Business Economics Game Theory

Economic is a study of choice how limited resources are allocated efficiently for the interest of public welfare. In a national economy, there are mainly three types of economic system. There are command economy, free-market economy and mixed economy. Many of the countries adopted a mixed economy system; this means that some co-ordinations are planned while others are left to the market. Most of the decisions are de-centralized while there are some decisions made centrally. The factors of production, capital, land and labor, are own mainly private but some owned by the public. The incentive is a mixture of both material and morale.

There are four types of market structure, namely, perfect competition, monopolistic, oligopoly and monopoly. It is the interest of this paper to look at oligopoly. In an oligopoly market structure, there are a few large firms and there is a significant barrier to enter the market, while the product differentiation is unknown.

In this market, the one different characteristic compare to perfect competition and monopoly is strategic interdependence. In oligopoly, the action of firm A will affect firm B, similarly the action of firm B will affect firm A. The firms in this market will act and re-act to each others decisions.

It is very complex to study oligopoly due to the strategic interdependence. Economist therefore, has built a model to study oligopoly. The model is called the game theory. Game theory has a military root. It is a mathematical analysis of strategy. The analysis is done by putting oneself into the shoes of all the players. By doing so, one can predict the behavior of each player and advise the best strategy.

It is the interest of economists to find out whether oligopoly market structure is efficient and if there is equilibrium.

In this case of efficiency, Pareto efficient would be the main concern. Pareto efficient is concerned with how resources are allocated. A resource allocation is Pareto efficient when resources cannot be re-allocated to make one person better off without making another worst off.

In the analysis of game theory, it is the interest of the economist to find an equilibrium point and whether the market is efficient. In equilibrium, the concept proposed by John Forbes Nash, later name after him Nash equilibrium, states that each player will always make the best decision taking into account the decision made by the opponent.

The assumptions made by economists are name as the rule of the game. There are five rules to the game, the player, the action, the outcome, the information and the communication. The player is an individual, a firm or a nation that make decisions. The actions are all the alternatives between which players decide. The outcomes are all possible combinations of all players’ possible moves. All the players will have payoffs. The information is what players know about their opponents, actions and payoffs. The communication is whether players can make binding agreements e.g. collude with each other.

The most popular game is known as “The Prisoner’s Dilemma” and there is also other game such as “Chicken Game”. In this article, only “The Prisoner’s Dilemma” game will be discussed and analyzed to study the interaction between firms in oligopoly market structure.

The Prisoner’s Dilemma

“The Prisoner’s Dilemma” game is the result of two players not trusting each other. This can be understood by looking at a typical petrol station price war. The owner of the pump station Shell and owner of the Exxon may come together to collude on the per liter price they would sell to the consumer. Since, colluding is illegal; therefore there is no contract to bind their agreement.

Even after the verbal agreement between both owners, there are in reality two options that each of them can decide to take: to set a high price as agree to collude or to set a low price to compete.

In this example, the following assumptions are made: both station charged SGD1.60 per liter and sell 5000 liters per day. A research done by an independent company shows that if the station charged SGD1.50 per liter, it is possible to sell 7500 liters per day. If both stations decided to cut price to SGD1.50 per liter, then both stations will only be able to sell 5000 liters per day.

The assumptions above indicates that the profit taken by both stations if they sell at SGD1.60 per liter is SGD1.60 per liter multiply by 5000 liters equal to SGD8000 per day. If one of the stations decided to drop price to SGD1.50 while the other station remained at SGD1.60, the station which dropped the price would capture 7500 liters per day and leaving 2500 liters per day to the station which did not drop the price. Therefore, the profit taken by station that dropped the pump price is SGD1.50 per liter multiply by 7500 liters equal to SGD11250 per day. While the profit taken by the other station that did not drop the pump price is SGD1.60 per liter multiply by 2500 liters equal to SGD4000 per day. Finally, when both stations decided to have a price war, both will drop the pump price to SGD1.50 per liter. Therefore, the profit taken by both firms is SGD1.50 per liter multiplies by 5000 liters equal to SGD7500 per day.

From the data gathered above, a table can be constructed to analyze how each pump station can play the game.

		Exxon
		SGD1.60 per liter	SGD1.50 per liter
Shell	SGD1.60 per liter	SGD8000 , SGD8000	SGD4000 , SGD11250
	SGD1.50 per liter	SGD11250 , SGD4000	SGD7500 , SGD7500

Here is how the analysis done, Shell’s best reply to Exxon when Exxon is charging SGD1.60 per liter is to drop price to SGD1.50 per liter, because the profit SGD11250 is greater than profit SGD8000.

On the other hand, if Exxon is charging SGD1.50 per liter than the best reply by Shell is also charging SGD1.50 per liter. This is because the profit SGD7500 is greater than SGD4000 if Shell did not drop the price.

