# Game Theory

#### Introduction

This essay is aiming at evaluating the standard of products price, with the attempt to give explanation of why the price is usually set between monopoly price and marginal costs of oligopolistic firms. Model of game theory is applied so as to reach the objective in this essay. This chapter is chiefly divided into three sections: firstly there would be an introduction of game theory in order to form a brief idea of this concept, including historical evolvement of game theory, its major assumptions and its feasibility of applying to monopolistic and oligopolistic industries. Secondly, the main focus would be put on Oligopolistic industries, Cournot-Nash model is adopted in this section. Thirdly, characteristics of monopoly industry would be displayed; pricing strategy under such situation would also be discussed. Finally, this essay will end by a conclusion of the topic of this research, why prices are above marginal costs in oligopolistic industries and for what reason they are usually below the monopoly price.

#### Introduction of Game Theory

The main economic concept in this essay is game theory. One definition for game theory is mathematical analysis of competitive situations to identify choices that will lead to a desired outcome. (Osborne and Rubinstein, 1999) It is a special branch of mathematics which has been developed for studying decision-making in complex circumstances. On the other side, according to Camerer, (2003) Game theory can be defined as the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behaviour impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions. (Davis, 1970)

The idea of Game historically dates back to the Talmud and Sun Tzu's works. (Dimand and Dimand, 1996)However, the contemporary codification is attributed to John von Neumann and Oskar Morgenstern, (1953) they published the Theory of Games and Economic Behaviour in 1944. In the early 1950s, John Nash (1951) generalized these results and provided the basis of the modern field of Game Theory. A rapid rise in theoretical developments led to the founding of the first academic magazine devoted to the field by Oskar Morgenstern in 1972. Few corporations nowadays think about their strategy without adding some game theory models or game elements into their strategy process.

This essay chiefly uses game theory to study economics of cooperation. Through action of studying economic markets with differing numbers of buyers and sellers, fluctuating values of supply and demand, game theory helps analyse competition in maximizing profits and promoting the widest distribution of goods and services. However, any model of the real world must make assumptions that simplify the reality, because the real world is too complex to analyse with any precision. Therefore, applying of game theory must be taken under two major and necessary assumptions: rationality and common knowledge. (Reny, 1985)

Mankiw and Taylor (2006) held the point of view towards function of game theory at examining economic behaviour. They suggested that game theory is not an essential tool for monopoly market. For in monopolised market there is only one firm dominate the whole market, strategic interactions are absent. But conversely, game theory could be rather using for analysing the behaviour of oligopoly corporations.

#### Oligopoly Industries

An oligopolistic industry is a market dominated by a small number of participants who are able to collectively exert control over supply and market prices. (Mankiw and Taylor, 2006)The basic dilemma suggests that whatever the point chosen on the profit frontier, each member finds it profitable to produce more than the quota allocated to him. Moreover, each of them has an incentive to cheat no matter the other members cheat or not. This dilemma is set under a situation where each player has two strategies. Profits are such that for each player when cheating is a dominant strategy. For example, the best strategy no matter what strategy the other player chooses. This can be illustrated by the basic game theory model.

Game theory is the framework used to analyse situations of interdependent or strategic decisions, i.e., decisions whose output depends on the decisions of all agents involved. The main elements of the theory are: set of players, set of strategies and each player's payoff. (Osborne and Rubinstein, 1999) Thus, since an oligopoly is a situation in which firms decision depends on the decisions of the other firms, game theory provides the appropriate framework to analyse oligopolistic industries. The players are the different firms; they choose strategies regarding some variables such as price, output, capacity, advertising, research and development expenditures, etc. and the payoffs are the profits. The main concepts of game theory are: Nash equilibrium - a situation in which each player is choosing the best strategy available, given the strategies chosen by the other player; dominant and dominated strategy; sequential and repeated games.

By giving am examples the game theory will be illustrated in order to explain why prices are above marginal costs in oligopolistic industries by using the Cournot-Nash model. The model assumes that there are two equally positioned firms; the firms compete on the basis of quantity rather than price and each firm makes an output decision assuming that the other firms behaviour is fixed. (Kreps, D. 1990)Suppose player 1 and 2 are the only firms in this market. The market demand curve is assumed to be linear and marginal costs are constant. To find the Cournot-Nash equilibrium one determines how each firm reacts to a change in the output of the other firm. The equilibrium is the intersection of the two firm's reaction functions.

For example, assume that slope coefficient of demand curve= -1, the player 1 is demand function is: Price = (60 - Q2) - Q1

Q2 is the quantity produced by the other player and Q1 is the amount produced by player 1. This function is based on the assumption that the higher the total quantity, the lower the price in oligopoly industry. Player 1 begins the process by following the profit maximization rule of equating marginal revenue to marginal costs so that Player 1 is total revenue function is,

TR=P*Q = Q1*(60 - Q2 - Q1)

= 60Q1- Q1*Q2 - Q12.

The marginal revenue function is,

MR = 60 - Q2 - 2Q1.

MR= 60 - Q2 - 2Q1 = 12

MC=MR=12

So that the reaction function result will be,

Q1 = 30 - 0.5*Q2

Q2 = 30 - 0.5*Q1.

The Cournot-Nash equilibrium could be determined by solving the equations simultaneously which results in Q1= Q2= 20 and P=60-20-20=20>12 the marginal cost. Consequently, price of the product is greater than marginal cost in oligopoly industry.