Key Assumptions of Game Theory

Introduction

Game theory, a mathematical tool for understanding the dynamics of strategic interactions among decision-makers, forms the foundation of our analysis. While its theoretical underpinnings rest on the assumption of rationality and complete information, it is essential to recognize that real-world scenarios often deviate from these idealized conditions. Strategic decisions made by individuals, such as managers, may be driven by diverse motives, including the pursuit of growth, revenue maximization, or corporate social responsibility, challenging the assumption of purely rational behavior. Furthermore, the elusive quest for complete information, wherein all players possess a comprehensive understanding of payoffs associated with strategy changes, often proves unattainable in practice.

Our investigation delves into specific game models, such as the Prisoner's Dilemma and the Cournot Duopoly, to shed light on the consequences of strategic behavior within the realm of economics. The Prisoner's Dilemma predicts that two oligopolistic firms engaging in strategic actions invariably find themselves in a suboptimal position due to their inclination to collude initially and subsequently betray each other. This prediction aligns with historical evidence, notably observed in the U.S. Automobile Market during the 1950s.

Another model we explore is the Cournot Duopoly, which posits that a duopoly, characterized by the presence of two firms, yields more favorable market outcomes than a monopoly. In this approach, firms engage in competition based on quantity adjustments, as increasing prices would result in a decline in market share (Ferguson, n.d.). While this model presents challenges in empirical testing, economists widely accept its conclusions as accurate.

To enhance the Cournot Duopoly model's accuracy, it is imperative to acknowledge the information disparities among players and the existence of multiple Nash equilibria, each representing an ideal outcome for a player. This model offers valuable insights into the behavior of oligopolistic firms, elucidating their avoidance of non-price competition, the perceived rigidity of prices, and their susceptibility to collusive temptations. Moreover, it can be applied to dissect the collaborative efforts of larger entities like governments on issues such as international trade.

In this comprehensive report, we embark on a detailed exploration of game theory, an indispensable analytical tool. Game theory empowers decision-makers to anticipate and respond to their opponents' actions strategically, optimizing their outcomes. The decisions made by fellow players in the game exert profound influence on the overall results, rendering the study of this dynamic field crucial to our understanding of economics. It is crucial to distinguish between non-cooperative and cooperative game theory. One prominent example of the former is the Nash Equilibrium, wherein no player has an incentive to alter their strategy, even when possessing complete knowledge of their opponents' choices (MBA Crystal Ball, n.d.). Our investigation will revolve around various instances of Nash Equilibrium, notably the Prisoner's Dilemma and the Cournot Approach, and their profound implications for the field of economics.

An Overview of the Game Theory

Cooperative game theory introduces a different dimension, where players collaborate within groups and vie against other such groups. This concept finds an intriguing parallel in organizations like OPEC, where member states collaborate to restrict oil supply, thereby driving prices upward and maximizing profits. In the following sections of this report, we will delve into the foundational principles of cooperative game theory, its practical applications, as well as the inherent limitations that it grapples with.

A central tenet of game theory is the assumption that all participants act rationally, driven by a relentless pursuit of maximizing their payoffs within the game (Economics Discussion, 2019). While this assumption forms the bedrock of the model, its applicability to the real world remains contentious. Real-life decisions can often be influenced by emotions or impulsive choices. For instance, an investor might eschew a financially sound football team in favor of one they have supported since childhood, sacrificing potential higher returns for sentimental reasons. Similarly, in the realm of oligopolistic firms, managers may prioritize factors such as growth, revenue, and corporate social responsibility over strict profit maximization.

The second assumption posits the existence of a finite number of competitors and a predetermined set of outcomes (Ferguson, n.d.). In this construct, all possible outcomes must be foreseeable before the game commences. However, this assumption faces real-world challenges. Unexpected events can disrupt the anticipated outcomes, rendering the predetermined nature of the game moot. Additionally, the practicality of firms possessing comprehensive knowledge of both their own payoffs and those of their competitors is questionable. As Osak (2010) aptly points out, many firms lack sufficient information to make informed strategic decisions.

Furthermore, the idealized concept of complete information, where each player possesses knowledge of their opponents' payoffs (Kovach, Gibson & Lamont, 2015), does not align with the complexities of reality. Information imbalances often exist, giving some players an advantage in strategic decision-making. This variance in information availability can significantly impact the fairness of the game.

However, the notion that players only concede when it enhances their probability of winning finds resonance in real-life scenarios. The TV game show "Golden Balls" serves as an illustrative example, where contestants face the choice of splitting or stealing the prize money in the final round. In many instances, participants opt to share the prize, driven by ethical considerations and a desire to avoid betraying their counterparts (Investopedia, 2019).

Lastly, the assumption that players can seamlessly adopt multiple strategies and adjust their pricing in response to competitors encounters practical obstacles. Industry-specific regulations, such as price ceilings, can constrain firms from altering their prices beyond a certain threshold, making such strategic flexibility challenging to achieve in practice.

Prisoner’s Dilemma

One of the pivotal applications of game theory, the Prisoner's Dilemma, illuminates the intricate dynamics of strategic interactions where the decisions of one player influence the outcomes for all participants. This model revolves around the prediction that when two rational decision-makers employ strategic behavior to enhance their individual positions, they ultimately find themselves in a collectively disadvantaged state (Tragakes, 2015).

