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Risk and game theory

game theoryThe Cuban Missile Crisis is frequently cited as an example of the use of Game Theory.

I am talking about the situation confronting the Kennedy government when they found that the USSR had installed missiles in Cuba that were capable of hitting American cities with nuclear weapons.

Here is a link to a summary of the crisis, if you are not familiar with it.

Here is a different link about Game Theory and the Cuban crisis.

I see this as an excellent example, not only of Game Theory, but about risk management.

Game Theory is not limited to international crises.

I think there are situations in today’s business world that could benefit from similar thinking.

For example, take these situations:

  • You want to increase your market share and one approach is to lower prices. But how will your competitors respond? Will this lead to a price war? Will your existing customers be tempted to treat your product or service as a commodity and switch to buying from the lowest cost source instead of respecting your innovative offering and showing loyalty to your brand? Will the move erode your margins and negatively affect your share price, spooking investors? Will it succeed because your competitors will be unable to respond effectively? Do you have the cash and other reserves to support a prolonged period of lower margins?
  • Your engineering team is struggling to produce a full range of next generation products that are price competitive. What will happen to your current customer base if you decide only to move forward with a limited range? What will your competitors do? Will they similarly focus on the more profitable lines or will they seek to take advantage of your decision not to offer a full range? Will a focus on a more limited range of products enable you to gain a lead in innovation and gain market share? How will you explain this to your investors so that they don’t sell your stock? Is there an option to hire more people and support the full range, even if that means that your product will not be available for several months after your competitors’?

Each is a critical decision that your executive team and board have to make. Each option presents a variety of risks and opportunities.

It is important to consider not only your actions but also those of the other parties.

I will leave it to my friend, Ruth Fisher[i], to pick up the explanation of how Game Theory can help you assess the situation, understand and assess the risk, and then make an informed decision.

Ruth here.

What I like about using Game Theory to analyze a situation is that it forces you to understand what motivates each of the players who affect outcomes for that situation.

Let’s consider the basic setup of the game in Norman’s first example. Figure 1 illustrates the major players in the Market Share Game.

Figure 1: The market share game

Your company, [1], competes against another company, [2], for customers, [3]. To win market share, your company must satisfy customers’ needs better than your competition does. In addition to winning customers, however, your company must also satisfy investors, [4]. You satisfy investors by maximizing the long-term value of the company.

When thinking about potential actions to take, you must consider the eventual impact of that action on your company’s profits over time: How will the action you take play out in the market? What will be your subsequent profits in the near future, the medium term, and over the long run? The answers to these questions come from evaluating how each of the players in the game will react to the action you take. In particular, you must understand

  • What aspects of your offerings do your customers value? How will your customers’ perceptions of product value change with the actions you’re considering? For example, will a price cut enhance the value of your offering to customers, eventually leading to more sales of your product in the future? Or will a price cut cheapen the value of (i.e., commoditize) your product in the eyes of customers, leading to fewer sales in the future?
  • How do your product offerings differ from those of your competitor? Will the action you take increase the value of your product to customers, relative to that of your competitor, over the short term, medium term, and/or long term? For example, a price cut that is immediately matched by your competitor won’t bring any long term value to your company. Alternatively, adding a feature to your offerings that your customers value, but that your competitor cannot match, will bring long term value to your company.

Let’s now consider Norman’s second scenario. You’re working on a new line of products, resources are scarce, and you have to decide whether (i) to focus your resources on only the most profitable products in the line, or (ii) to stretch your resources and offer the full line of products. I’ve illustrated the potential product line in Figure 2, where Product 1 is the lowest margin product in the line and Product 3 is the highest margin product.

Figure 2: Product line

The key questions in this scenario are whether or not

(i) There are complementarities (synergies) across the products in your company’s new line, and/or
(ii) There are complementarities (synergies) between your company’s new line of products and your company’s current (old) line of products.

More specifically,

(i) Do customers view Products 1, 2, and 3 as substitutes or complements for one another?

If they are substitutes, then you will lose fewer sales to customers by not offering the full line of products. For example, if you choose not to offer Product 1, then some customers who would have bought Product 1 might instead buy Product 2.

Conversely, if they are complements, then you will lose more sales by not offering the full line of products. In this case, if you choose not to offer Product 1, then you will lose sales to customers who still buy Product 2, but who would also have bought Product 1.

(ii) Do customers view Products 1, 2, and 3 as substitutes or complements for your current product offerings?
If they are substitutes, then you will lose fewer sales of current products to customers by not offering the full line of new products.

Conversely, if they are complements, then you will lose more sales of current products by not offering the full line of new products.

(iii) If you produce one of the new products, Products 1, 2, or 3, will that give you an advantage in the production or sale of the other new products? If so, then the margins on sales of Products 1, 2, and 3 are higher than you originally thought, and doing the full line will give you more of an advantage over your competition.

(iv) If you produce one of the new products, Products 1, 2, or 3, will that give you an advantage in the production or sale of your current product offerings? If so, then, again, the margins on sales of Products 1, 2, and 3 are higher than you originally thought, and doing the full line will give you more of an advantage over your competition.

Actually, the second situation benefits as much from a systems analysis – considering your old and new product lines together rather than in isolation—as from the use of game theory. In both cases, however, using game theory helps you understand how each player in a given situation will react to your company’s actions. In turn, this helps you better understand which option is best for your company.

Norman again.

If risk management is about anticipating what might happen and making informed decisions, then we have to consider how others will react.

But, too often we make assumptions about how they will react without considering what motivates them, and so on.

I believe Game Theory is an important tool for informed decision-making and risk-taking.

What do you think?

[i] Ruth D. Fisher, PhD, is the Principal at Quantaa, an economic consulting firm in Mountain View, CA. She is the author of Winning the Hardware-Software Game: Using Game Theory to Optimize the Pace of New Technology Adoption

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Norman D. Marks, CPA, CRMA

Norman D. Marks is an Author, Evangelist and Mentor for Better Run Business, as well as an OCEG Fellow and Honorary Fellow of the Institute of Risk Management. Mr. Marks has been a practitioner and thought leader in internal audit, risk management, and governance for a long time. He has led large and small internal audit departments, been a Chief Risk Officer and Chief Compliance Officer, and managed IT Security and governance functions. Read more
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