Brief
This paper focuses on elaborating on Nash equilibrium using the payoff matrix, which is a graphic representation of benefits or profits earned from sets of strategies respectively. Furthermore it gives an overview how firm a market such oligopoly make decisions.
Definition
Nash equilibrium refers to a firm making a decision, putting into account competitors. Unlike the market equilibrium, it is not governed by the market forces of demand and supply, rather by strategically decision making.
Under perfectly competitive market due to an enormous number of buyers and sellers; and the sale of homogeneous product, amounting to each firm possessing a small fraction of the market share, firms leave the price and quantity to the market forces of demand and supply, hence referred to as price takers. Under imperfect competition, however, since there are barriers to entry and products sold are either unique or differentiate, relatively there are either for or many firms.
Since in an oligopoly market has few firms partaking there is interdependence among firms, hence each firm has to behave in a strategic manner taking into the potential reaction of their competitors, and this is where the Nash equilibrium becomes useful. Whether in an output or price competition firms in this market should behave strategically, however on this paper the focus is on the price competition between firms to depict how firms maximize profits under this conditions, using the Nash equilibrium.
To denote this we use the payoff matrix, which is utilized to display profit or benefit yield by a firm from applying each strategy. To simplify this section, presumably there are only to firms: A and B.
According to the table above, firm A has a dominant strategy when charging $75 regardless of the strategy implemented by firm B. Similarly, firm B has a dominant strategy when charging $75. The Nash equilibrium will be the strategy that both firms have an advantage on, which is at the price of $75. This means both firms should charge $75 not $100. Most, however would argue that both firms should charge $100 because they would make a large profit margin compared to when setting the price $75.
To clear the confusion, presuppose the Nash equilibrium price is $75 as indicated, meanwhile the $100 is the collusion price. Both A and B collude and agree they are going to charge their products $100, suppose either A or B cheats and charges $75 (the Nash equilibrium price), the one charging at the price of $75 will make more profit. Thus under this conditions both are better off charging the Nash equilibrium price.
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