# Game Theory

# Definition

It represents how individuals should make decisions and how people make them. Game theory observes the interactions among two or more rational players and converts them into mathematical models.

**The concept’s key terminology is specific and contextual:**

- A game, in this case, refers to the circumstances surrounding two or more players’ actions.
- Players are a decision-maker in a game.
- The strategy is a predictable set of player interactions concerning the game’s circumstances.

The theory then describes the individuals in the model and their predictable interactions.

# Why Use It

Game theory is used to examine, predict, and explain a broad range of behaviors. Today, the concept is an umbrella term for the science of rational decision-making in animals, humans, and computers. It can be applied across many disciplines, including business, economics, social science, psychology, biology, and computer science.

**The two most common game types which explain most situations are cooperative and non-cooperative:**

- Cooperative games describe how groups of players form, react to each other, and take action to receive a collective outcome or payout.
- Non-cooperative games describe what individuals will do to attain goals. Zero-sum games are an example where two opposing sides vie for an advantage. A familiar example is rock paper scissors.

Apart from predicting behavior, the concept informs normal and ethical behavior theories.

# When to Use It

Game theory has many applications across a diverse set of fields, and scholars are split on what it is capable of indicating. Some think games can predict human behaviors on a small and large scale. Others believe it demonstrates how people would behave rationally but does not reveal actual outcomes.

**Regardless, game theory models human behavior in populations:**

- In business, it looks at economic entities and predicts how they compete. In this scenario, an organization functions to profit from its product or services and makes strategic decisions to enter new markets, develop new products, deprecate existing ones, or change pricing tactics to maximize earnings.
- In political science, players in a game are usually politicians, voters, states, and special interest groups. Games illustrate how they’ll react to the economy, public issues, war bargaining, and social choice theory, to name a few.
- In project management, players are investors, managers, customers, and contractors. Games depict how parties work in their best interests and frequently make choices that negatively affect other players.

# How to Use It

Game theory observes strategic interactions between two or more players and how they should behave in situations, whether through cooperation or competition—their goal is to win the game and have the largest payout or payoff. The Nash Equilibrium is a decision-making theorem where the optimal outcome is one in which folks have no reason to deviate from their initial strategy, so they stay the course.

**In this context, a game is:**

- A scenario with at least two players and potentially an infinite number.
- A player is either a singular or a group of people, such as organizations.
- A player can execute any number of strategies or actions.
- The outcome results from the choices players make.
- A payout or payoff is the player’s reward and represents the value of the result.

**There are several assumptions about each game:**

- Players are aware of the rules.
- They are rational decision-makers.
- They will act in their interest and seek to maximize their payout/payoffs.

**Two overarching game types exist, combinatorial and classical:**

- Combinatorial games have no element of chance. Two players compete against each other, taking turns where each has perfect knowledge of the game. Nothing is hidden. Examples include Chess and Go.
- Classical games often have both elements of chance and hidden information. Examples include Poker and Economics.

**The following are essential game types:**

- The
**Prisoner’s Dilemma**is a game that exhibits why two people behaving rationally might not cooperate, even when it’s in their best interest. The original game is about two separated prisoners who cannot communicate; each must choose between cooperating with the other. - The
**Dictator Game**is for two players. Player 1 chooses how to split a cash prize with Player 2, which cannot affect Player 1’s decision. The result: 50% keep the money, 45% give the other player a smaller amount, and 5% split it equally.

In the Ultimatum Game, Player 1 has some amount of money and must give a portion to Player 2, who can choose to take it or leave it. If Player 2 rejects the money, neither player gets anything. - The
**Volunteer Dilemma**is where a player must take on a job for the common good. The worst thing that can happen is if no one volunteers. Meerkats exhibit this in nature when foraging for food. They warn the others and put them at risk. - In the
**Centipede Game**, two players can take an ever-increasing amount of money over a set number of rounds. The player who takes the pot receives the larger share, and the losing player gets a smaller share. - An
**Asymmetric Game**is one in which the same strategy may not benefit players equally. Players and their strategies are based on their opponent’s actions. An example is a new entrant in an existing market who chooses a different approach than an incumbent to compete. - The
**Constant-sum Game**is where two or more players compete for the same increasing payoff. When one player wins, it is at the expense of others.

