Final answer:
In a non-cooperative game between firms Alpha and Beta, both firms must strategically choose between high and low pricing to maximize profits, taking into account how their competitor may respond. The firms' revenues vary drastically based on their own and their competitor's pricing choices, showcasing the relevance of game theory in competitive business strategies.
Step-by-step explanation:
The scenario described involves two firms, Alpha and Beta, engaged in a non-cooperative game in the same market. Both firms have the same constant average costs of $2 per unit and can set either a high price of $10 or a low price of $5. When both firms choose a high price, the demand is split evenly at 10,000 units. Conversely, a low price by both firms leads to an 18,000-unit demand, also split evenly. If one firm sets a low price and the other a high price, the low priced firm sells 15,000 units, while the high priced firm sells only 2,000. This situation represents a classic example of game theory, specifically a pricing game where firms must strategically decide their pricing to maximize profits without the option of cooperation.
In the given market scenario, the firms' pricing decisions are crucial. If Firm Alpha sets a high price and Firm Beta follows suit, each firm would gain $40,000 in revenue (splitting the 10,000 units evenly at $10 each, less the $2 average cost per unit). However, if Firm Alpha sets a high price and Firm Beta undercuts with a low price, Firm Alpha's revenue drops significantly to $16,000 (2,000 units at $10 each, less the average cost), while Firm Beta's revenue soars to $57,000 (15,000 units at $5 each, less the average cost). Thus, each firm must consider the potential responses of their competitor when making pricing decisions.
This analysis highlights the importance of understanding competitive strategies and the implications of price setting in a non-cooperative market environment. The insights gained apply not only to theoretical models but also to real-world business practices where firms must anticipate competitors' actions and make strategic decisions accordingly.