GAME THEORY IN FINANCE
Corporate Finance and Game Theory
The subtext of games in everyday transactions and financial markets
Globalization has brought about significant changes in society, more entities are connected all over the world and a synthetic parsimonious framework of getting work done has come into place. One of the underappreciated and lost themes in the subtext of globalization is the basic interaction and exchange of ideas among entities that constituted a market in its truest form since inception.
With the evolving markets, new intricate structures and fairly complex to comprehend contract designs are traded. Contracts that are traded in the volumes of millions, such a system is inherently designed in a way to increase the barriers of entry to the industry and yes, you guessed it right — the bankers are to blame for this.
Once delved into, they are just stepped inflated variations of market interactions.
Interactions can be understood and appreciated if one is willing to step aside from the business and trading noises and manage to look at the bigger picture. That is when we see that how all of this can be shaved off to fragments of market interactions and moment-to-moment decision-making.
Once we begin to perceive the bigger picture, our beloved theory of games and strategy comes into play. Game theory is a theoretical framework to conceive social situations among competing players and produce optimal decision-making of independent and competing actors in a strategic setting. Games are abstract models which simplify complex real-life situations to focus on the essentials of a neatly defined game i.e. a function of players, the conditions, and their payoffs. Applications at different levels with the bound complexity of a situation, of course, bring about greater vicissitudes of this model of thinking but as we implied, the bigger picture is often easier to connect the dots on.
Every market transaction can be broken down in such a way as the buyer, seller, the conditions include the trading leverage which is just the ratio of the actual amount of physical goods involved in the contract, and finally, the payoff is the difference of the prices respective to each party. Finance, evolving from an interactive human market to an industry exists in all forms at all levels in our society, be it a teenager stocking up dogecoins as a devotee of the Twitter feed of Elon musk or the middle-aged investment banker hustling out a company’s data to put up a fair valuation for his bank to buy/sell while idolizing the latest update on Excel and Benjamin Graham’s evergreen fundamental investing principles.
Trading and game theory introduction
Trading in the equity markets has come a long way and is ever-evolving. One of the reasons behind it never maturing as an industry is the insignificant barriers to public participation and the inherent idea behind wealth creation by a business entity in its truest sense; forming a settlement between the socialistic and capitalistic school of thoughts of a society. In game-theoretical terms, this is seen as a positive-sum game, making a deterministic decision (bet) over a company’s equity and waiting out for capital gains as the company grows. Now, you might think there exists a profit and loss side here which is true, but we need to realize in equity the prices are defined by the founding rock of economics; supply-demand, so the greater interest of people in a company takes it to a higher value and thus this be seen as a positive-sum game with an equal chance of downside risk involved after all.
Trading of contracts of securities, known as the market of futures and options is just the buying and selling of an exercisable right to buy/sell in the future. Now here, the buyer’s profit is necessarily the seller’s loss and vice versa considering the enclosed nature of the contract and the prices in the FnO market move similarly to equities. There is no official movement of physical securities and the contracts are often cash settled on maturity thus, this is the perfect instance of a zero-sum game. Since the time frames are in the future, these are considered to be probabilistic bets. Hence, bringing out the beautiful yet sometimes ugly competitive strategy making and market manipulations.
To get an idea of the extreme competitive outlook of the market, we should see how different fund managers (market participants) think. They are in a strategic game with each other to outperform on their return with respect to the benchmark index. For the finance enthusiasts out there, this value is known as the manager’s ‘alpha’.
Evolutionary game theory and Real options
This is where we begin to apply evolutionary game theory which studies the players who change their strategies over time based on behavioral rules that are usually not rational. To model such evolutionary games, we use Markov Chains where the state variable is the strategy being used or how the game was being played in the past (historical data). This helps in analyzing the movement of security with the help of historical price movement.
Things with evolutionary game theory get interesting when it comes down to decisions between business entities away from the general public. Institutional investor decisions, mergers, and acquisitions preparing valuation toolkits, and the wonderful world of risk management fall under this category. A classic culmination of games and corporate decisions is the Real options theory. Concerning business managers, instances of real options include;
- option to expand/contract
- option to abandon
- option to wait
- option to switch
- representation of a manager’s perspective of different possible paths of building or deferring projects, each stage’s payoff defined by the NPV(net present value) of the firm
Business valuation and Strategy
Anyone in the business world is very well aware of the cloudy valuation system where everyone is constantly trying to offer up a fair price of an entity with various statistical models, fundamentals, and industry comparative diligence in place. And yet even the most brilliant statisticians and economists of the world are still figuring this system out. A significant breakthrough that often claims to fill in a ‘hole’ to this historic valuation framework is realizing a strategic option growth value that realizes the flexibility and the potential growth value.
This methodology, allows managers to pan out a lattice of possibilities at every step in the future charting out various decision paths and hence, calculating a probability cum risk-adjusted price to the entity. This makes room to make strategies to play out with the decision chart whereinto time the efficient timeframe of holding or selling the entity by making use of our classic payoff matrices for each step.
*example of using payoff matrices as a way to figure out a relatively dominant strategy
Conclusive remarks
In conclusion, we realize the imperfect nature of the field of finance and business and how every step is the result of a vast synthetic network of human interactions and decisions.
This makes us appreciate the immensely competitive nature of the industry and how this, like every other game and the bread and butter of economics, is an attempt at optimization.
References;
Real Options Theory: An Alternative Methodology Applicable to Investment Analyses in R & D Projects- Jerson Silva, Hugo Tadeu
