Game theory: what it is, what it's for, and applied examples

La games theory It has become an absolutely essential tool for analyzing strategies and making decisions in situations where the outcome depends as much on one's own actions as on the behavior of other agents. Although it might sound like something out of a video game or entertainment, the truth is that its applications have a real impact on matters such as economics, politics, biology, psychology, and even our daily lives, whether we are trying to negotiate a salary increase or choosing which restaurant to go to with a group of friends.

It is no coincidence that one of the greatest mathematicians of the 20th century, John Nash, is remembered for the gigantic boost he gave to this discipline by conceptualizing the famous Nash equilibriumYou'd be surprised how many seemingly simple situations we experience daily can be analyzed using this approach. Throughout this article, you'll find a comprehensive and very accessible overview of what game theory is, its origins, key concepts, essential examples, and also a look at its criticisms and limitations.

What is game theory?

In basic terms, the games theory It is a branch of mathematics that seeks to understand how rational agents interact in situations where everyone's success depends on what others doEach participant—referred to as a "player"—must choose their actions considering the possible actions and strategies of the other participants. This interaction can take many forms: from a business negotiation to an international political decision or even a family dynamic.

In this discipline, the term "game" does not refer solely to board games or games of chance, but to any structured situation involving incentives, consequences, and multiple actors making decisions. For example, competing in a market to attract customers, engaging in salary negotiations, or deciding whether to cooperate with or betray a colleague under certain rules can all be analyzed from the perspective of... games theory.

Origin and historical evolution

The formal starting point of game theory is marked by the Hungarian mathematician John von Neumann, who, along with Oskar Morgenstern, published the work "Theory of Games and Economic Behavior" in 1944. These early approaches were especially focused on what are known as zero sum gameswhere what one agent gains exactly the other loses, as in chess or poker.

The great conceptual leap came when John Nash —Nobel Prize in Economics in 1994— introduced the concept of Nash equilibriumUnlike the zero-sum model, Nash showed that there are many situations where the optimal actions of the participants do not necessarily imply that one loses if the other wins, but that both can maximize their well-being or at least have no incentive to change strategy if the others do not either.

Since then, the theory has expanded into countless more flexible models, addressing not only competition (non-cooperative) but also cooperationand transcending economics to embrace biology, computer science, political science, or psychology.

Why is game theory so relevant?

La games theory It has proven to be a crucial tool for understanding and anticipating behavior in a wide variety of contexts, allowing analysis of everything from fierce competition between companies and the formation of trade agreements, to the balance of power between countries or stock market movements.

In biology, to cite another field, it is fundamental for studying phenomena of natural selection where organisms compete or cooperate to survive. In politics, thanks to this theory, it is possible to better understand the tug-of-war between rival parties, governments, and international negotiations. Even in psychology and sociology, it allows us to explore the logic behind group decisions, altruism, or interpersonal rivalries.

Key concepts of game theory

Understanding the essential concepts is vital to delving deeper into the fascinating world of game theory. Here we review the most important ones:

• Strategy: It's essentially each player's action plan within a game, considering the possible options and outcomes. We can distinguish between pure strategies—where a player always chooses the same action—and mixed strategies—where they alternate between different options with varying probabilities.
• Nash equilibrium: This concept, as proposed by Nash, represents a state where no player can improve their outcome by simply changing their own strategy, given what the others are doing. In other words, everyone is optimizing by considering the decisions of the others.
• Zero-sum games: These are situations in which one person's victory is exactly the other's defeat, as in chess or certain sports.
• Payment matrix: A fundamental tool for visualizing all possible combinations of actions and their consequences for each participant.
• Sequential and dynamic games: Here, the players do not act at the same time, but rather decisions are made in different stages, where knowing what the opponent has done before can be key to deciding your own play.
• Decision tree: A graphical scheme that visually represents the possible paths and choices in sequential games, clarifying how the different alternatives and outcomes develop.
• Perfect balance in subgames: It is an extension of the Nash equilibrium for dynamic games, and it determines which strategies are rational in each substage of a game, discarding unrealistic threats.

Main types of games

The variety of applications of game theory is reflected in the different types of games it studies:

• Non-cooperative games: Each player seeks their own benefit without forming stable alliances, with direct competition being the main focus.
• cooperative games: Participants can coordinate, forming coalitions to achieve common goals and share the benefits.
• Simultaneous games: All players decide at the same time, without knowing what the other chooses.
• Sequential games: Decision turns follow one another, so there is information about previous moves, like in a game of chess or business chess.
• Games with perfect or imperfect information: In the first case, the entire history of plays is public knowledge; in the second case, there is uncertainty or partial information.

