Game Theory on Picking Halloween Candy And Loans

Bank Game Theory - Competing For Loans

Many parents have dealt with the issue of how to divide up Halloween candy among siblings. It’s not easy. If all houses gave out the same candy, it wouldn’t be a problem. But houses give out different candy, or they allow you to choose, and those in the front of the pack had different choices as those in the back. Whatever the case, candy is not all the same. As a result, candy is distributed unevenly forcing parents that are concerned with equality to employ some game theory. While helpful in Halloween, the clever methodology that we bring you today is also applicable any time there is a finite set of options and a competitive system for choosing each option. This applies to appetizers, shopping or marketing for commercial loan in your market. 


The Problem Explained


To better understand the problem, let’s say there are four loans of different profitabilities in a market with four banks. Each bank needs to allocate its finite resources and prioritize which loans they are going to go after. Each bank has different preferences for each loan.


Let’s take four loan choices:


Game Theory in Banking


These are all real-life examples from last month, real probabilities of defaults (PODs), real risk-adjusted returns on capital (RAROC) and represent actual choices banks had to make. Let’s denote the banks as Bank A and Bank B. While banks can compete on more than one loan, to keep things simple, we will assume that banks have limited resources and can’t throw their full sales and marketing effort behind every loan. We will also stipulate that banks know their market and understand the competition, so information is free-flowing, and each bank’s strategy is fairly transparent given past market moves.


Each bank has different preferences due to their risk tolerance, structural capabilities, and portfolio. These preferences are:


Bank A: Muni > Retail > Hospitality > Industrial Owner Occupied (OO)

Bank B: Retail > Hospitality > Industrial > Muni


Even though loans have different returns, to mimic real life, let’s ignore the returns for now and simplify the example by assigning points. This is a fair constraint, as even through hospitality offers the best return, some banks just don’t understand the asset class or have a limited preference for it in their portfolio. As such, each bank will get four utility points for their first preference, three points for their second, two points for their third and one point for their least favorite. Thus, we take their preference above and assign points:


Bank A: Muni (4) > Retail (3) > Hospitality (2) > Industrial (1)

Bank B: Retail (4) > Hospitality (3) > Industrial (2) > Muni (1)


The Common But Sub-optimal Strategy


First note that if you don’t have a pricing model and a portfolio strategy, your bank will lose this game every time. You will be at a loss for which loans you want, how to price to win and how to structure to win. This is why we write about our portfolio strategy and give our relationship profitability model, Loan Command, away at our cost so all banks can effectively compete in their marketplace. For the sake of this example, let’s assume both banks have both a clear strategy and a loan pricing model.


Bank A goes after the Muni loan and wins it (getting four points). Bank B goes after the Retail loan and wins it (getting four points). So far so good. Bank A, knowing Bank B has a signed commitment letter on the Retail loan, goes after the Hospitality loans and wins it (getting two points). In response, Bank B goes after the Industrial loan.


Bank A now has six points which isn’t bad, but it isn’t optimal. Had the bank had a better strategy, they could have done better.


Optimizing Strategy


Bank A should have gone after their second choice first and won the Retail loan. That would have given them three points of utility. Bank B would have then taken their next best alternative and gone after the Hospitality loan. This allows Bank A to next go after and focus on the Muni loan, their favorite and gain four points. This would have given Bank A seven points of utility instead of six – a better strategy.


Bank A knows Bank B doesn’t have the expertise to structure muni deals so why put maximum resources there? By taking game theory into account, Bank A can allocate resources to their two favorite loans by keeping track of and understanding their market. Game theorists will recognize this problem as part of the Nash Equilibrium, and the quick practical summation of the strategy is this:


Competitive Loan Markets


Another way to think about this is that if you discover a profitable customer type or loan structure that other banks don’t know about and are not competitive with, a little marketing and sales focus will go a long way. However, if you are trying to go after medical professionals, multifamily or the hundreds of other hyper-competitive loan markets, then you are going to have to spend sales and marketing dollars to differentiate your bank. In addition, you need to come up with products such as long-term fixed-rate loans and cash management services that set your bank apart.


If you read this as said – OK, but my market is more complicated than just competing against one other bank, we hear you. We used to have to compete for Halloween candy against much older (and bigger) siblings plus their friends. You know what? Your odds of optimizing a strategy go up, not down. This is counterintuitive, but in multi-player games where competitors have a greater relative advantage, game theory becomes even more important.


In the future, we will build on this methodology and show you how the smallest community banks can have the best odds of getting the loans they want when competing against larger banks. Until then – Happy Halloween and we will be keeping our eye on our favorite candy – the Twix Bar.


P.S. Actually, it’s the 3 Musketeers bar, we just didn’t want you to pick it first in case we ran into you tonight.