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.
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.