How game theory impacts on businesses
By: Samuel Fraga Mateos
Tags: Game Theory, Business Strategy, Business, Strategy

Game theory? Still don’t know what it is? No, it is not a new series that Netflix has released. You definitely should start reading about this because it can help your business. Game theory is used in a wide variety of fields such as economics, politics, or sociology and plays a fundamental role in strategy and negotiation. If you are the owner of your business or participate in decision-making for your company as a manager, you will surely be exposed to situations that require great planning and anticipation. What are the next steps that my business is going to take? How am I going to negotiate with my main supplier? How can we create value for our clients? How are we going to achieve our objectives?

Although it may seem a bit geeky, game theory is an area of applied mathematics that studies situations (or games). These situations often require to adopt a strategy to solve them. The word strategy originates from the Greek term strategos and refers to the “art of leading armies”. We often stereotype the term strategy negatively because of its warlike etymology. However, leading an army and leading it to victory requires a set of strategic decisions, and that’s the meaning in the most generic form, a strategy is an action plan to obtain the result we desire, let’s see it with an example.

Imagine tonight you want to see the film on your favorite TV channel. You think that it’s no problem, you just have to switch on the TV, select the desired channel and sit on the sofa. That’s easy! But something happens: an old friend whom you haven’t seen in a long time calls you and wants to hang out to catch up. Assuming you want to see your friend, the situation is completely different. On the one side, you can stay at home and see the film but maybe your friend will be disappointed. On the other hand, you can go out with your friend but you’ll miss the film. Now, you have to build a more elaborated strategy. One valid solution could be to meet your friend early and go back home on time to see the TV film. That way, both are happy. Problem solved.

Think about this more complex situation: you’re living with your partner. Both of you have some money saved and you are looking forward to buying a pool table for the living room. However, your partner wants to buy a beautiful puppy. You cannot afford the costs of both options so, assuming you don’t want to sleep on the couch, you have to develop a strategy. In this case, you should take into account your desire to have a pool table and your partner’s desire to have a Golden Retriever puppy, but you should also take into account the importance of the relationship for both of you. Additionally, you must take into account your partner’s unwillingness for having a pool table in the living room and your little desire to take the puppy for a walk. Welcome to an interdependence scenario.

We talk about strategic interdependence where both the actions the individuals take and the results obtained depending on the actions that third-party actors will take. In other words, whatever the action you choose, the results of those activities do not only depend on what you want. Due to this high level of dependency among individuals who are part of a situation and the number of variables, a complex strategy needs to be adopted.

Different types of games

Once we understood what the basic concepts around game theory are, let’s classify them in two main categories based on the followed rules: simultaneous-move and sequential-move games. As the name means, in the first ones all the players take their actions at the same time and, on the second, the players take actions in turns. We should mention the static games, a subtype of sequential-move games where the players don’t know the remaining player’s actions until they’ve played.

We can also categorize games based on the number of times the game is played. We have one-time games, where the game is played just once and repeated games where the game is played more than once.

To cooperate or not to cooperate?

Let’s explore the widely-known prisoner’s dilemma to understand how a game works. The prisoner’s dilemma is a specific case of simultaneus-move games. Imagine the following situation:

Two individuals commit a robbery but are unable to escape and the police catch them. The police take them to different interrogation rooms and the two subjects do not have any communication between them. The police offer them the same agreement, as follows:

If you do not confess to the crime and your partner confesses, you will be sentenced to 20 years in prison and your partner to 1.

If you confess to the crime and your partner does not confess, you will be sentenced to 1 year and your partner to 20.

If you both confess to the crime, you and your partner will be sentenced to 10 years each.

However, if neither of you confess to the crime, we do not have enough evidence, so both of you will be sentenced to 3 years each.

We can represent these four options in a matrix:

The prisoner’s dilemma matrix

This game allows us to demonstrate that even though the most tempting offer may be to not confess for both of the prisoners (it would be the best solution to the game, since it would only take 3 years each, making a total of 6), either of the two Prisoners may be tempted to betray their partner to lower their sentence to 1 year. However, if both prisoners follow the same logical reasoning, it will lead to a game equilibrium situation called Nash equilibrium, even if this is not the optimal solution (taking 10 years each and making a total sentence of 20 years).

Achieving the coordination

Let’s have a look at another scenario of a simultaneous-move game but this time, we’ll focus on a more realistic situation. There are two firms, A and B, that have to choose between two technologies, 1 and 2, and adopt the chosen one. They have to do it at the same time and independently. Technology 1 is better than Technology 2, so let’s assume that we get a payoff of 10 for the first one over the payoff of 5 for the second one. We’ll also assume the following statements:

If both firms choose the same technology, they both get the same payoff.

If the firms choose a different technology, since they’re not compatible, they’ll get zero payoffs, understanding that they’re incompatible and they can’t, for example, exchange files.

Let’s see the game matrix this time:

Pareto Coordination Game matrix

What can the firms do in this situation? Let’s examine the possible solution:

Firm A’s best strategy is to choose the same technology as Firm B.

The same affirmation is valid for Firm B.

There are two equilibrium situations (Nash equilibrium): if both firms choose Technology 1 (which have a total payoff of 20) and if both firms choose Technology 2 (which have a total payoff of 10).

Unlike the prisoner’s dilemma, there is no incentive that encourages any company to choose another option than the one that is best for each unilaterally.

The Prisoner’s Dilemma and the Pareto Game are just two simple examples of games that can be applied to a multitude of everyday situations we are exposed to in our companies. Situations where we have to think about the best course of action my company can take and try to anticipate the other actor’s actions, think strategically. Should I cooperate or compete? Should I create value or demand value? Will the other party break our agreement? Will I sell to this client just one time or more than once? If the answer is more than once, can I waste this time to succeed in the long term? Although this story is only a brief introduction, there is a large number of situations in which game theory can help us come up with a better strategy.

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