How Game Theory Can Help You Decode The Financial World

9 min readJul 16, 2024

***Image by*** ***Aidan Howe*** on ***Unsplash***

Some people often view trading or investing as a form of informed gambling but what if I told you that’s not remotely true? Akin to the majority of the world, finance, too unfolds in a way that can be studied and to an extent, predicted.

This is where the highly understated Game Theory comes in. Introduced by Hungarian-born American mathematician John von Neumann and his colleague Oskar Morgenstern, a German-born American economist in 1944, it was further popularised by John Nash who won the 1994 Nobel Prize in Economics for his work.

Game Theory significantly influences not only mathematics and finance but also fields such as evolutionary biology. Did you know that evolutionary Game Theory allows us to model the behaviour of organisms according to the strategies they use to compete for resources or cooperate?

What exactly is the Game Theory?

It is a branch of applied mathematics that examines the rivalries between competitors with mixed interests.
It helps one analyse a certain kind of situation where all involved parties, termed players make interdependent decisions.
The outcomes each player receives from the combination of strategies they employ are termed payoffs.

Why is this interdependency important?

The whole mechanism of Game Theory revolves around each decision being influenced by a variety of factors. This is caused by interdependency — each player is forced to consider the other players’ potential decisions before they can come to their own choice. Credited to Nash is a fundamental concept of Game Theory — the Nash equilibrium; which represents a stable state where no player has a reason to deviate from their chosen strategy.
This interdependent approach is also what helps describe how a solution to a particular game would look like. A solution should be able to describe not only what the optimal decisions of players are but also, what outcomes may result from these decisions.

Game Theory is all around us.

For example, the well-known Prisoner’s Dilemma is a Game Theory scenario where two prisoners must decide independently whether to betray each other or remain silent. This can have the following outcomes:

If both betray, they receive moderate sentences;
If one betrays and the other remains silent, the betrayer goes free while the silent prisoner receives a harsh sentence;
If both remain silent, they receive light sentences

Now what would a general solution to this look like?

Considering a single game, a solution is for both players to betray. This is because betrayal is the dominant strategy for both players; each player’s most plausible response, regardless of the other player’s choice, is to betray. Thus, both end up betraying, leading to a worse collective outcome than if they had both cooperated.

What if I told you that we’ve actually seen this unfold in real life?

The 2008 Financial Crisis is a case study of what not to do and a beautiful illustration of the Prisoner’s Dilemma.

The 2008 financial crisis, triggered by the collapse of Lehman Brothers, was largely driven by risky lending practices and the subsequent bursting of the housing bubble. This crisis also highlighted the interdependencies within the financial system.

Using the Prisoner’s Dilemma, we can understand the behaviour of banks and financial institutions that led to this crisis. Each bank had the choice to either engage in risky lending practices (defect) or adhere to more conservative lending standards (cooperate).

Both Cooperate: If all banks chose conservative lending, the financial system would remain stable, but individual profits might be lower.
One Defects, One Cooperates: If one bank engaged in risky lending while others did not, the defecting bank would reap high profits, at least initially, while the cooperating bank would see lower profits.
Both Defect: If all banks engaged in risky lending, it would eventually lead to a systemic crisis, resulting in massive losses for all.

Driven by short-term profit incentives and competitive pressures, most banks chose to defect, leading to widespread risky lending. This collective behaviour contributed to the financial collapse i.e. both prisoners betrayed each other and received the worst collective outcome.

Several individuals actually foresaw this eventual collapse as explained by Michael Lewis in his book titled “The Big Short: Inside the Doomsday Machine” and the subsequent movie ‘The Big Short’. It provides a critical look at the factors that led to the crisis, including the complex financial instruments and questionable practices that contributed to the economic downturn.

This is all to show that Game Theory is quite essentially, everywhere.

Now how exactly does this theory dictate what we often deem chance?

The ultimate goal of Game Theory in any scenario is to provide an optimal framework that is most likely to provide a favourable decision after due strategic analyses. It provides a structured approach to conduct this analysis of players’ interactions and make decisions based on how they might act.

It is important to note that Game theory is not simply the science of chance. It involves analyzing decisions under uncertainty but it primarily deals with strategic behaviour, not random chance.

In the context of financial markets, Game Theory often manifests as a subset of itself called the Auction Theory. Much like Game Theory — auction theory studies how different auction designs and bidding strategies influence the outcomes. It analyzes various auction formats and their impact on bidder behaviour, seller revenue, and overall market efficiency.

