The Mathematics of Strategy: Understanding Game Theory Through Nash Equilibrium

What is Game Theory?

Game Theory is the quantification and examination of how individuals, entities, governments, and firms make decisions in a competitive system, mainly through the mathematical model of Nash Equilibrium. In this competitive system, individuals, called players, compete for business, opportunities, resources, and profits, and their actions affect the actions and outcomes of other players. This model helps identify the optimal rational decision for all players through cooperation or conflict. Also known as the “science of strategy,” game theory considers choices, payoffs, and incentives to analyze how players behave in competitive environments. The cool thing is that game theory can be applied to various sectors in addition to economics, such as computer science and politics, really shaping how entities react and shape decisions off each other.

The Nash Equilibrium- How Game Theory works?

With Game Theory, many complex mathematical calculations are involved. However, we can group most of the mathematics under the Nash Equilibrium. A Nash equilibrium is a situation in which each player in a competitive environment makes the best decision they can, while taking into account the decisions of others. It works as follows: there are two or more firms in a competitive environment. “I” denotes players in the system, and S represents the number of strategies available to the players. Each player has an opportunity set of payoffs, which are the outcomes each player receives depending on the choices of the other players, represented by u(s,...). 

This model wraps together all of the aforementioned variables to represent a “steady state” of strategic interaction in the competitive environment. Firms can therefore use this equation to identify the stable choices that will yield the highest profits and output, thus furthering a capitalist whole.

The impact of Game Theory on solving present-day issues in Finance and Economics

In the modern day in economics and finance, Game Theory, specifically the Nash Equilibrium, is applied in many different ways and has a great impact in various financial settings. For instance, with oligopoly markets, markets where a handful of large firms are interdependent in their decisions, game theory can be used to explain why prices can be rigid.

For example, in the oil market, OPEC nations control the vast majority of global production. Under an oligopolistic model, they are interdependent in their decision-making. When each producer decides how much oil to produce, the price of oil creates an oligopolistic system in which each player’s payoff (profit) depends on the outputs of their competitors and on their own output. Suppose prices fall when one country increases its production; all players bear the negative consequences. Alternatively, suppose a country slashes production; prices rise, and rivals expand output to capture market share. This economic phenomenon of the interdependence of firms on one another through the oligopolistic model is based on Nash’s ideas and on Game Theory. This example, with its subexamples, illustrates the far-reaching effects of Game Theory and the Nash equilibrium across contemporary financial markets and sectors.

Hope you enjoyed my research and commentary on Game Theory and the Nash Equilibrium. See you in 2026!