and 60C, Hence by using IJ2 and ID2 this is more beneficial to both parties due to there being greater overall bundles in addition to a greater combination of products. This then follows both the “convexity” and the “more is better” axioms of consumer preference. A contract curve is drawn through all of the Pareto optimal points of trade, which shows the various positions of exchange of products that equalise the marginal rates of substitution of the two exchangers.
One particular drawback is that indifference curves usually only focuses on two goods, whereas in real terms it would be very rare that there are only two options of what to spend income on. Although it is possible to create an indifference map that takes into account three goods this is the furthest that the model can progress. There is also no scope for risk, uncertainty, or other factors that could influence a consumers preference map, this is because this form of analysis sticks rigidly to the assumption of ‘Ceteris Paribus’. Indifference curve analysis relies upon a consumer behaving rationally, however it is quite possible for a consumer, or anyone, not to behave in a rational way. Hume (1740) argued that reason alone was not a motive to act rationally, and that passion and impulse were of more importance in decision making.
Game Theory:
Perhaps one of the most discussed theories in microeconomics is that of Game Theory. Perloff, (2012, p.505) defines game theory as “formally describing games and predicts their outcome conditional on the rules of the game, the information that players have, and other factors”. There are certain factors that must be present for a “game” to exist. There must be players, strategies, orders of moves (time) and payoffs or rewards for each outcome. Providing that a player behaves rationally, we can assume they will follow a dominant strategy. This is a strategy that gives the player the best final outcome in comparison to all other potential strategies.
The prisoner’s dilemma is a paradox in decision analysis where two parties end up worse off by pursuing self-interest. Furthermore it shows how if all parties in a game apply a dominant strategy there will be no real winner. Tucker (1952)formalized the game as we know it today with prison sentence rewards and named it “prisoner’s dilemma” It can be seen in figure 3 (Kane, 2013) The prisoner’s dilemma is set up so that both parties choose to protect themselves at the expense of the other participant; this is achieved by opting to confess. Following a logical thought process to help themselves, both participants are consequently worse off than if they had cooperated and trusted each other. Evidently, receiving confessions from both players is the Nash equilibrium (where each player is assumed to know the equilibrium strategies of the other players, and no player has any advantage by changing their own strategy).It is therefore also the Pareto optimal point. This game can be expanded, giving the players 3 or more strategies each. Although this makes the game more difficult it can be solved using the method of iterated elimination of dominated strategies. This means that when a player notices that a possible strategy is strictly dominated by another strategy (all options of other strategy give a better outcome) then the strategy will not be considered. The prisoner’s dilemma is summarised well by Matt Ridley,
“broadly speaking any situation in which you are tempted to do something, but know it would be a great mistake if everybody did the same thing, is likely to be a prisoner’s dilemma” (1996, p.55).
A particularly fascinating application of the prisoner’s dilemma was its use in the cold war. Simplifying research by Cobb (2012). The two players (NATO and the Warsaw Pact) had to choose whether or not to build nuclear weapons. If neither chose to do so, valuable money, time and potentially lives would be saved. All players would be considerably better off if both avoided building nuclear weapons. However if one side built weapons and the other did not then that player would have a huge advantage. Therefore the only rational choice is for both sides to build nuclear weaponry. This puts both players on an equal level. However both are now financially worse off than when they started. Although it could be argued that the application of game theory has saved the world from nuclear war. Steiner and Schelling (1960, p.210) studied a similar model and came to the conclusion that world peace would be the most plausible solution.
As shown in the film A Beautiful Mind (2002), the prisoner’s dilemma and Nash Equilibrium challenge Adam Smith’s (1776) marketplace model, which implies that the pursuit of self-interest results in collective benefit. One can observe many political disputes as partially flowing from disagreement regarding which model is more appropriate in a particular situation. For example when a firm or person is operating in a market with many available players, the option to cheat (confess) will not be taken as it would tarnish a firm’s reputation. This point is made well by Tullock (1985) and essentially implies that if you do not choose to cooperate in the short term, you may not have anyone to cooperate with in the long term.
Game theorists have the assumption that players have perfect knowledge of both their own and opponents payoffs. When applied to the real world in more complicated applications this is often not true. It is often not possible to discover an outcome until the “game” has been played. Traditional game theory does include the factor that humans are intelligent and will often change their strategy when a game is played multiple times. It is assumed that players of a game will always apply a dominant strategy, however, this may not occur if players know each other or know that they will later come into contact with each other.
Oligopoly:
