Game theory in negotiation. The dilemma: to compete or cooperate.

How can Game Theory help in sales? In the following post, we will try to answer starting from an absolute concept: business and commercial negotiations are activities that require high strategic, relational, and communication skills. It is a tautology, a statement that is always true, but, especially in B2B, it assumes highly complex connotations. B2B is, in fact, the realm of Complex sales, also known as Enterprise sales.

Especially in the B2B markets, in the most disparate sectors, where the relationship between the supplier company and the customer plays a fundamental role, it is interesting to focus on the most appropriate tools and strategies to achieve one’s goals.

The relationships between these parties are usually long-term, characterized by relational continuity and stability. That is due to both the relationship of interdependence and trust generated between the company and the customer in the supply processes and because the product/service development times can be exceptionally long. These characteristics of the B2B market imply a greater level of difficulty in winning new customers. Still, at the same time, once a relationship has been established, it will be more difficult for it to end as long as the supplier manages to generate value: value that, over time, will be the cement to build a stable and interdependent bond.

Are you wondering how to win the competition in the B2B market and establish a long-term relationship with the customers you have acquired? Let’s see how the famous theory known as Game Theory could be useful in the sales field to answer this question.

Let’s start from the context: the birth of Game Theory

As Wikipedia reports, game theory can be defined as an actual discipline aimed at analyzing and describing, through mathematical models, the choices that rational agents make in situations of strategic interaction. The goal of game theory is to find a “solution to the game” that will be given by the combination of the decisions made by the players during the interaction.

Although the first reasoning and publications related to the mathematics of games date back to the XVI century, as already some dissertations on the subject date back to some thinkers of Ancient Greece, the birth of modern game theory coincides with the publication in 1928 of the article “On the Theory of Games of Strategy” by John von Neumann. The article was then followed by the publication of the book “Theory of Games and Economic Behavior” in 1944, written again by von Neumann, this time together with Oskar Morgenstern. The studies conducted by these authors have allowed numerous statisticians and economics scholars to model and analyze decision-making behaviors in situations of uncertainty in the following years. For example, in 1950, The RAND Corporation applied the game theory studies in the investigation by mathematicians Merrill M. Flood and Melvin Dresher for possible applications to global nuclear strategies. However, the most significant development of game theory took place in the 1950s, with the elaboration of numerous concepts, including the concept of the nucleus, game in extended form, repeated game, and Shapley value. Yet, above all, we witnessed the first applications of the theory of games in political science and philosophy. The surprising aspect of this theory is that its boasts various fields of application: from a chess game to political and economic negotiations between states; from candidates competing in a political election to the analysis of situations related to corporate and strategic management.

It’s such an interesting and complex discipline: much so that many game theorists are among the winners of the Nobel Prize for Economics. For this reason, we would like to use Game Theory in the field of sales.

Before going into detail, however, let’s define the rules of the game!

The postulates and essential elements of Game Theory

Before going into the heart of the discussion and applying this theory to commercial negotiations and sales, we would like to make some premises:

When we speak of “games”, we do not only mean standard board or role-playing games, but we refer to any situation of strategic interaction between subjects or entities where the strategic behavior of each individual has a significant impact on both the decision-making process and on the final result of the game;
The goal of the contenders in the game is to maximize their winnings;
The result of the game depends both on the sequence of strategies implemented by the player himself and on the strategies adopted by the other players;
It is natural and logical that the decisions made by a player collide or agree with the decisions made by the other players, which is why various types of games are born based on the different situations (e.g., cooperative or non-cooperative games; games repeated over time or finite games; games with perfect or imperfect information; zero-sum or non-zero-sum games);
The players must have rational behavior.

The elements that make up the foundations of the game are:

PLAYERS
STRATEGY: move or set of moves that an individual intends to make
PAYOFF: compensation, outcome, or winnings that each player obtains based on the strategy adopted by all players
PAYMENT FUNCTION: it is the rule that quantitatively defines the winnings of the contenders according to their behavior
DECISION MATRIX: it is a double-entry matrix that permits to bring out the value of the win each player would get from each interaction.

Based on these premises and fundamental points, let’s move on to see how this theory can also provide interesting insights into the management of competitive situations in the markets or the conduct of commercial negotiations between customers and suppliers. Therefore, in these latter cases, the “players” are the companies and the persons that operate in them or a trader, buyers, customers, and suppliers.

