EARNING VIA GAME THEORY
Trading and Nash Equilibrium
Effect on the Market’s Behaviour
“Dharma or Ethics and Morals are the Fundamental Set of Rules created for those who want to play the Game, by those who are Inside the Game.”
― Vineet Raj Kapoor
INTRODUCTION
Game theory is quite a fancy name, which naturally attracts a lot of people’s attention.
Among the versatile topics in game theory, one of the prominent concepts is that of Nash Equilibrium.
In any sort of game, we need a strategy. The Nash Equilibrium is the optimal solution and a strategy in non-cooperative games — rules of which you would not want to break even in the absence of a “Police Force.” A simple example of this is vehicles in a stoplight. Even in the absence of traffic police, ideally, one would not benefit from breaking the rules and cause self-harm. Thus the situation in which no plate has an incentive to change their initial strategy and cannot gain anything from thus deviating is the Nash Equilibrium.
To quickly find the Nash equilibrium or see if it even exists, reveal each player’s strategy to the other players. If no one changes their strategy, then the Nash equilibrium is proven.
So, in today’s blog, let’s deep dive into what Nash Equilibrium is and how it can affect traders’ behavior in a market.
Nash Equilibrium and Trading
Trading is the perfect example of a free market with no regulation in the strategy dimension (no ‘police force’).
Before we begin explaining Nash Equilibrium in trading, it will be useful to know that there are 2 types of games being played in the market -
Game 1: Retail Traders versus Large Traders
Game 2: Traders against themselves
All players (traders, in our example) must face the second game — including the big and established players. All of us are human beings with loud psychological traits, which play a major role in our decision-making.
Nash Equilibrium in trading refers to operating within a framework that dramatically increases self-preservation likelihood in the long term. However, the rules of this certain framework are non-obvious and highly counterintuitive.
The stoplight logic taken up in the beginning is symmetric in nature, meaning that it remains constant and unaffected in both short and long terms. However, trading logic is asymmetric, i.e., its short-term and long-term functions are different.
It is imperative for traders to believe that, unlike popular belief, stop-light logic is different from trading logic. If a trader behaves in a certain way that makes him feel productive in the short term, he will probably fail in the long term. By the same token, if the trader behaves in a way that appears to be uncomfortable and counterproductive in the short term, he will probably succeed in the long term. This also proves that overly simplistic thinking does not work in the market. This may upset some people that think trading is a simple game, but allow me to prove it using a real-life example.
Imagine that two manufacturers dominate the mixer grinder industry. Both manufacturers A and B make 1 million mixer grinders a year for a price of Rs. 2500 each, and earn a profit of Rs. 20 million annually. However, Manufacture A believes that the market is bigger than what it is presently and could decide to make 2 million mixer grinders a year for a reduced price of Rs. 2000. In this scenario, his profit would jump to Rs. 35 million. However, Manufacturer A also knows that if he increases production, his competitor, Manufacturer B, will follow suit. With more mixers in the market, the price will drop to Rs. 1500 per unit, and Manufacturer A’s profit will dip to half a million rupees annually (lower than the initial annual profit). Thus, the two are already in a Nash Equilibrium state, and given the competing firm’s expected response, neither business can make more money by unilaterally deciding to boost production.
It is revealed how a company cannot decide to raise production unilaterally but must consider the response of another company and the emergence of Nash equilibrium.
The Analysis and Aftermath
Analyzing the situation, it may seem that there is no solution for progress in the market for any manufacturer. Some products have an oligopoly (like the market for bathing soap bars), wherein no single seller is able to dominate the market. But sometimes, monopolies (Nestle’s Maggi) and duopolies (Coke vs. Pepsi) do emerge.
To achieve this, the manufacturers go on different routes rather than the obvious ones. These scenarios may or may not involve breaking the Nash Equilibrium.
One possible way is to introduce a unique design so that its profits won’t be affected by rival-raising production. This could be tied up with other products or taking funding from a large investor so that it can hold up the reduced profits in the short term to dry out its competition in the market in the longer term.
This example is a perfect illustration of why Game Theorists look at decisions not in isolation but as part of a system of interactions. In the modified words of Sir Arthur Conan Doyle, a larger game is always afoot!
Nash Equilibrium and Trading (InfoGraphic)
Effect of Nash Equilibrium in a Particular Market