An Oligopoly is a common form of market structure with limited competition, in which a market is shared by a small number of producers or sellers whereas a duopoly only has two dominant firms. Many of the models used when analysing this market structure focus on duopolies for simplicity reasons. There have been a number of contrasting models for an oligopolistic market, arguably the three most important, and the three that this report will focus on, are the Cournot model, Stackelberg model and Bertrand model.
In the Cournot model each firm assumes that rivals will continue producing at their current output levels. Each firm has the assumption that its competitors production levels are fixed, and will not be effected by their own production levels. This was developed by Antoine A. Cournot (1838). Each firm has a best response possible for every situation, this is the reaction function and is shown by (Perloff 2012) in figure 4. The best response curves show which output a firm will pick to maximise profit following its belief of its rivals output, Cournot equilibrium is found where the best response curves intersect. In contrast to this, the Stackelberg model assumes that firms do not decide on output simultaneously, instead, there is a price leader and a price follower. Henceforth, backwards induction is used to find the equilibrium. Cournot’s model is a simultaneous game, whereas Stackelberg’s is a sequential game. It can be seen from diagram 4 below that in the Cournot model, output for the two firms will be the same, however, output in the Stackelberg model is higher for the leader and lower for the price taker. If the firms are price takers then they will produce where demand equals to marginal cost.
Within the Bertrand model each firm assumes that rivals will continue charging their current prices, the model was created by Bertrand (1883) in a review of Cournots model. Bertrands argument is that firms will choose the price to set rather than quantities, and that price should equal marginal cost. One problem with this model is that it assumes that consumers will always buy the lowest price product; which does not take into account factors such as product differentiation, location and the cost to the consumer of obtaining market information.
The emergence of cartels is fairly common in oligopolies. This can have a negative effect on the consumer. A cartel is an agreement between competing firms to control prices and output. A cartel will form if the incumbent firms in the industry believe they can formulate higher profits by colluding together. If two firms collude, they could operate as a monopoly, therefore producing less and charging a higher price. Following Stigler (1964) many economists now accept that collusion is not a viable option in the long term as each firm has the incentive to cheat. This could be achieved by raising either price or quantity. Although cartels are illegal in most countries this has not stopped them forming. Research from Levenstein and Suslow (2006, p43-95) showed that although cartels are often successful in raising prices in the short term, most break up before five years. This is because when there is an incentive to cheat (and get away with it), most firms will take that opportunity. As shown in the recent failed cartel within the US airline industry involving “Qantas” (BBC 2007)
In disparity to this however, an oligopolistic market does not necessarily mean that the firms will collude. Coca cola and Pepsi have a duopoly of their market, yet they are fiercely competitive and are forced to spend vast amounts each year on advertising. This level of competitiveness drives down prices through price wars, causes firms to differentiate products, and encourages innovation. Ultimately all of this is good news for the consumer.
Another interesting example of an oligopolistic market is the current UK petrol station industry. Although the price of oil has fallen dramatically in the previous year, the firms inside the market are unwilling to drop their prices to match the fall in costs. This is because of price rigidity and collusion, if one firm dropped the price of petrol then all other incumbent firms would follow the price drop. This would consequently reduce profit for all firms in the industry. This shows how oligopolies can often have a negative effect for consumers.
Conclusion:
In conclusion the biggest problem in the application of microeconomics is the principle that consumers will always behave rationally, as previously noted, rationality is hard to define. In addition to this microeconomic theories are based on the static assumption of ‘Ceteris Paribus’ which means ‘Other things being equal’. This assumption is unrealistic, the way we think and act are constantly changing, decisions can vary from day to day in response to to many different factors. Many of the microeconomic models do not go into the complexity needed to completely analyse our everyday behaviour. For example indifference curve analysis is limited to two or three products and some of the theories behind oligopolies can only be used for duopolies. However this does not make these models obsolete by any means.
For the aforementioned reasons, there is no doubt that microeconomics can, if applied correctly, cover aspects of our everyday lives and give us a detailed insight into how and why we act as we do. However, this being said, microeconomic theories should only be used as one of many tools to help aid our knowledge of the economic world. The study of Microeconomic theory helps in achieving the correct allocation of resources, commodities and output mix for the maximization of the social welfare.
APPENDIX
Figure 1 : Consumer Maximisation (Perloff 2012, p.115)

Figure 2: Edgeworth Box and Contract Curve (Perloff 2012, p.349)

Figure 3: The Prisoners’ Dilemma (Kane 2013.)

Figure 4: Duopoly Equilibrium (Perloff 2012, p.487)

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