Game theory is a field of mathematical study that analyzes strategic decisions in situations where the outcome depends on the actions of several participants or “players.” John von Neumann is considered one of the pioneers in this field, along with Oskar Morgenstern, who published the book Theory of Games and Economic Behavior in 1944, laying the foundations for modern game theory.

Von Neumann focused on zero-sum games, where one player’s gain is exactly equal to the other player’s loss. In other words, the total gains and losses in the game add up to zero. A typical example is the game of poker, where what one player wins, the other loses.

“All the scientific advances of the last decades seem to come together in a single brain, that of the Hungarian mathematician,” says Chilean writer Benjamin Labatut, author of the biographical novel MANIAC

A non-zero-sum game is an interaction where some combinations of actions provide a net gain (positive sum) or loss (negative sum) for both parties. An example of this is the exchange of surpluses, such as when shepherds and farmers trade wool and milk for grain and fruit.

In a zero-sum game, a player seeks the highest gain for themselves and necessarily seeks the maximum loss for the other player to achieve the highest possible return. In a positive-sum (non-zero-sum) game, a rational and self-interested player can benefit the other with the same choice that benefits themselves. Positive-sum games are referred to as win-win situations and are reflected in the phrase: “Everyone wins.”

Treating a non-zero-sum situation as a zero-sum situation, or believing that all situations are zero-sum, is called the zero-sum fallacy. This fallacy has become a mindset, a way of thinking that is carelessly applied.

The zero-sum fallacy is an error of reasoning that occurs when someone assumes that a situation is a zero-sum game, where one person’s or group’s gains must necessarily come at the expense of another person or group’s losses.

Characteristics of the Zero-Sum Fallacy:

  1. Assumption of Finite or Fixed Resources: The zero-sum fallacy is based on the idea that resources, power, or opportunities are limited, and any gain by an individual or group must be offset by an equivalent loss elsewhere.
  2. Competitive Thinking in Unnecessary Situations: This fallacy fosters a purely competitive approach, even in situations where all parties involved could benefit (positive-sum games).
  3. Ignoring the Possibility of Growth or Cooperation: In many contexts, especially in economics, politics, and interpersonal relationships, it is possible for all actors involved to increase their well-being through cooperation or the creation of additional value. The zero-sum fallacy ignores this possibility.

When people are forced to interact, their decisions do not determine whether they are in a zero-sum game or not; the game is part of the world they live in. But people, by neglecting some of the options on the table, may perceive that they are in a zero-sum game when in reality, they are in a non-zero-sum game. Moreover, they can change their environment so that their interaction is not zero-sum.

For these reasons, when people become aware of the game theory structure of their interaction (whether it is positive-sum, negative-sum, or zero-sum), they can make decisions that bring them more valuable results.

In the context of sports, particularly in climbing, positive-sum games can be observed in situations where cooperation and competition generate mutual benefits for all participants, including competitors, coaches, teams, leagues, and even the fans. Here’s how they relate:

  1. Cooperation Between Teams or Competitors
    • Joint Training: Teams or competitors can train together, sharing techniques and strategies. Although they compete in a specific tournament, this type of cooperation can raise the level of all involved, resulting in more competitive and exciting tournaments and events.
    • Sharing Resources: Clubs and gyms that share facilities or technical knowledge can improve their performance, benefiting both the teams and the development of the sport in general.
  2. Leagues and Tournaments
    • Creating Leagues: The creation of a league or tournament can be a positive-sum game. All the actors involved benefit from having a platform to compete, attract more followers, generate revenue from ticket sales, broadcasting rights, and sponsorships.
    • Healthy Competition: A league where all climbers compete fairly and equitably can raise the overall level of the sport, making events more attractive to fans, which in turn generates more revenue for everyone involved.
  3. Talent Development
    • Youth Development Programs: When clubs and leagues invest in developing young talent, they not only improve the quality of their own teams but also contribute to the growth of the sport in general. This can lead to greater competitiveness in future leagues, benefiting all teams and competitors.
    • Knowledge Exchange: Coaches and players who share tactics and strategies can raise the level of the sport in general, benefiting all participants by creating a more competitive and stimulating environment.
  4. Social and Economic Impact
    • Community Impact: Sports can have a positive impact on local climbing communities, from creating jobs to improving social well-being. When sports teams collaborate with their communities, the economic and social benefits multiply, benefiting both teams and local residents. Events that address local issues or promote low-impact practices, space clean-ups, etc., are essential for bringing the sport closer to the community.
    • Sporting Events: The organization of major sporting events like the Olympics or the World Cup, or in our region, the recent inclusion of the Copa Sudamericana is a clear example of a positive-sum game. Although there is competition, the participating countries and hosts can benefit from tourism, improved infrastructure, and national pride.
  5. International Relations
    • Sport as Diplomacy: Sport has been used as a tool of diplomacy, where international competitions can improve relations between countries. This can generate mutual benefits, such as cultural exchange and peace.

To avoid falling into the zero-sum fallacy, it is important to recognize situations where cooperation, innovation, or exchange can generate mutual benefits. This involves carefully analyzing contexts, considering growth opportunities, and understanding that many situations are not strictly competitive. Recognizing and overcoming this fallacy can open the door to more creative and beneficial solutions for all parties involved.

Positive-sum games manifest when cooperation, talent development, and the organization of training camps, leagues, and events benefit all participants. This approach not only raises the level of competition but also maximizes the economic, social, and cultural benefits for players, teams, communities, and fans.