To cooperate or not to cooperate in the Hamletic “Prisoner’s Dilemma”

The most famous application of Game Theory is known as the “Prisoner’s Dilemma“: a full information game proposed as a game theory problem by Albert Tucker in the 1950s. The dilemma starts from the following situation: two criminals are accused of having committed a crime at gunpoint. The investigators arrest both of them but lock them in two different cells to prevent them from communicating. The two criminals are then questioned to see if they actually committed the crime. Therefore, each of them is faced with two possible behaviors: to cooperate or not to cooperate with the police. The function of players is as follows:

If only one of the two cooperates by accusing the other, the collaborator manages to avoid the penalty; the other is sentenced to 7 years in prison
If both accuse the other, they are both sentenced to 6 years
If neither of them collaborates, both are sentenced to 1 year (guilty of illegal carrying of arms)

The aim is to minimize their sentence for each of them, but neither of them knows what the other will choose to do. This game can be represented with the following decision matrix:

	Collaborate	Not collaborate
Collaborate	(6,6)	(0,7)
Not collaborate	(7,0)	(1,1)

By analyzing the different combinations, it emerges that in this game, which can be defined as non-cooperative, the best strategy is to collaborate because, after all, we do not know what the other will choose to do. The aim is to minimize one’s possible sentence.

Collaborating: risks 0 or 6 years

Not collaborating: risks 1 or 7 years

This result is known as Nash Equilibrium, from the name of the well-known American mathematician and economist John Nash, who at that time elaborated a theory that contrasted with the thought previously developed by Adam Smith and elaborated a criterion applicable to a range of more games compared to the criterion proposed by von Neumann and Morgenstern. Nash, with his theory, argued and demonstrated that the best result for a group is obtained not so much when “everyone acts only based on what is best for himself” as Smith argued, but when “each member of the group acts based on what is best for himself and the group”.

Here is the video from the 2001 film A Beautiful Mind directed by Ron Howard and starring Russell Crowe, dedicated to the life of Nash, in which this concept is proposed simply and linearly.

Obviously, this is a cinematic recreation, a streamlining that is in some ways goliardic and which does not consider the underlying mathematical formulation, defined precisely as the Nash Equilibrium. Still, we believe it can be an excellent way to translate a concept that is also complex.

In fact, the concept can also be seen with the Italian scholar Vilfredo Pareto, the famous author of the Pareto Principle, who highlights other possible concepts helpful in defining these situations in his studies known under the umbrella of Pareto Improvement and Pareto Efficiency. There are, therefore, differences between Nash’s and Pareto’s thinking, but we refer to external insights Nash equilibrium and Pareto efficiency.

In the previous example, it can be seen that, intuitively, the Nash equilibrium is not the best possible solution either individually or collectively. In fact, there is a better solution for both, what economists call Pareto efficiency: the best strategy for everyone, which, in this case, would be if they were both silent (1,1). To learn more about this topic, see the studies of the “Tor Vergata” University of Rome.

But now, let’s leave the theory behind and stick to our thesis and try to bring these issues into the world of sales.

How Game Theory Applies in the B2B World: The Negotiator’s Dilemma

The Prisoner’s Dilemma highlights that in some cases, pursuing rational and more cooperative behaviors could lead to the achievement of results of value for both parties. So, let’s now apply these concepts to the B2B world, particularly in sales, to a potential negotiation situation to understand how to achieve one’s commercial objectives through a cooperative and non-conflictual approach by applying the concepts underlying the Game Theory.

Let’s move on from the Prisoner’s Dilemma to the Negotiator’s Dilemma!

Negotiation is a situation of interaction between parties that has the exchange of resources between the parties as its object. Each party tries to obtain the best possible result, which, however, depends on the choices/strategies made by the counterpart.

Let’s imagine the following situation.

We have two individuals representing our players: a seller/supplier (SS) who wants to propose the goods/services of his company and a potential buyer/customer of these goods/services (GS). The goal of the “game” is, therefore, to close a deal.

However, the counterparties find themselves in a situation of conflict of interest: the seller/supplier aims to obtain the order and gain a new customer by trying to have the highest profitability; the buyer/customer, on the other hand, is guided by the objective of obtaining a new good/service to replace an existing supplier or for a new project of his company, all at the lowest possible cost, with the best guarantees and with all the desired ancillary services. They are players of the same game who, as is now clear, pursue different objectives and strategies.

Let’s now turn to their possible moves.

The seller’s moves can be: to increase or decrease the price of the good/service while increasing or decreasing the guarantees and related services. The buyer’s moves may instead be choosing this new supplier, negotiating or not the price, guarantees, and related services, or staying faithful to the current supplier, or, in a different case, giving up the new project.

Negotiator’s Dilemma: “To communicate or not to communicate?”

Having now defined the perimeter of the game and being aware that communication plays an important role in a negotiation process since each party needs a series of preliminary information to decide its move, a doubt now arises: is it convenient for the parties give out information during the negotiation?

Can we, therefore, say that the Negotiator’s Dilemma is “To communicate or not to communicate?”.

The players must choose whether to cooperate with the counterpart, then the seller/supplier, and vice versa, thus giving information and opening the conversation with the risk of giving an advantage to the counterpart or competing, giving up information, thus keeping the negotiation more closed and rather trying to induce only one’s interlocutor to give information.

Now we add complexity to complexity, aware, however, that any reader who has come this far has an idea of what a commercial negotiation is in any sector of the B2B world.

