# A Marketer’s Guide to Game Theory

What’s your next move? That’s the key question every strategist needs to answer.

Game theory can help guide you. It has proved useful in fields such as economics, politics and negotiations, but is much neglected by marketers. That’s unfortunate because there are valuable insights to be gained.

Here’s a quick guide to get you started:

### **A Bit of History**

In the 1920’s, mathematical wizard John von Neumann began to think about why he was such a lousy poker player. He realized the problem was that while he was playing cards, he should have been playing his opponents so he worked out theorem to solve the problem.

In 1944, he teamed up with economist Oskar Morgenstern to write *Theory of Games and Economic Behavior,* a book so important that it made the front page of the NY times (previously an honor bestowed only on Einstein’s relativity) .

The big deal was that they proved that all 2 player zero sum games (where one player’s gain is another’s loss), had an optimal solution. It was a breakthrough for fields as diverse as economics and military strategy.

However, most real life situations are not pure conflict. We usually interact with each other for mutual benefit. 6 years later, the problem of non-zero games was solved by John Nash, the subject of the movie *A Beautiful Mind*.

**The Nash Equilibrium**

A Nash equilibrium occurs when both players can’t do any better by changing their strategies, given the likely response of their opponent. Nash proved that for every non-zero sum game, there was at least one solution.

This had a vast effect on how competitive strategy was thought about. Rather than a simple battle of wills, a mix of cooperation (implicit or explicit) and competition was required.

Moreover, Nash equilibriums are not only stable, but self reinforcing. Once a point of stability is reached, changing the status quo is both difficult and costly (and, some equilibriums, like prisoner’s dilemmas, can have negative consequences).

**Competitive Budget Setting**

For a good example of the Nash equilibrium at work, let’s look at a situation where two competitors are setting their marketing budget. At the starting point, both have equal budgets and equal profits.

We’ll assume that they have two options: They can either spend on advertising to differentiate their brand or they can discount to drive sales. Both actions can increase sales and have associated costs. We’ll also assume that money not spend on advertising goes into discounting.

As we’ll see, the effectiveness of either strategy will be affected by what the other company does. So it’s impossible to know if their actions will be effective untill they see how it plays out in the marketplace.

Let’s look at a likely scenario:

Now we can see that even this simple example leads to a complicated matrix of payoffs. Simply deciding to discount or to spend money on marketing tells us relatively little about the success of our efforts.

However, if we look for a Nash equilibrium, the picture becomes clearer.

With a little bit of analysis, we can see that most of the boxes in our payoff matrix are unstable, meaning that at least one player would be better off choosing another action.

If they both choose to increase their ad budget, they end up in an sustainable ad war and a similar situation arises if they both choose to discount. Doing nothing would just perpetuate a stalemate.

However, if they each take opposite strategies (lower left and upper right boxes), both maximize sales and profits. We have two equilibrium points because it doesn’t really matter who chooses which strategy, just that they’re different.

This actually does reflect what happens in the real world. Although equilibrium is rarely reached in one step, markets eventually do segment. Moreover, once a stable point is reached, it’s incredibly difficult and costly to switch strategies. A brand differentiator who slashes prices or a discounter who tries to charge a premium is in for a long, hard slog.

**Multi-Player Games**

Of course, most markets are made up of more than two competitors. These situations are called n-player games and they are usually based on coalitions.

Let’s take a simple example of a market where there are two discounters, two brand differentiators and a fairly consistent flow of niche players moving in and out of the category.

We can see that there are two natural coalitions, but neither is dominant. If one coalition would like to control the agenda inthe form of industry initiatives, government lobbying, etc. they will have to draw smaller players into their sphere.

What’s interesting here is that the size of the company has very little to do with influence. The only thing that matters is the likelihood of casting the 51st vote and, in this example, all players are roughly equal in that respect.

Again, although we are looking at a fairly simple model, it goes a long way toward understanding what happens in the real world. Sony’s ill-fated Betamax video standard, although technically superior, failed when it was confronted with a coalition of smaller players led by JVC.

In many cases, being seen as the most powerful player can be a disadvantage because it encourages antagonistic coalition building (a situation that Google seems determined to head off).

**How to Use Game Theory**

In reality, game theory is hard to implement directly because we rarely know the actual values to plug into the models.

However, it is extremely useful in helping us understand basic forces at work. It forces us to discipline our thinking and shows how even given some simple rules, we can arrive at some surprising conclusions.

While much of the literature surrounding game theory is highly technical, Dixit and Nalebuff have written a highly readable book that will guide you through the basic concepts.

Good luck and play nice.

– Greg

Hello Greg,

Thanks a lot for another wonderful post.

I have a question. So according to the last matrix brands take different strategies to maximize profits. Can’t brand A take lower left strategy like brand B does and spend 75 getting 1500, instead of spending 125 to get 1500?

I often have trouble understanding these matrices so I would really appreciate it if you explain a bit more.

Thanks

[Reply]

Greg Reply:

June 9th, 2010 at 2:08 pm

Katya,

Sorry, that part isn’t as clear as I would have liked.

