Explaining Business Decisions Using Game Theory (Nash Equilibrium): Part 1
We all have heard the term “Game Theory” somewhere. It is widely used in Economics, Politics, Mathematics and recently Artificial Intelligence. So, what is Game Theory? If you ask me, I would say that game theory is a branch of mathematics that explains how decision makers make decisions. Game Theory itself has an extraordinary explanatory power to depict the behavior of competitive players in any format.
In this write-up, I will discuss how players make decisions that are surprisingly different from what it should be and how game theory can explain the scenario. The aim is to introduce you to applications of Game Theory and Nash Equilibrium and if this helps, I will write on further advanced concepts on it.
Now, to explain Game Theory, I will bring a very common example: price cut or discounts of products. Many companies bring different tech products and to boost their sales, they either cut their prices or give some lucrative discounts to increase sales. However, we will see how Game Theory can explain their rational behavior and dominant strategy. Let’s start:
Let’s assume a scenario where two players are in the market — Player A and Player B. There is no product differentiation. Both sell the same kind of product and neither has superiority over the other products or any benefit(e.g. lower price, quality of product etc.) and hence users prefer products both equally. Player A sells per unit at X USD and Player B sells per unit at Y USD where right now X = Y.
The price of the product directly controls the market share, so there are two possible cases:
- X=Y: if they both price the product the same, each of them gain 50% of the market share since there is no product differentiation.
- X≠Y: Whoever prices the product lower gains 100% market share. Here we are assuming a completely elastic market (a market where all users purchase the item that is lower in price)
The top executives of the Company A and B have options to cut the price of their product by 20% to gain more market share. They take this decision independently. Let’s assume, total market size is 100M USD. If Player A cuts the price, as a competitive response, what should Company B do? — well, if you analyze the situation, company B has two choices: 1) cut price to match the competition 2) no price cut or no response at all.
So there are four cases that might happen:
Case 1: A cuts price by 20% and B doesn’t cut the price, so A gets 100% market share which after the price cut is 80M.
Case 2: B cuts the prices and A doesn’t. It means B will now gain 100% market share of 80M USD but A will gain nothing.
Case 3: Neither of them cut prices, and they remain at equal price and get 50%-50% market share (because our assumption is: at equal price they gain equal market share and market is purely elastic, each which in this case is 50M and 50M respectively.
Case 4: Both A and B cut the prices, the market size shrinks to 80M (since both cut prices per unit by 20% of the 100M market) and due to equal unit price, they both gain 40M and 40M respectively.
We can see the market share scenario in the below table that is called a Pay-off Matrix:
Both players are rational players and will play independently. This means each player will try to make the best decision for their own benefit regardless of what other players take. Player A will see if they cut prices they will get either 40M or 80M but if they don’t cut the price they will end up having 0M or 50M so they will take the decision of price cut. For player B, the case is symmetric(i.e. same) here and will view their results the same way. Hence, they will both decide to cut the price and will end up having 40M and 40M of Market revenue each. This (40, 40) is called the Nash Equilibrium of the business case. I think we all have seen these types of cases in different ride-sharing, food delivery and e-commerce business-es where they decide to cut their prices or give aggressive discounts that ultimately leads them to a price war or game of discounts in which only the market (buyers) have benefited from.
Now, if you look closely, you can see if they hadn’t cut their prices or given discounts (case 3) both together, they could have both gotten 50M each — so the decision to cut prices actually led to a 10M loss for each.
Interestingly, each Player did have a dominant strategy: “gain more market share”. Player A, for example, saw profit in cutting down the prices. But, when they both choose their dominant strategies, their market shares are 40M and 40M, respectively. Nothing to sneeze at, but cooperation would have gotten them more, 50M and 50M. This predicament is called the “Prisoners’ Dilemma”. Its remarkable feature is that: both sides play their dominant strategy to maximize their own payoff, and yet the outcome is jointly worse than if both had followed the strategy of minimizing their payoff.
This is a classic and simple example of “Nash Equilibrium”.
I really hope that you are now familiar with the great explanatory behavior of Game Theory and Nash Equilibrium — as I mentioned, it mathematically explains how decision makers make decisions that may lead to a undesirable outcome, jointly. Using this concept, you can explain human behavior, strategy behind different real life sports, decisions of politicians, movement of international politics, psychology of criminals and much more.
Thank you so much for spending time here and reading this. For any suggestion, and also if you want further articles on these topics, you can directly email me at: amon163c@gmail.com.
