Tag Archives: cheating in game theory

## Oligopoly Pricing: A Game Theory Overview

1 Aug

Oligopoly pricing behavior has characteristics of a specific game of strategy. Like chess or poker. The best way to play such a game depends on the way opponent play. Oligopolists (in our case players) must pattern their action according to actions and reactions of rivals. The study of oligopolists behave in this strategic situations is called game theory. We will use game theory model to analyze and explain the pricing behavior of oligopolists. Let’s assume that in our oligopolistic market system are only two firms that produce CDs simply called “A” and “B”. Each firms- “A” and “B”- has a choice of two pricing strategies: increase the price or lower it. The profit of each firm depends on what strategy it chooses and what strategy its rival chooses.
There are four combinations of strategies possible for these two firms, and letter cells in the table below express them. For example, cell W represents low-price strategy of firm “B” and high-price strategy of firm “A”. This table is called payoff matrix because its cells represent the profit(payoff) each firm makes that result from combination of strategies of firms “A” and “B”. Cell W represents that after firm “A” chooses to adopt high-price strategy and firm “B” chooses to adopt low-price strategy, then firm “B” will make 4 million dollars and firm “A” will make only 1 million.

Mutual Interdependence
The Data in the payoff matrix are just hypothetical one, but relationship is very realistic. Remind the fact that oligopolistic firms can increase their revenues, and influence rival’s profits, by changing its price strategies. Each firm’s payoff depends on its own pricing policy and that of its rival. This mutual interdependence in economics is very well demonstrated by figure above. If both firm “A” and firm “B” adopt a high-price strategy then revenue of each one will be 3 million of dollars. If firm “A” uses a low-price strategy while firm “B” uses a high-price strategy then firm “A” will increase its market share and profit from 3 to 4 million of dollars, however firm “B” will lose 1 million of dollars, since its revenues will decrease from 2 million to 1 million of dollars. So, firm “B” high-price policy will be efficient only if firm “A” will also choose to employ a high-price strategy.
Collusive Tendency
The figure above suggests that oligopolists will benefit from collusion, or better said cooperation with rivals. An example of benefit can be when both firms are following high-price strategies, so each firm will get a profit of 3 million of dollars (cell X).
Note that either firm “A” or firm “B” can increase its profit by switching from high-price to lo-price policy. So, the profit can become 4 million of dollars, but the firm that keeps high-price policy will get only 1 million of dollars as revenue. If the firm that right now employs high-price strategy switches to low-price strategy will increase its revenues by 1 million so it will be able to collect 2 million (cell Z). The effect of all this will be switching the profits from 3 million (cell X) to ones which worth 2 million (cell Z).
In real situation, however independent actions of oligopolists may lead to competitive low-price strategies, which clearly will be beneficial to consumers but not also to oligopolists whose profits will decrease.
How can oligopolists avoid low-profit outcome of cell Z? They may collude, rather that installing independent and competitive price. Each firm will increase its profits from 2 to 3 million dollars (from cell Z to cell X).
Cheating
The payoff matrix explains why oligoplists may be tempted to cheat on a collusive agreement. Suppose that our firms “A” and “B” agree to maintain high-price policy, both of them earning 3 million of dollars (cell X). Both firms are tempted to cheat so that they will be able to increase their revenues to 4 million of dollars. If firm “A” cheats and diminishes its prices then it will increase its revenues from 3 to 4 million of dollars (cell Y), while if firm “B” cheats secretly and moves to low-price policy while firm “A” keeps high-price policy then firm “B” will increase its revenues by 1 million of dollars moving from cell X to cell W.