Goal Conflict and Game Theory

The divergence of goals between the various organizational areas is a subject of constant conflict in the business world. Despite the great efforts expended during the strategic planning at the end of each year, the impression is always left that the goals between departments under different directorates conflict. And what is observed falls on the concept of fallacy of composition, where the effort to meet individual goals does not lead to the global maximum.

It is quite common to see, for example, the commercial and finance areas in conflict: while the commercial area has a clear goal for attracting customers, which can be achieved through more generous payment terms, the finance area wants to reduce capital spin. This generates a conflict of interests, and it is practically impossible for both targets to be met, perhaps the company's global objective. Another hypothetical case involving conflict of goals: the purchasing area, with the objective of reducing unit costs, decides to buy in larger volumes, causing an increase in costs related to inventories, which would go against the area's cost reduction targets Logistics. Finally, there are many examples that illustrate the internal conflicts that exist in companies.

The best definition of strategic planning is an arduous task and generates a series of difficulties, but as in any business reality, such problems need to be faced and resolved. And among the tools that exist today for conflict resolution, we highlight the Game Theory.

The film "A Beautiful Mind", winner of the Oscar for best film in 2001, portrays the story of one of the greatest mathematicians of all time, the American John Nash. Despite Russell Crowe's brilliant performance, emphasizing the difficult life of the mathematician to deal with his genius and his schizophrenia, the film fails to substantially alter the mathematician's biography for commercial reasons, leaving aside the academic brilliance and phenomenal contribution that John Nash made to mathematics, economics and other fields of science.

Game Theory basically deals with strategic player interactions. The intention of this post is to present, in a simple and practical way, how some of its concepts can be used for basic applications of conflict resolution between two players. First, we must understand how the Winnings Matrix works in a Game, what Dominant Strategies and the Nash Equilibrium are all about, and also understand the classic Prisoner's Dilemma.

The Gains Matrix is ​​a simple form of approach that allows you to visualize how the interaction of choosing two agents affects the results obtained by each of them. Let's see an example: In a game where two people, called here A and B, can choose two different strategies - A chooses between high or low and B chooses between left and right - the Winnings Matrix allows the visualization of the gains obtained by each person, as a matrix: the first number refers to A's gain and the second to B's gain.

Figure 1 – Example of Earnings Matrix

Source: ILOS

In this game we can observe that there is, for each player, in an isolated way, a better strategy: For A it will always be better to choose “low”, and for player B it will always be better to choose “left”. In this case, the natural result would be down and left, resulting in a gain of 2 for player A and 1 for player B. Dominant Strategy, as there is an optimal choice for each player whatever the choice of the other.

However, to the dismay of strategic decision makers, what is observed is that the dominant strategy does not occur so often. Usually the choice of players affects the choice of the other, so that it is impossible to predict the outcome without knowing your choices in advance. In contrast to the dominant strategy's strong requirement that A's choice be optimal for all B's choices, we could have optimal choices for A given B's choice. Nash Equilibrium, which defines games in which there is an optimal choice of A Dada B's choice is an optimal choice of B given A's choice.

An example of a game in which the existence of a dominant strategy is observed is the classic Prisoner's Dilemma: Two prisoners, partners in crime, are interrogated in separate locations. Each one has two possible choices: to confess to the crime and involve the partner's participation or to deny his participation, remaining silent. If both confessed to the participation of the other accomplice, they would each receive a sentence of 3 years in prison. If only one confessed to the participation of the other and that other denied it, the penalty for the one who denied it would be 6 years, while the one who testified would be released, as a benefit for helping to resolve the case. If both denied, each would be jailed for 1 year. Figure 2 presents the Prisoner's Dilemma gains matrix. Note that the negative number represents a loss, so in this case, the smaller the loss, the better.

Figure 2 - Gains Matrix in the Prisoner's Dilemma

Source: ILOS

In this game, we can observe that there is a dominant strategy: Whatever B's choice (confess or deny), prisoner A will be better off if he confesses, and vice versa. In this way, the dominant strategy would lead to the situation in which both would confess, each serving a 3-year sentence. However, if both kept silent and denied the crime, the two would improve, getting only 1 year of imprisonment each. So the question remains: how to coordinate the choice of both, so that the strategy of denying is chosen by both parties? In what situation should they trust each other?

What is observed is that if the game took place only once, confessing seems reasonable. Remember that if the player cheats (confesses), he may have the benefit of being immediately released from prison, in case the other denies participation. But if this game is repeated over and over again, would confessing be the best strategy?

When we are in a case of repetitive games, the rational and most efficient thing is to choose a cooperative strategy, in a coordinated way. In a series of experiments led by Robert Axelrod, tested in a computational tournament, it was proven that in games where there is always the perspective of a new future round (that is, a game with infinite sequential repetitions), the best strategy is the so-called “ eye-for-an-eye”: the player always tries to cooperate, until his opponent circumvents cooperation. If this happens, the player “punishes” his opponent by cheating on the next move, and will continue to cheat until his opponent decides to cooperate again, leading to the return of the player's cooperation move on the next move. That is, the player will always seek cooperation, punishing when his opponent cheats and forgiving his opponent when he cooperates.

If we imagine different departments as “players” and try to apply the Game Theory Gains Matrix to define the best gain in terms of goals, we would be in a situation of repetitive games: since year after year those same departments will coexist and need to “play” again to decide their goals, the cooperation strategy should be chosen by both. Although it seems like an obvious conclusion, it is not so easy to apply, since there is an enormous difficulty in defining the players' earnings for defining the Matrix.

The Game Theory tool is powerful, and its application is still quite restricted to financial areas. However, its concepts can be used in the most diverse situations, where there is conflict and negotiation between the parties is inevitable. There is a provocation in the air: Where else could we apply such concepts in the business environment? In which areas along the supply chain, permeated with strategic decisions, could we use such a tool?

References:

VARIAN, Hal R. Microeconomics-basic principles. Elsevier Brazil, 2006.

AXELROD, Robert M. The evolution of cooperation. Basic books, 2006.