Clearly, in a situation like this, each player at the moment of the decision does not know what the other party will decide. In this case, returning to the discipline of game theory, we are talking about games with imperfect information.

This situation thus leads to the realization of four possible scenarios with seller/supplier protagonists with the buyer/customer that could be obtained based on the behavior adopted by each player. Let’s analyze the decision matrix together:

	COMPETITIVE Style	COOPERATIVE Style
COMPETITIVE Style	Stall or break in the relationship	Unbalanced agreement (advantages for SS)
COOPERATIVE Style	Unbalanced agreement (advantages for BC)	Effective agreement (advantages for both)

The four scenarios highlighted by the matrix can now be summarized and described according to 3 different situations:

One of the protagonists collaborates, and the other competes

In the event that the negotiation activity takes place as a competitive game, in which the counterparties do not collaborate through continuous defense and attack actions until finally, in terms of the game, there would be a winner and a loser. In this case, the unbalanced agreement would seem to be advantageous for one of the parties, but, as initially said, in B2B, relationships are usually based on long-term relationships, characterized by continuity and relational stability. However, any relationship started in a situation of imbalance, in common experience, is destined to end soon, which, in the perspective of mutual benefits in the long term, is neither the goal of the seller/supplier nor the goal of buyer/customer.

Both protagonists compete

In this case, if both protagonists of the game decide to compete, there would be a stalemate or a break in the relationship. This would not lead any of the players on the field to achieve their goals. The seller/supplier would not get the order and would not earn, while the buyer/customer would not fulfill the mandate to obtain a new good/service to replace an existing supplier or for a new project. In this case, no one would win, with an obvious loss of time and no result for both parties.

Both protagonists cooperate

This scenario, on the other hand, is based on the implementation of a cooperative strategy. It will therefore be necessary to identify at least one element of exchange during the negotiation that allows each of the counterparties to find satisfaction in a reciprocal relationship. In this case, we are therefore talking about collaborative strategies in which, at the end of the negotiation, unlike the first scenario, there will not be a winner and a loser, but rather two winners. This strategy is therefore based on communication and transparency in which the parties express their interests and the results that each one wants to achieve.

The first option is often the one that occurs most frequently because it is seen as the only way to better achieve one’s goals. But are we sure that competing is the optimal solution to achieve your business goals?

From the table, it can, in fact, be noted that both parties would receive a benefit if they decided to communicate and give information on their needs and business situation (cooperation), while a competitive negotiation could deteriorate relations with the counterpart (element as mentioned instead fundamental in B2B relationships based on the relationship and trust between the parties) and would lead to obtaining sub-optimal results for both players.

The problem is that neither side wants to make the first move because aiming for cooperative negotiation would entail the risk of both players exposing themselves too much and providing the other party with too much information. In fact, in the event that only one party communicates, a situation would be created whereby the person who transferred information would be at a disadvantage in favor of the other party instead.

How then to solve this dilemma?

The negotiator’s dilemma goes beyond that of the prisoner because it has a few more elements:

Repetition: during a negotiation, the parties have the opportunity to meet several times to negotiate and exchange information. This allows us to carry out a more cautious, reciprocal, and incremental exchange of information and thus gradually establish trust
Dialogue: the presence of a communication channel allows the parties to clearly express their intentions
The possibility of “punishing” the interlocutor if he does not respect the commitments made and destroys the relationship of trust

Conclusions

The above reasoning helps us understand that there are ways to effectively manage cooperation in contractual relationships, trying to protect oneself from a competitive attitude of the interlocutor and aiming for value co-creation. Viewing the negotiation as a clash between the parties and adopting a competitive strategy to achieve a “win-lose” result is not always the best solution.

Indeed, in negotiations and the B2B market, the relationship between the parties plays a fundamental role. If the parties work together and cooperate, they generate more significant value than what they would have by acting individually and, above all, by wasting resources and energy to “fight”.

Obviously, the best strategy to be implemented must be assessed on a case-by-case basis: choosing the most appropriate negotiation strategy based on the circumstances and on our interlocutor is necessary. For this reason, it is important to learn to interpret the other party’s behavior to try to predict better what the consequences of our actions could be. The secret of the greatest negotiations is precisely their ability to observe the counterpart, read their behavior, and try to steer the negotiation towards a cooperative direction by investigating the interlocutor’s needs. If you want to deepen this topic, you can read the post “The power of the Socratic method in a commercial negotiation“.

If you still do not trust our observation point, will you perhaps find it interesting to understand how a computer system would behave?

As mentioned several times, it is a system based on rational players. So how would a computer system behave?

For the more curious, we recommend that you learn more about Axelrod’s Tournament with this content on the Standford University website.

There would then be other insights on the subject, but we invite you to contact us to get to know them.

You will discover the golden rule of human behavior!

And what do you think? Do you also believe that cooperating is better than competing? Please write us in the form below and tell us your opinion.

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Sales and Game Theory. The negotiator’s Hamletic dilemma: Compete or Cooperate.