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Risk and Game Theory

December 1, 2017 Leave a comment Go to comments

The 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

Ruth figure 1Your 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

Ruth figure 2

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


  1. Rick Nason
    December 1, 2017 at 8:43 AM

    Another great article Norman (and Ruth). Yes, Game Theory is an important tool for decision making (I have to say that as I teach game theory in my quantitaitve decision making MBA class and in Exec Ed seminars), and yes, Game Theory is a great tool for risk management. More importantly, I believe that this article also nicely illustrates that risk management is strategic management and vice versa. Risk management is management, and management is nothing more than risk management. That is not to ignore the importance of risk management as a discipline, but to point out that risk management should not be left as an afterthought to the strategic (or tactical) plan.

    • Norman Marks
      December 1, 2017 at 8:47 AM


    • December 2, 2017 at 2:11 AM

      ‘Risk management is management, and management is nothing more than risk management’. Couldn’t agree more, except I would prefer, ‘Risk management is management, and management is all about managing risks (and opportunities).
      One audit my department carried out, which I would recommend to any IA department, is the board approval process. Does it include a thorough opportunity/risk analysis including the use of game theory and other modelling?

  2. December 1, 2017 at 9:23 AM

    Agree with the article, the point about risk mgmt = strategic management in Rick’s comment (and the “Amen!”).
    I also see this as a concrete example of how proper risk analysis needs to go much deeper into likely and potential responses of the whole business ecosystem, taken broadly, than it usually does in the still-too-typical “estimate the likelihood and impact and put it in a matrix” approach many companies follow. At the risk of blowing my own horn, I wrote about that at https://www.mckinsey.com/business-functions/risk/our-insights/risk-seeing-around-the-corners , though the article is 8 years old and so in many ways rather dated (and doesn’t talk about game theory specifically).

  3. December 1, 2017 at 2:57 PM

    Thanks Norman and Ruth. It’s a timely article on game theory in the context of plays like that of Amazon in retailing. How do existing retailers react and compete with Amazon’s online and market dominance capacity? In Australia at least the anti-trust regulators have warned traditional retailers to not expect any regulatory support. So that’s out as a soft landing factor. Consumers are the winners, at least for the short-medium term. To some extent Amazon is getting an easy entry path because existing operators are not doing enough work ‘anticipating what might happen’. Instead, they are sitting back thinking it’s just another competitor…. which its not. Both market share and margins are being challenged if not under serious threat even for those with existing large market shares. In the current environment just about anything seems possible so the real challenge is in assigning good estimates of likelihood to ‘what might happen’ and the associated impact. That is, risk management can add something to game theory.

    • December 8, 2017 at 8:21 AM

      Thank you, David, for your thoughtful comments. I absolutely agree with you about Amazon. The company frightens me terribly. It is massively vertically integrated and it leverages power (and profits) in some markets (AWS) to gain advantage (subsidize losses) in other segments (particularly non-US sales). Amazon also has tremendous conflicts of interest, as it competes with its customers in 6 of the 7 market segments in which it participates. Yes, consumers win in the short run, but they’re going to find themselves with exactly one choice of vendor — Amazon — in the long run. I analyzed Amazon’s situation and mapped out its various segments. If you’re interested, you can find my analysis posted on my blog here: http://www.quantaa.com/blog/504-playing-the-amazon-monopoly-game

  4. Hans Læssøe
    December 4, 2017 at 1:03 AM

    Great and well explaining article, which demonstrates that to be truly effective, risk management must be a part of the decision process. asking someone to manage the risks emerging from decisions you have already made is inadequate and inefficient.

  5. Don Whitehouse
    December 8, 2017 at 7:03 AM

    The use of the words “Game Theory” is intriguing, which is why I decided to read the article. From an implementation perspective, here are some questions I have.

    Are there discrete steps for implementing and practicing Game Theory? If so, what are they?
    How much time and effort is required?
    Do you need a degree in Decision Science to make it work?
    Can a plug and play algorithm be created in a spreadsheet and used to assess various assumptions or scenarios or do I need to buy software? . . . and
    How can Game Theory be of value to Internal Auditors?

    It seems that next logical steps would be to gather as much data as possible and start with a regression analysis and then to create an algorithm for doing scenario analysis.

    Please consider writing follow-up articles about the steps required to implement game theory including any useful spreadsheet formulas that can be used.

    • December 8, 2017 at 10:43 AM

      Hi Don,

      Game theory is a tool that’s used to “map out” particular situations and figure out what is likely to happen under various scenarios.

      In some cases game theory is employed by means of modeling situations using mathematical equations. In these cases, the equations can be used either to solve for optimal solutions and/or to generate simulations to see how the situation plays out under different scenarios.

      However, game theory can also be employed using less rigorous methods. Most situations can be mapped out visually and textually, and then one can use those mappings to better understand situations and draw conclusions.

      My sense is that you cannot use software, because each situation is different.

      I start with the main player, Player A, and understand
      * what his purpose is: maximizing profits from sales of a product (a simple company), maximizing the value of an ecosystem (Amazon, Apple), gaining market share, etc., and
      * which actions are available to Player A to achieve his purpose (raise or lower prices, introduce a new product or service, buy up a complementary vendor, etc.)

      Then I look at the major players that affect Player A’s ability to achieve his purpose: competitors, customers, suppliers, etc. For each of these major players, I try to understand these same two things: what each of their purposes is, then what actions each player can take to achieve his respective purpose. Customers can buy or not buy from you or a competitor. Competitors can raise or lower their prices or introduce a new product or service. Vendors can continue to supply Player A or refuse to continue to supply.

      Often simply by mapping out the scenario, you get a much clearer understanding of the game: what the dynamics look like, how the market will respond to Player A’s actions, etc. Then you can start choosing actions for the different players. If Player A chooses to lower his price,
      * what will his competitor do that will help the competitor best achieve his purpose?
      * what will customers do that will help those customers best achieve their purposes?

      We will definitely considering some follow-up articles.

  1. January 13, 2018 at 11:57 AM

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