The matrix assumes that what isn’t spent on advertising goes into discounting. So they aren’t really saving money by not advertising. I’ll amend the text to better reflect the trade-off. Thanks for pointing it out.

However, it’s important to remember that the main point about Nash equilibriums is the tendency toward stability and that there can be multiple equilibriums.

Therefore:

– Before making a major strategic change you need to consider that the market will work against you. It’s not something to be taken lightly so if you attempt it, it better be worth it.

– When a market is forming, it’s important to make sure that you are comfortable with where your position is heading. Get in a bad place and you could be there for a while.

– Never assume that your market status quo is necessary or even desirable. As I’ve moved from country to country, one thing I’ve learned is that everybody has their own version of “normal.”

– Greg

[Reply]

Thanks for highlighting the virtues of game theory. A great introduction. I’ve been a marketer for most of my 29-year career, a practitioner of game theory for the last 7 years, and now a strategy consultant specializing in game theory. A few followup points, particularly, under your last category of “How to Use”.

1. Your Next Move(s). The real value of applying game theory to strategy is not to plan your next move, but as would any good chess player, to plan a series of moves, all designed to anticipate or impact the moves of others.

2. Game Theory and Strategy. If you are in a fast-moving industry involving new entrants, M&A, technology disruption, obsolensce, new business models, or consolidation, then you can benefit from game theory as the process will force you to analyze the expected behavior of all the other players in your market. That sounds like marketing apple pie, but is actually quite hard to do without an a means to codify those behaviors. Game theory provides that means.

3. Decision Making. Often, the strategy team in most organizations will endlessly argue the virtues of Strategy A vs. Strategy B until everyone gets tired, turf lines are drawn, and/or someone (usually highest in persuasion, pay-grade, or title) stands up and declares a decision. This is sometimes efficient; sometimes effective. Game theory changes the debate from A vs. B to “what is most important to each player”. This debate is far more enlightening and less territorial.

4. Securing Approval. If decision-making occurs as in the point above, that isnt convincing to a board of directors who needs to approve the decision (eg, a proposed acquisition). To offset the weak decision process, the team gathers mountains of facts and evidence to justify the decision. Board members dont live the problem everyday, dont read the mountains of evidence, so it all degenerates to a “trust me” presentation. Conversely, a decision based on a game model is extremly convincing and compelling to both management and the board of directors.

5. Coalitions and More. In addition to coalitions, game theory will often suggest the optimal competitive positioning in the marketplace, alliances, and most importantly, the optimal timing of premium-valuation exit strategies.

Regarding textbooks, you cite a good one. I often recommend “Games, Strategies, and Decision Making” by Harrington as well.

Thanks again for highlighting the virtues of game theory.

[Reply]

Greg Reply:

June 9th, 2010 at 9:37 pm

Bill,

Thanks for a very informative comment. The one thing I would add is that convincing a board of directors is also an n-person game, so the same rules apply.

Also, thanks for the Harrington tip. I’ll check it out.

– Greg

[Reply]

Excellent post, Greg!

Stan

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Greg Reply:

June 9th, 2010 at 11:08 pm

Thx:-)

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Hi Greg, Thank you for another great post. I feel smarter already!

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Greg Reply:

June 13th, 2010 at 7:51 am

James,

Thanks (although I thought you were pretty smart already:-)

– Greg

[Reply]

Great post Greg. I’ve always wondered how I can apply Game Theory to my clients’ campaigns…if only I had John Nash’s IQ. *sigh*

[Reply]

Greg Reply:

July 1st, 2010 at 8:54 pm

Well, at least you don’t have his other problems:-)

– Greg

[Reply]

I am fascinated by game theory. I read A Beautiful Mind years ago (the movie does a great job of following the book). That started me down a path of reading that continues to draw me into game theory. Greg, I’m afraid I will need to bend some of my next blogs around game theory. I blog for Dentists, and they are certainly not playing a zero sum game.

Thanks for the great post, and the excellent comments!

[Reply]

Greg Reply:

July 23rd, 2010 at 10:25 pm

Thanks, Joe. Have a great weekend.

– Greg

[Reply]

Good one, Greg!

I already read that book and as a matter of fact I would recommend their previous work “Thinking Strategically” which is , to me at least, more clear and better at exposing the main points. It does however lack some of examples that are in the “Art of Strategy.”

Goog news is that, as others pointed out already, Game Theory is not just another theoretical gimmick that pleases our intellect only. It now has vast applications in everyday lives of individuals as well as in businesses, notably in marketing, strategy and innovation.

Cheers,

H.

[Reply]

Greg Reply:

March 1st, 2011 at 3:35 pm

Hayk,

You’re right. However, since “The Art of Strategy” is newer and easier to find, I cited that one. As for me, they are roughly equivalent.

– Greg

[Reply]

hi dear Gerg

can you send me this article I will modeling this with your information so I need all of this paper?

thank

[Reply]

Greg Reply:

October 10th, 2015 at 7:17 pm

Not sure what you mean by send. It’s on the web. You can copy and paste.

– Greg

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