Finance as a rigorous study is relatively young compared to most of the sciences that statistics and mathematics have popped out over the last century and a half, the most notable initial proponents of which are the CAPM and EMH models derived during the mid-1900s and of course the Black-Scholes (-Merton, if you want to be pedantic) model. Prior to that the world was going through the industrial revolution and presents a whole new level of weird in decision making as they were essentially decisions done on a different paradigm, so we’ll skip past that for now. So, in terms of finance growing as a discipline it had quite a bit of mathematical theories and properties to leverage and see if any of their specific objectives (usually getting the best payoff) can be squeezed into and studied, you know, by standing on the shoulders of giants.
In doing so, differential equations and probability theories were employed to measure something past mathematicians didn’t really investigate when developing probabilities, to win a game against someone with a different set of information than yourself. The consequence of which is that the models as they were in their original form did not always work in the real world as most of the earlier models assume rational actors.
Enter Game Theory.
By incorporating the gamification of events, finance as a field found a way to include behavior into equations to rationalize a decision, especially for corporate finance. Initial forays into this looked into dividends as a signal, IPO decision making, auctions, and so on. However, dropping rationality in decision making in everyday lives accumulated over millions of market participants in favor of behavioral models that try to bridge irrationality is quite a hard balance to strike and shaped how academics in Games in Finance slotted their ideas into three main research themes initially: Higher Order Beliefs, Heterogeneous Prior Beliefs, and Information Cascades.
Higher Order Beliefs
Higher order beliefs are an essential but often overlooked aspect of research in finance and game theory. In standard financial thinking, it’s not just about fundamental data; it’s also about what people believe about these fundamentals, what they think others believe, and so on. Surprisingly, mainstream finance research often ignores these considerations, especially when it comes to models with rational actors. However, game theory, which deals with strategic situations involving coordination, tells us that even rational actors are significantly influenced by higher order beliefs.
Heterogeneous Prior Beliefs
Heterogeneous prior beliefs, a key research theme in finance and game theory, address how differences in what people believe are modeled. In traditional economic and financial models, there’s an assumption known as the “common prior” assumption. This means that while rational individuals might have access to different information (resulting in uneven information distribution), it’s also assumed that their subsequent beliefs are based on a shared initial belief regarding some state space. In simpler terms, this assumption implies that any variations in what people believe are attributed to disparities in available information rather than differences in their original beliefs.
Information Cascades
Information cascades, a significant research theme in finance and game theory, explore situations where individuals make decisions sequentially, and their actions are influenced by the decisions of those who acted before them. The usual examples used to illustrate information cascades looks into how the decision of an individual were influenced by “experts” such as purchasing stock at its IPO or the bank run started by Peter Thiel on SVB. However, there’s a catch: these information cascade arguments often assume that the decision sets are too crude to fully reveal what people know. But in some situations where actions are more nuanced and can convey richer information, this assumption might not hold.
To complicate things further, there are scenarios in markets where information cascades can still happen, even when prices provide rich information. This can occur when transaction costs make investors reluctant to act on small pieces of information, and then a sudden public signal prompts them to trade. Additionally, when private information is rich and multi-dimensional, prices may not effectively reveal it, creating opportunities for information cascades.
Since then, in the current view of Game Theory in Finance those main themes haven’t evolved much and the idea has now been generally applied on the following broad themes: Market Behavior and Dynamics, Strategic Decision Making, Investment and Risk Management, and last but not least on Regulatory and Compliance.
As Game Theory’s influence across finance spreads, of course it is important to note that the use of Game Theory on Finance is not without its misgivings. The most quoted of which is Ariel Rubenstein that likens the use of Game Theory as applying “fables” with practical limitations stemming from the necessity for mathematical precision, a language that we are still learning.