When R/Tensorflow/Keras, Network Theory & Game Theory (Nash equilibrium) face reality: Market Power in Atlanta, GA.

1. Introduction

The interaction between large and small companies is a critical component of the economic landscape, particularly in a diverse and dynamic region such as Georgia. This study (a second part of this one: here) examines the strategic decisions of five major companies—CNN, Coca-Cola, Delta, Home Depot, and UPS—when engaging with smaller firms. The focus is on understanding how different strategies, namely cooperation and competition, impact the payoffs for both large and small companies. The analysis employs game theory, particularly concepts of Nash equilibrium and Pareto efficiency, to elucidate these interactions.

2. Theoretical Framework

The analysis is grounded in microeconomic theory, specifically the strategic interactions modeled through game theory. In a simplified form, these interactions can be represented as a two-player game where each player (in this case, a large company and a small company) can choose between two strategies: cooperate or compete. The outcomes of these strategies are represented in a payoff matrix, which outlines the rewards each company receives based on the combination of strategies chosen.

1. Cooperation vs. Competition: Cooperation between firms can be understood through the lens of collusive behavior or strategic alliances. When firms cooperate, they typically coordinate their actions to maximize joint profits, often leading to outcomes that are Pareto efficient, where no party can be made better off without making another worse off. Competition, on the other hand, represents a non-cooperative scenario where each firm seeks to maximize its individual payoff, potentially at the expense of the other. This competitive behavior often leads to outcomes that are suboptimal from a collective standpoint, as firms allocate resources towards rivalry rather than value creation.
2. Nash Equilibrium: The concept of Nash equilibrium is pivotal in this analysis. A Nash equilibrium occurs when no firm has an incentive to unilaterally change its strategy given the strategy of the other. In this context, the equilibrium can either be cooperative, where both firms cooperate, or competitive, where both firms choose to compete.
3. Pareto Efficiency: A Pareto efficient outcome is one where it is impossible to improve one firm’s payoff without reducing the payoff of the other. In the context of this study, cooperation tends to lead to Pareto efficient outcomes, as it maximizes the combined payoffs for both large and small firms.

3. Methodology

The analysis involved building and training a Recurrent Neural Network (RNN) model using the keras package in R. The process began with data preprocessing, which included normalizing the data and organizing it into a suitable format for time series analysis. The data was then split into training and testing sets.

Next, a sequential RNN model was defined, where layers such as LSTM (Long Short-Term Memory) or GRU (Gated Recurrent Unit) were used to capture temporal dependencies in the data. The model's architecture was carefully tuned by adjusting the number of units in each layer, adding dropout layers to prevent overfitting, and selecting appropriate activation functions.

The model was compiled using an optimizer like Adam and a suitable loss function based on the type of prediction task (e.g., mean squared error for regression). During training, the model's performance was monitored using validation data, and early stopping was applied to avoid overfitting.

After training, the model's performance was evaluated on the test data. Various metrics such as RMSE (Root Mean Square Error) and R-squared were computed to assess the accuracy and reliability of the predictions. Finally, the results were visualized using R's plotting functions to interpret the model's predictions and compare them against the actual values.

4. Results and Discussion

The empirical results of the study reveal significant insights into the strategic dynamics between large and small companies in Georgia.

Mutual Cooperation: When both large and small companies opt to cooperate, the results are strikingly favorable for both. For instance, when CNN, Coca-Cola, Delta, Home Depot, and UPS engage in cooperative strategies with smaller companies, both parties receive the highest possible payoff of 4 each. This scenario exemplifies a cooperative Nash equilibrium, where the benefits of collaboration are fully realized. The outcome is also Pareto efficient, as it maximizes joint value creation and ensures that neither party can improve its payoff without harming the other.

Mutual Competition: Conversely, when both large and small companies choose to compete, the results are notably less favorable. In this scenario, the large companies receive a payoff of 3, while the small companies receive a payoff of 2. This outcome reflects a competitive Nash equilibrium, where both parties’ attempts to maximize individual gains lead to a collectively suboptimal result. The inefficiency of this outcome can be attributed to the misallocation of resources towards competitive actions rather than cooperative value creation, a common phenomenon in non-cooperative games.

Asymmetric Strategies: The analysis also considers scenarios where one company chooses to cooperate while the other competes. Interestingly, these asymmetric strategies result in balanced payoffs of 3 for both large and small companies. While this outcome avoids the inefficiencies of mutual competition, it also fails to capture the full benefits of mutual cooperation. The equal payoffs suggest that while the cooperative party mitigates the potential losses from competition, it does not fully capitalize on the gains available through joint cooperation.

Microeconomic Implications: The findings of this study have important microeconomic implications for understanding firm behavior and strategic decision-making in competitive markets. The superior outcomes associated with mutual cooperation suggest that companies can benefit from forming strategic alliances or engaging in cooperative behavior, even in a competitive market environment. Such behavior can lead to more efficient resource allocation, higher joint profits, and more stable market conditions.

It is noteworthy that in the "game" of averages, Medium companies have greater market power overall than Large companies.

Moreover, the study underscores the risks associated with competitive strategies. While competition can drive innovation and efficiency, it can also lead to destructive behaviors where firms prioritize short-term gains over long-term value creation. This dynamic is particularly evident in the lower payoffs observed in the competitive equilibrium, highlighting the potential for market inefficiencies when firms fail to cooperate.

Policy and Strategic Recommendations: For policymakers, these results suggest that fostering an environment conducive to cooperation among firms, particularly between large and small companies, can lead to more robust economic outcomes. Policies that encourage collaboration, such as tax incentives for joint ventures or support for industry-wide standards, could help mitigate the inefficiencies associated with competition.

For business leaders, the findings highlight the importance of strategic cooperation in achieving sustainable competitive advantage. By identifying opportunities for collaboration, whether through partnerships, mergers, or strategic alliances, firms can enhance their market position and achieve superior economic outcomes.

5. At the end…

The strategic interactions between large and small companies in Georgia reveal a clear preference for cooperation over competition, as reflected in the higher payoffs for both parties when they choose to collaborate. The study’s application of game theory to these interactions provides a robust framework for understanding how firms can navigate competitive markets and achieve Pareto efficient outcomes. Ultimately, fostering cooperation, both at the firm and policy levels, can lead to more stable and prosperous economic conditions for all parties involved.