How Technology Alters the Branch Game Theory Problem

Game Theory in Branching

In branch banking, there was always the dilemma in gathering customers. The number of customers a branch would attract was a mathematical function based on location of the nearest competing branch, services/products, brand and price. All things being equal, customers tend to choose the branch that is the closest. Lower the price of a product, increase the brand value (marketing) or offer some unique services/products, and a branch could pull from a wider service area and increase market share. This explains why major banks such as Bank of America and Wells Fargo generally have larger circles of influence and larger branches compared to community banks, as they tend to have more valuable brands and a wider array of products and services.


Optimizing Branch Location


Bankers that have a background in game theory will recognize the above non-cooperative problem as a Nash equilibrium around a condition of geography where each branch tries to optimize their profit by locating their branch strategically and then maximizing the other elements to reach a market share equilibrium. While some bankers would want to locate their branch away from other branches, that turns out to be the wrong strategy. While that would maximize utility for the population as a whole (as you would get more people close to a branch) it comes at the price of hurting profits for those banks not located in the middle of the greatest population.


If you work the math, you reach the counter-intuitive solution that it is better to cluster your branch around a population center. Adding competitive branches does not alter the math enough to change the strategy. From an intuitive standpoint, locating in a central location exposes your branch to the greatest number of households / businesses, which is a material driver of the branch usage function. In addition, not only is time to the branch important, but so are traffic patterns and parking which are other reasons to locate in a central location regardless of competition. This Nash function explains why gas stations, hotels, and fast food restaurants are often clustered together.


The New Nash Equilibrium


While the Nash equilibrium concept has been the fundamental strategy in branch banking for almost 200 years, the equation is now being altered by technology, particularly mobile banking. Solving for location of a branch becomes less important as households / businesses have already started to choose their bank based on technology ease of use. This will soon become the dominant strategy if it is not so already.


There are a couple important takeaways here that will alter the strategy for a bank that understands the new Nash equation. First, ease of technology has now replaced geography as the primary condition in the Nash equation. Because of this, it means that banks must have similar technology as their competition in order to maintain their market share. In other words, technology is now a substitute (in part) for the branch. Thus, banks that are trying to increase profit and market share will increase their investment in technology while decreasing their investment in physical branches.


Another takeaway is that banks are now less dependent on geography. This may seem obvious, but it has far-reaching strategic implications as it means banks have more economic incentive than ever to redefine community and organize around another construct other than geography. Maybe it is an industry, affinity or other customer segment, but whatever it is banks can now seek a community that encompasses a greater geographic span and may or may not have a geographic limitation.


The Benefits of the New Nash Equilibrium


Unlike the new equation in the past, reconstructing the Nash equilibrium around technology means that more households and businesses can enjoy a greater range of banking products and services. Unlike the branch equation in the past, this will increase the overall utility for society. The other outcome is the rapidness of change.


In a normal Nash equilibrium equation, the cost of the strategic choices is the same. One branch costs pretty much the same as the others.  However, when you substitute technology for a branch, not only may you increase market share, but you also lower your cost structure by making delivery less expensive. This gives more of an economic incentive for banks to swap branches for technology and will serve to speed up the rate of change.


Banks would be served well to understand how technology is altering the game theory problem of increasing market share. While the Nash equilibrium doesn’t say anything about what the optimal strategy might be, the highest profit path most likely is a mix of both branches and technology depending on the sensitivities of the customer. However, the important takeaway here is that from a strategy point of view, banks need to think of technology not as another banking product, but as a complement or substitute for delivery within a market share strategy.