Practical and famous examples of game theory

To clarify concepts, it is helpful to use several well-known examples that are commonly used in the study of game theory.

The prisoner's dilemma

It's difficult to talk about game theory without mentioning the famous prisoner's dilemmaTwo individuals are accused of a crime and faced with the temptation to betray their partner or remain silent. If both remain silent, they receive a light sentence; if both betray each other, the sentence is harsher; if only one confesses and the other remains silent, the snitch goes free and the other receives the maximum sentence. Logic predicts that both will confess, although cooperation would be better for both. This example illustrates how rational individual decisions can lead to suboptimal results for the group..

The Monty Hall Problem

Based on a television program, the contestant must choose between three doors. The host reveals one of the doors that does not contain a prize and offers the opportunity to switch. Analyzing this problem mathematically demonstrates that it is advantageous to change one's choice, a fact that many initially reject based on intuition. This example helps to understand cognitive and probabilistic biases in decision-making.

The hawk-dove model

This study examines the conflict between players who can choose between an aggressive (hawk) or peaceful (dove) strategy. If both are aggressive, both lose; if both cooperate, both win; if one cooperates and the other is aggressive, the aggressive player wins. This is widely applied to military strategies and political negotiations. The key is to anticipate the opponent's behavior and decide on the stance that optimizes the consequences.

Commercial games and business competition

Game theory has also proven crucial in competition between companies. For example, two companies must decide whether to lower prices or not: if both do, profits decrease; if only one does, it gains market share at the expense of the other; if neither does, both maintain profits. These dynamics determine market strategies, product positioning, and advertising campaigns..

Dynamic games with multiple stages

In complex cases, such as long-term conflicts between countries or companies, decisions are made in several stages. Players must anticipate their rivals' potential future responses before acting. This is where the following is frequently used: decision tree to outline the options and outcomes. For example, if one country decides to invade another, the latter can choose to surrender or retaliate, and the result depends on the chain of decisions (see more details and examples in CeCo).

What is pedagogy: meaning, history, branches and key tools

Criticisms and limitations of game theory

Despite its enormous success and widespread use, the Game theory has also received criticism:

• Oversimplification: Many models assume that players always act in a fully rational manner and that they know all the rules, which rarely happens in reality.
• Lack of context: Theory often overlooks historical, cultural, and emotional details that can decisively influence human behavior.
• Ambiguous predictions: In some games, different possible equilibria are presented, and theory does not always indicate which one will occur in practice.
• Emphasis on individual rationality: Often the model does not take into account trust, loyalty, or altruistic or solidarity-based motivations.

It is also often emphasized that, while it allows for structuring problems, Predicting exactly what each person will do is impossible.Because we rarely react in a perfectly logical way—emotional factors, past experience, or simple chance all play a role. Despite this, game theory remains an essential methodological framework for understanding complex conflicts, negotiations, and agreements.

Applications of game theory today

Today, no one doubts that game theory has transcended academic boundaries to be used in key areas:

• Economy: It determines pricing policies, public auctions, market strategies, and consumer behavior.
• International policy: Governments shape negotiations, alliances, and treaties by considering the reactions and strategies of other countries.
• Evolutionary biology: It is used to analyze survival strategies between rival or cooperative species.
• Technology and artificial intelligence: Developers program algorithms to make optimal decisions in relation to other agents in complex systems.
• Social and behavioral psychology: It allows for a deeper understanding of individual and group motivations, evaluating cooperation, conflicts, and altruistic behaviors.

The truth is that, far from being limited to abstract theory, games theory It has its place in current debates, whether we're talking about international debt negotiations (for example, the Greek case), supermarket pricing, or even online dating platforms. It has more impact than you might think!

After this comprehensive review of the history, foundations, models, and critiques, it is clear that the games theory It is much more than complex equations or mathematical models. It is a powerful conceptual framework for understanding competition and cooperation in all aspects of modern life. Whether analyzing disputes between corporate giants or understanding why two friends decide to share or not share the last slice of pizza at a party, this theory provides us with the tools to examine the logic—and passion—behind our choices. And while human behavior is often unpredictable, the games theory It will continue to be the intellectual compass used by economists, psychologists, politicians, and anyone curious to better understand the world of interdependent decisions.