Even with its misses and hits as it was applied in finance, the enduring allure of game theory as a pragmatic problem-solving tool remains undiminished. Textbooks, both introductory and advanced, tantalize with the promise of its “real-world applications,” hinting at a transformative role within the social sciences. Yet, upon closer examination of these claims, one finds that the examples often harken back to the familiar narratives of traditional game theory, featuring classics like the Prisoner’s Dilemma and the Chicken Game. Even comprehensive volumes such as the “Handbook of Game Theory with Economic Applications” may fall short when it comes to providing concrete examples or empirical data that validate the field’s evolution.
Beyond these traditional applications, game theory has also made significant inroads into various other domains. Market Behavior and Dynamics find themselves under the scrutiny of game theoretic models, which strive to unravel the complexities of interactions between market participants, shedding light on the behavior of buyers and sellers, price dynamics, and market outcomes. In the realm of Strategic Decision Making, game theory equips decision-makers with valuable tools to navigate scenarios involving competition, cooperation, and negotiation, offering insights into optimal strategies and their outcomes. Investment and Risk Management, as crucial financial domains, benefit from game theory’s ability to analyze complex financial interactions, assess risk, and develop strategies for successful investments. Lastly, Regulatory and Compliance issues are tackled with game theory, where models help in devising efficient and fair regulatory mechanisms, ensuring that industries adhere to compliance standards while minimizing inefficiencies. However, how developments in the underlying mathematics will also impact how current strategies are being applied by the game’s current players. The issues of which were observed and noted by Larry Samuelson in his article: Game Theory in Economic and Beyond, but we’ll only briefly go through them as a crash course to see where we stand.
As most game theorists like to point out, the crux of the issue lies in the stringent assumptions imposed by game theory models. These models demand an almost unattainable level of precision in terms of information, requiring knowledge of each player’s payoffs, the game’s rules, and the overarching structure. These assumptions create a substantial disconnect between the theoretical constructs of game theory and the intricacies of real-world decision-making.
At the heart of game theory lies the concept of equilibrium, with Nash equilibrium occupying a central position. Conventionally, it was believed that rational players should naturally gravitate towards equilibrium, with its existence considered self-evident in most cases. However, this perspective doesn’t always align with the intricacies of practical scenarios. The vagueness surrounding equilibrium analysis in real-world situations raises fundamental concerns about its applicability.
In response to the problem of multiple equilibria, game theorists introduced equilibrium refinements. Consequently, this effort led to an ever-growing assortment of refinements, leaving scholars and practitioners at an impasse. This development questions the fundamental relevance of Nash equilibrium and its various refinements when it comes to real-world scenarios.
While there have been pockets of success in applying game theory to areas like auctions and matching, these applications are not without their complexities and uncertainties. For instance, auctions require meticulous consideration of factors like common values, risk preferences, and market structures, often leading to numerous modeling choices. In the case of matching, a common real-world scenario, organizers often grapple with ethical dilemmas as they are required to make value judgments. Despite some accomplishments in these areas, the practical applicability of game theory continues to be a subject of debate.
The last notable observation of game theory’s evolution is the transition from a cooperative to a non-cooperative approach in game theory aligning with the rise of “microeconomic foundations”, which may go as far as implying the shift to non-cooperative approach as an abandonment done for ideological reasons. This shift raises questions about the motivations behind the evolution of game theory and its practical relevance. The cooperative approach, known for its “satisfying” matchings within coalitional game theory, represents a fascinating departure from the non-cooperative paradigm that became dominant in the 1970s. This transition is intriguing given that cooperative game theory once held a prominent place in the field, particularly in the foundational work of John von Neumann and Oskar Morgenstern, who sought to address the circularity inherent in strategically interdependent situations. They aimed to provide players with strategies that were independent of their expectations about their opponents’ intentions.
Furthermore, Von Neumann and Morgenstern gave special attention to what they termed “orders of society,” essentially institutional arrangements. The multiplicity of these orders reflects the diversity of real-world societies where individuals form groups, or coalitions, to cooperate. The emphasis on “order” underscores the focus on scenarios where groups maintain stability, and various cooperative solution concepts align with this perspective.
Revisiting the cooperative approach may provide new avenues for bridging the gap between the theoretical underpinnings of game theory and the multifaceted realities of real-world decision-making, offering a fresh perspective on problem-solving that balances individual and collective interests. However, this transition presents an intriguing paradox – one of the most significant practical successes attributed to game theory, namely matching, represents a form of planning that doesn’t entirely conform to that individualistic line of thinking as shifts between cooperative and non-cooperative approaches affect the historical and ideological nuances of game theory’s evolution.