For example, the winner’s curse phenomenon is a scenario in auctions where the winning bidder tends to overpay due to competition. This eventually leads to a realization that the item’s value is lower than the bid price. This often occurs because bidders base their bids on incomplete information and may overestimate the item’s true value.

Remember the dot-com boom that birthed companies like Google and Amazon?

The late 1990s saw a massive surge in investments in internet-based companies, leading to the dot-com bubble. This is something known as herd behaviour, where investors mimic the actions of others, leading to bubbles (prices of assets rise quickly becoming much higher than their real value) and crashes (prices suddenly drop significantly, often after a bubble).

So, many investors, driven by the fear of missing out, poured money into tech stocks with little regard for their actual business models or profitability — a classic illustration of the winner’s curse phenomenon.

Investors i.e. the bidders in the dot-com era were trying to outbid the others to secure shares in tech companies. This intense competition and hype led many to overvalue these companies, resulting in massive overbidding. When the bubble finally burst, it became evident that many of these companies were not worth their inflated valuations, leading to significant financial losses for the “winning” investors who had overpaid.

We’ve seen the Game Theory in action but how does it help us decode the system?

Firstly, to truly understand this, we need to wrap our minds around some of the core fundamentals of Game Theory.

The first is the aforementioned Nash equilibrium. A fundamental concept where each player’s strategy is already optimal i.e. at a stable state, given the strategies of other players.

In financial markets, a Nash Equilibrium can help predict stable states where no trader can benefit by changing their strategy alone. A 2021 study, Modelling the Stock Market Through Game Theory by Kylie Hannafey, explains how the Nash equilibrium can be applied to businesses in the stock market.

The second is the concept of Zero-Sum Games i.e. situations where one trader’s gain is another’s loss. Understanding these dynamics helps traders develop strategies to maximize their payoffs. Many interactions in finance are not one-off but occur repeatedly. Repeated Game Theory helps in understanding how cooperation or competition evolves among market participants.

And finally, we have behavioural biases. Behavioural economics examines how psychological biases influence decision-making by learning about investor sentiment, overconfidence, and herding behaviour which can provide valuable insights.

Let us consider a simple question. How can you choose which stocks to invest in? Or how can we ‘predict’ which one will perform better?

Applying Game Theory to investment decisions involves a systematic approach to analyzing the interactions between the players. Here’s an oversimplified way of using Game Theory to approach it:

1. Define the Players and Their Objectives

The key players are identified — you i.e. the investor, other investors, and potential companies and each player’s objective is defined; to maximize their returns on investment. For you, this means choosing stocks that are likely to perform well.

2. Gather Information

This is research. Data on preferred stocks is collected including past performance, current market conditions, company financials, and news. Now you analyse your competitors and understand their behaviour. Are they bullish (expecting prices to rise) or bearish (expecting prices to fall) on certain stocks? What trends are they following?

3. Identify the Strategies

List the potential actions you can take, such as buying Stock A, buying Stock B, diversifying across multiple stocks, or not investing at all and consider the possible actions of other investors.

4. Construct the Payoff Matrix

Create a payoff matrix that shows the expected returns for each combination of your strategies and those of other investors — essentially a table listing the results of every possible strategy.

5. Analyze the Equilibrium

Determine if there is a Nash equilibrium, where no player can benefit by changing their strategy while the other players keep theirs unchanged and identify the strategy that maximizes your payoff.

6. Decide, Monitor and Adjust

Based on the analysis and factoring in external influences, select the investment strategy that offers the best balance of expected returns and acceptable risk. Keep track of market performance, and other investors’ actions and be prepared to adjust your strategy in response to new information or changes in market conditions.

And there you have it.

Photo by Jonathan Petersson on Pexels.com

The key is always to consider not only the fundamental analysis of stocks but also the strategic behaviour of other market participants.

Game Theory, while vast and sometimes appearing convoluted provides a robust toolkit for predicting and understanding stock and trading patterns in financial markets. It is in simple terms — strategic analysis. By doing so and anticipating the actions of various market participants, Game Theory helps investors, firms, and regulators make more informed decisions. And it can help you too.

It would also be prudent to keep in mind that while Game Theory can provide insights, predicting financial markets with high precision remains extremely challenging due to the complex and often unpredictable nature of human behaviour and external factors. This is because Game Theory assumes rational behaviour, but in reality, market participants often act irrationally due to behavioural biases which is why behavioural economics plays an integral role in analyses.

Whether it’s pricing strategies, market entry decisions, or understanding the dynamics of financial bubbles, Game Theory offers insights with high returns into the growing world of finance, providing a framework for understanding and navigating the complexities of financial markets and perhaps, even charting the course of ‘chance’ itself.