At the outset, both firms in this scenario opt for a low pricing strategy, each reaping profits of $20 million. However, they soon recognize that by colluding and jointly implementing a high pricing strategy, they can collectively amass profits of $50 million. A dilemma then ensues: each firm faces the temptation to betray the collusive agreement, reverting to a low pricing strategy to seize their rival's market share and boost their individual profits to $70 million. Furthermore, both firms harbor the belief that if they do not initiate this betrayal, their competitor will seize the opportunity. Consequently, both firms lower their prices, reverting to the $20 million profit margin.

The game theory posits that two firms employing strategic behavior inevitably end up in a suboptimal position due to their mutual incentive to cheat, underscoring the notion that price competition within the domain of oligopolistic firms should be strenuously avoided (Tragakes, 2015). This model unravels the web of strategic interdependence that characterizes oligopolies, where conflicting incentives to cheat or collude continually shape the competitive landscape. Regrettably, empirical testing of this prediction encounters substantial challenges, as discussed earlier in the limitations of game theory. Nonetheless, historical instances provide compelling evidence supporting the conclusions drawn from the Prisoner's Dilemma.

During the 1950s, General Motors (GM), Ford, and Chrysler enjoyed dominance in the U.S. automobile market and collectively conspired to introduce their own iterations of small cars. However, the 1970s witnessed a divergence in their strategies. Chrysler initiated sustained price increases for its small cars, with GM and Ford intended to follow suit. In a bid to seize a portion of Chrysler's market share, GM opted for a smaller price hike than Chrysler. This strategy initially succeeded, until Chrysler decided to revert to its initial pricing, effectively nullifying GM's advantage. This historical example vividly illustrates the intricacies of conflicting incentives to cheat and collude within the strategic interplay of oligopolistic firms, ultimately leaving them worse off.

Cournot Duopoly Model

The Cournot Duopoly Model employs game theory to predict that firms operating within a duopoly market structure offer more societal benefits compared to monopolies. This assertion arises from the model's assumption that within an industry, two firms produce a homogeneous product, act strategically without collusion, and exhibit complete rationality. In this scenario, firms aiming to increase profits can consider raising prices, but such a strategy comes at the cost of market share loss. Therefore, Cournot's approach seeks to maximize both market share and profits by determining optimal prices (Ferguson, n.d.). These prices are mutually accepted by both firms, constituting a Nash Equilibrium. Given that this approach emphasizes competition through quantity adjustments, it forecasts that this market structure can better generate socially optimal quantities of goods compared to monopolies.

While this model presents valuable insights, it is challenging to empirically test due to its theoretical nature. Nonetheless, economists widely accept its predictions, largely agreeing that monopolies are generally detrimental from a societal perspective. In practice, monopolies are either illegal or subject to government regulation, potentially leading to outcomes more favorable than those observed in duopoly settings.

The Cournot Duopoly Model yields normative conclusions. It advises players to select options that are likely to yield better outcomes, even if it means receiving lower rewards with reduced risk. Additionally, it underscores the advantages of forming alliances and engaging in cooperative game theory, as this can transform potential adversaries into allies.

Improving Game Theory

Enhancing game theory to address its inherent challenges would be valuable in making it more relevant and beneficial for various stakeholders in society. The model is designed to analyze individual behavior in strategic situations where opponents possess limited information about each other (Kovach, Gibson & Lamont, 2015). While this notion may align with the practices of many oligopolistic firms striving to shield information from rivals, it may not always hold in the real world. In such cases, the model's accuracy diminishes, and it becomes less effective in providing solutions for complex real-world conflicts characterized by information disparities among key players (Kovach, Gibson & Lamont, 2015). One avenue for improvement could involve developing distinct game models for each player, accommodating the differences in information, beliefs, and understandings within the game.

Another limitation lies in the model's assumption that players consistently act strategically and consider their competitors' responses. In reality, not all managers operate with such a mindset, rendering some of the model's conclusions inapplicable. Additionally, effective utilization of the model depends on managers' ability to discern the expected positive and negative payoffs of their actions. However, this is often challenging since "most firms will not have enough knowledge of their own payoffs, let alone those of their competitors" (Osak, 2010). Unfortunately, these inherent challenges remain intractable, necessitating a growing demand for empirical tests of these theories. However, conducting such tests is exceedingly difficult due to the model's highly simplified assumptions (Reinganum, 1984).

Conclusion

Game theory significantly enriches our understanding of oligopolistic firms by highlighting their complex web of interactions. Each business decision made by one firm can reverberate throughout the industry, profoundly affecting the profits of others (Osak, 2010). The model enables firms to formulate optimal strategies based on pre-calculated payoff matrices, offering valuable insights into their behavior, including incentives to collude and cheat. This understanding extends to the operations of cartels like OPEC and various forms of tacit collusion among oligopolistic firms.

Furthermore, game theory finds relevance in government decision-making, particularly in the context of international trade. Governments often face strategic dilemmas, such as whether to participate in cooperative agreements or pursue independent strategies. For example, countries seeking allocative efficiency in common access resource markets, like fisheries, may collaborate through cap-and-trade schemes. However, such agreements introduce complexities, as countries may anticipate the actions of others, potentially affecting their own decisions. This illustrates how governments can utilize game theory to inform their choices in international trade and cooperation.

In summary, game theory offers a powerful tool for analyzing strategic decision-making in competitive settings, providing valuable insights into human behavior and interactions. While it operates within certain assumptions that do not always mirror reality, its applications remain instrumental in elucidating complex dynamics and guiding decision-makers across various domains.