Question

Construct a strategic form payoff matrix involving two firms and their decisions on high versus low advertising budgets and the effects of each on profits. Show a circumstance in which both firms select high advertising budgets even though both would be more profitable with low advertising budgets. Why won't they unilaterally cut their advertising budgets?

Short answer

Both firms choose high advertising due to the risk of losing profits if only one switches to low. It shows a classic Prisoner's Dilemma where self-interest keeps them from choosing the mutually better strategy.

Step-by-step solution

Define the Players and Strategies

We consider two firms, Firm A and Firm B, as the players involved in this strategic interaction. Each firm has two strategies available: "High Advertising Budget" and "Low Advertising Budget." These strategies define each firm's actions in their potential competitive scenario.

Assign Payoffs Based on Strategy Combinations

Construct a 2x2 payoff matrix where each cell contains a pair of numbers representing the profits for Firms A and B respectively. Assign the payoffs as follows: 1. Both choose High: (4, 4) indicating lower profits due to the cost of high advertising. 2. Both choose Low: (6, 6) indicating higher profits without the heavy advertising cost. 3. A chooses High and B chooses Low: (3, 7) implying Firm A's advertising overwhelms B. 4. A chooses Low and B chooses High: (7, 3) implying the opposite scenario.

Identify Dominant Strategies for Each Firm

A dominant strategy is one that results in a higher payoff regardless of the other firm's choice. In this matrix, both firms will compare the outcomes of their strategies. * Firm A finds High brings 4 (if B chooses High) and 3 (if B chooses Low). * Firm B finds High brings 4 (if A chooses High) and 7 (if A chooses Low). Thus, both firms might choose High regardless of the other firm's decision due to fear of being worse off if the competitor chooses High.

Evaluate the Nash Equilibrium

The Nash Equilibrium occurs when neither firm has anything to gain by changing only their own strategy. Here, if both firms choose High, even though (4, 4) is less profitable than (6, 6), neither firm shifts to Low alone due to the risk of being outcompeted (getting 3 if they go Low while the other remains High). Therefore, (High, High) at (4, 4) is the Nash Equilibrium.

Conclude on Unilateral Decisions

Neither firm will unilaterally cut its advertising budget because doing so could lead to lower profits if the other firm maintains a high budget. The strategic position and competitive dynamics force them to stick with high advertising to avoid an even worse outcome, even though mutual cooperation with low advertising would be better.

Key concepts

Strategic Form Payoff Matrix

In game theory, a strategic form payoff matrix is a tool used to represent the potential outcomes of a situation involving multiple players or firms, each with distinct strategies. Imagine you have two firms, Firm A and Firm B, both deciding on their advertising budgets. Each firm has two choices: maintaining a high advertising budget or opting for a low one. The strategic form payoff matrix is organized in a grid-like structure, where each cell within the matrix contains a pair of numbers representing the potential profits for each firm based on their strategic choices.
For example, when both Firm A and B choose a high budget, the matrix records profits of (4,4), indicating lower profits due to high advertising costs. This setup also helps visualize other potential outcomes, such as if both chose low advertising budgets, they would earn (6,6) in profits. This graphical representation helps pinpoint how strategic decisions impact outcomes.

Nash Equilibrium

The Nash Equilibrium is a key concept in game theory where players, like firms in our matrix, reach a stable state. Here, no player can gain an advantage by changing their strategy while others keep theirs unchanged. In the advertising budget scenario, both firms choosing a high budget results in profits of (4,4). Despite (6,6) being a more profitable outcome, the state (High, High) where each firm earns 4 is a Nash Equilibrium.
This is because neither Firm A nor B would reduce their advertising budget unilaterally. Moving to a low budget alone risks facing a lower payoff, such as Firm A getting 3 if it chooses Low while Firm B remains High. Therefore, both firms stick with High, fearing being outcompeted and losing profits if they change.

Dominant Strategies

A dominant strategy in game theory is one that achieves a better payoff for a firm, no matter what the opponent does. In our example, both firms appear to have dominant strategies encouraging them to spend heavily on advertising. When Firm A adopts a high advertising budget, it ensures a profit of at least 4, even if Firm B opts for low. Conversely, choosing a low budget guarantees only 3 if Firm B stays High, which isn't preferable.
Similarly, Firm B's dominant strategy is to also pursue a high advertising budget. This results in a payoff of 4, regardless of Firm A's action, compared to 7 or 3 in varying scenarios if Firm A decides differently. The fear of being outperformed pushes each firm to stick with their dominant high-budget strategy to avoid financial losses.

Advertising Budgets

Advertising budgets in competitive business landscapes significantly impact a firm's strategy and profitability. Budgeting decisions not only define a firm's market presence but also gauge its competitive stance against rivals. In the examined strategic form matrix, the firms are tempted to choose high advertising budgets constantly. This is because by doing so, they prevent being at a disadvantage in visibility and market impact. However, cost issues arise because prolonged high spending can diminish overall profits, as evidenced by the lower (4,4) earnings when both firms choose high. On the flip side, if both firms settle for a low advertising budget, they avoid the high costs and yield more substantial profits like (6,6). However, the challenge with lower budgets is the perceived risk of losing out in competitiveness if the other doesn't follow suit.

Competitive Strategies

In a competitive market, firms craft strategies considering both internal strengths and external market factors, against the backdrop of rivalry. To thrive, firms analyze and predict competitor behaviors to fine-tune their strategies, as seen in our scenario. Both firms, A and B, know the pivotal role of advertising to stay relevant and secure strategic advantages. Thus, they are inclined to choose high advertising budgets, as it seems to help maintain market shares and prevent losing ground to competitors. This collective decision, however, confines them to a less optimal profit scenario in terms of costs. The key takeaway is that while competitive strategies are vital, sometimes they require collaborative agreements or industry standards to maximize overall profitability, avoiding mutually detrimental high-cost strategies.