Similarly, for Exxon, the best reply to Shell if Shell was charging SGD1.60 per liter is to charge SGD1.50 per liter. Again, looking at the profit, when Exxon charge SGD1.50 per liter knowing that Shell will charge SGD1.60 per liter, the profit is SGD11250 which is greater than SGD8000. So the best reply for Exxon is to drop pump price to SGD1.50 per liter.

The same strategies apply, if Shell dropped price to SGD1.50, Exxon will also drop the price to SGD1.50, because the profit SGD7500 is greater than SGD4000.

Both Shell and Exxon will always play the best option that is by dropping the price to SGD1.50. It can be observed from the table, the profit SGD7500 being underline, this means Nash equilibrium for Shell and Exxon. It can be observed that at this point, Nash equilibrium, it is not Pareto efficient. If both firms colluded and fixed the price at SGD1.60, both will make a profit of SGD8000 which is SGD500 more.

Studies show that the best way to play “The Prisoner’s Dilemma” game is by “Tit-for-Tat” strategy. Tit-for-tat is “A type of trigger strategy usually applied to the repeated Prisoner's Dilemma in which a player responds in one period with the same action her opponent used in the last period.” (Shor)

Tit-for-tat can be played by Shell and Exxon and both will gain profit greater than if they played a defected strategy. The game starts by Shell and Exxon charging SGD1.60 per liter. Since both companies are being nice to each other and would not drop price, both company will have SGD8000 per day.

Shell may first to break and start to lower pump price to SGD1.50 per liter, so Exxon should follow. After some times, Shell increases the price back to SGD1.60 per liter, again Exxon should follow.

Exxon may break from the lower pump price and charge SGD1.60 per liter. In this case, Shell should follow and increase the pump price to SGD1.60 per liter. When both companies always follow what the other company is doing there will not be fierce price war that may drive the company profit down. In the long run, the profit make by both Shell and Exxon will be higher if they used tit-for-tat strategy.

Limitation of Game Theory

In the case of Shell and Exxon price war, according to Nash equilibrium, the best way to play the game is for both petrol stations to drop the price to SGD1.50. This means that both firms play the best response towards what the opponent would do. This may be mathematically true but this is irrational. Player, such as firms make rational decision, as such there is a high chance that firm will choose to charge SGD1.60 because at the end of the day both firm make higher profit compare to charging SGD1.50. Therefore, in the game theory, the rational behavior of the player is not taken into consideration. This has broken the first assumption where player simply make decision but rather player make rational decision.

The second limitation is the assumption made on information. In the assumption, we simply state that player knows about their opponent, actions and payoffs. Unfortunately, in real world this rule can be easily broken. For a firm to know what his competitors are doing and what the competitors know, the firm needs to hire consultant. Firm needs to consult the marketing agency to find out what the other firms’ action would be and what would be the payoffs. This consultation comes with a cost. If the cost of hiring a consultant to find out more about the opponent, in our case for example Shell hire an external consultant to find out more about Exxon, is hire than the payoffs, in this case if the cost is higher than SGD500 per day, it would not be efficient for Shell to have this information. This is simply too costly.

In most of the country, collusion is illegal. Any two firms come together to sign an agreement to peg the price of a product will be charged to court. Unfortunately, firms are very smart; they know how to collude with each other without written agreement. This can be observed by looking at the pump price around Singapore. If it is better profit for pump station to drop price in order to sell more, why are not the petrol stations doing it. This is because of unwritten collusion among the petrol stations. Shell in Singapore is the leader among the pack. Shell will drop price and other petrol station will follow, when Shell increase pump price the rest will follow. Indeed, by observing this behavior, there is an unwritten collusion between petrol stations in Singapore. When collusion happens, there is no way game theory can be used to analyze the strategic behavior of firms, because there is simply none.

Glimcher noticed the limitation of game theory when apply to chicken game the player may get only one chance to play the game. For this reason it is impossible for players to study the choice of his opponent and to make adjustment to his own choice since each player only play the chicken game once.

The other limitation mentioned by Glimcher is relating to how the equilibrium point is achieved. In game theory the static equilibrium can be efficiently described but the dynamic process by which equilibrium is reached cannot be efficiently described. This is a real problem because human behavior “must be devoted to solving dynamic problems – a problem for which we have no adequate theoretical tools.” (Glimcher, 2004)

Summary

The game theory is a very powerful tool used by economist to anticipate the next step that the competitors would take. It is also a tool for the firm to gauge the current position that the firm is in. Some firms may not have any ideas that they may be charging higher price compare to the competitors and losing customer day by day. By using game theory, the firm can decide what they would do next in an oligopoly market. In using the game theory in a “Prisoner’s Dilemma Game” the player could play the game with tit-for-tat strategy for the optimum payoff, while in a “Chicken Game” there is still limitation that need to be addressed. Although, there are some limitations to this theory, it has become critical tool for studying the oligopoly market.