Game Theory in business decisions part 2

Since taking our Business Analytic course, where we learned about game theory, I have been fascinated by how it can be used to solve business challenges. In my previous blog post, I provided a quick overview of game theory, its use in solving business challenges, and an illustration of how two coffee shops in Lekki competed using game theory.

In this article, I will be presenting another exciting application of Game Theory in business problems. Here is the story:

Two entrepreneurs named Musa and Ahmed want to introduce a brand-new payment app to the market. They must choose whether to work together or compete because they have different ideas about the functions and aesthetics of the app. If they work together, they can split the costs and risks of creating the software, but they must also divide the revenue. If they engage in competition, they can attempt to take more of the market, but they also run the risk of losing users to rival apps. Below is the payout matrix for this game:

Both Musa and Ahmed must decide at the same time and without knowing what the other will do. They must also take into account the expectations and preferences of their potential clients, who may prefer one app over another based on factors like quality, cost, and other features. How can Musa and Ahmed decide using game theory?

One possible approach is to use the dominant strategy method, which means choosing the strategy that gives the best payoff regardless of what the other player does. In this case, Musa’s dominant strategy is to compete, because he can get either 80% or 40% profit depending on what Ahmed does, which is better than getting either 50% or 20% profit if he collaborates. Similarly, Ahmed’s dominant strategy is also to compete, because he can get either 80% or 40% profit depending on what Musa does, which is better than getting either 50% or 20% profit if he collaborates. Therefore, the dominant strategy equilibrium of this game is where both players compete and get 40% profit each.

Another possible approach is to use the maximin method, which means choosing the strategy that maximizes the minimum payoff that can be obtained. In this case, Ahmed’s maximin strategy is to compete, because her minimum payoff is 40% profit if he competes, which is higher than her minimum payoff of 20% profit if he collaborates. Similarly, Ahmed’s maximin strategy is also to compete because his minimum payoff is 40% profit if he competes, which is higher than his minimum payoff of 20% profit if he collaborates. Therefore, the maximin equilibrium of this game is also where both players compete and get 40% profit each.

Both methods lead to the same outcome in this game, which coincides with the Nash equilibrium. However, this outcome may not be optimal for both players and for their customers. Musa and Ahmed might produce a better app with more user satisfaction and increased revenue if they worked together. They can also avoid a price war that may lower their profits and hurt their reputation. Therefore, they may want to find a way to cooperate and trust each other, such as signing a contract or using a third-party mediator. This example shows how game theory may aid in the analysis of strategic interactions and the selection of the optimum course of action based on objectives and expectations for business decision makers.