In a Simultaneous Game, players move simultaneously or are otherwise unaware of the other player’s actions. - A
**Sequential Game**is one where later players have some idea about earlier players’ actions. Later players may not know everything but have at least some idea of actions that were not chosen or other pertinent information. - In the
**Cournot Competition**, a player (organization) produces the same product as another player in equal amounts. The player with a similar product can make the goods at a lower cost, create more of the goods, or sell the goods at a lower price. The aim is to maximize profits, and market share plays a large part in achieving that goal. A Cournot Equilibrium is reached when neither player chooses to deviate from their current strategy and is satisfied with their response to the market. - The
**Bertrand Competition**is where players have homogenous products and a constant marginal cost. Each player then chooses the price and goes as low as possible to gain market share. - A
**Perfect Information Game**is one where every player knows all the actions previously taken by all players. - An
**Imperfect Information Game**is one where players are unaware of all the actions previously taken by all players. - In a
**Bayesian Game**, each player is assigned a set of characteristics, and other players have incomplete information about their opponents. They map probability distributions to these characteristics, and using Bayesian probability, they calculate the game’s outcome. - An
**Infinitely Long Game**is a theoretical one where infinite moves can exist. There is no winner until all actions have been taken. The game focuses on whether a winning strategy exists for any player. - A
**Differential Game**has two controls and two criteria to optimize. The players’ actions affect the system, and each works to control the system to reach their goals. **Evolutionary Game Theory**models Darwinian competition. A player may emulate or mimic previous strategies at the start and deviate from them consciously or unconsciously. Each organism has a specific set of issues to overcome, and its actions define its ability to survive and procreate.- A
**Stochastic Game**is a repeated game with probabilistic transitions. The game has a sequence of stages, from a few to infinite, and can have one or more players. Each player chooses a strategy at the start of each stage and receives a payoff depending on the current state. The game proceeds to a new random state in the sequence and considers the previous choices made by players in the earlier stage. The total payoff is the discounted sum of all stage payoffs. - In
**Metagame Analysis**, a situation is recreated as a strategic game in which players try to achieve their goals by choosing the options available to them. The analysis observes how stakeholders behave differently, what scenarios might occur, and describes which players have the power to control events. It has been used to analyze nuclear proliferation, among other applications. **Pooling Equilibrium**plays out in a signaling game where one player takes action, “a signal,” to relay information to another player who doesn’t have access to this knowledge. A player’s “type” remains unknown; other players choose actions and attempt to maximize their utility based on their beliefs.**Mean-field game theory**observes small interacting players’ decision-making in large populations.

# How to Misuse It

Game theorists use specific rules for each game, and real-world situations are often more nuanced. The rules are shattered when humans do not act rationally, a fundamental assumption for many games. However, game theorists argue their scientific findings hold as much weight as models physicists employ.

# Next Step

Game theory has applications anywhere organisms exist. Its mathematical footing gives breath to scenarios between players and makes sense of complex interactions.

**Ask yourself these questions in a challenging real-world context:**

- Are players acting rationally?
- Do they know the game rules?
- Are they working in their self-interest?

If so, a game might apply and help discern the stakes and payoffs.

# Where it Came From

Cardano wrote “Book on Games of Chance” in 1564, published posthumously in 1663, and originated some game theory ideas. Huygens published “On Reasoning in Games of Chance” in 1657. Antoine Augustin Cournot first used game theory analysis in 1838. Ernst Zermelo wrote “On an Application of Set Theory to the Theory of the Game of Chess,” which found an optimal chess strategy.

However, John von Neumann coined the term in his 1928 paper, “On the Theory of Games of Strategy.” Later, he co-authored a book with Oscar Morgenstern titled “Theory of Games and Economic Behavior,” where they discovered a method to find solutions for two-person zero-sum games consistently. Émile Borel extended that concept in 1938 with a minimax theorem for two-person zero-sum games.

Merill M. Flood and Melvin Dresher had the first mathematical discussion on the Prisoner’s Dilemma in 1950. John Forbes Nash Jr. presented the Nash equilibrium. John Maynard Smith applied game theory to biology in the 1970s.

# What Are Mental Models?

Mental models are thinking tools that help guide and shape our perceptions of the world. They simplify complexity so we can understand life better, make decisions confidently, and solve problems.