Translating Narratives into Games

students, in game theory, one of the most important skills is turning a story into a clear strategic model 🎯. Real life is full of situations where people, companies, teams, or governments make choices while thinking about what others will do. A story might say, “Two stores are deciding whether to lower prices,” or “Two classmates are deciding whether to study together or alone.” To analyze these situations, we need to translate the narrative into a game.

By the end of this lesson, you will be able to:

Convert a story into a formal game description.
Match real-world roles to players, actions, and outcomes.
State assumptions clearly in a simple strategic model.

The main idea is this: a narrative gives you context, but a game gives you structure. Once the structure is clear, you can ask deeper questions like who benefits, who loses, and what choices each person is likely to make.

From Story to Strategy

A narrative is a description of what is happening in real life. It may include people, goals, conflicts, and possible actions. But game theory needs more than a story. It needs a model with specific parts.

A basic strategic game usually includes:

Players: the decision-makers
Actions: the choices available to each player
Payoffs: the results each player gets from each combination of choices
Information: what each player knows when making a decision
Assumptions: the simplifications we use to make the model manageable

students, think of it like turning a movie plot into a board game 🎲. The movie may have many details, but the board game only keeps the important parts that affect decision-making.

For example, imagine two food trucks at a school event. Each truck can choose a high price or a low price. The story might mention weather, student preferences, and social media buzz, but the core strategic question is about pricing. In the game model, the food trucks are the players, the price choices are the actions, and the profit each truck earns is the payoff.

A good translation keeps the key strategic conflict and removes details that do not change the main decision.

Identifying Players, Actions, and Outcomes

The first step in translating a narrative is to identify the players. Players are the decision-makers whose choices affect the outcome. They can be individuals, firms, teams, or even countries.

Ask yourself:

Who can make a choice?
Whose decision matters for the outcome?
Are there one or more decision-makers?

Now identify the actions. Actions are the available choices for each player. A player might choose to:

Buy or not buy
Cooperate or compete
Advertise or stay quiet
Study now or study later
Raise prices or keep prices low

The set of actions should be specific enough to model the situation, but simple enough to analyze.

Next, think about outcomes. Outcomes are what happens after the players choose their actions. In game theory, we often care about payoffs, which measure how much each player values each outcome. Payoffs may represent money, time saved, grades, reputation, safety, or happiness.

For example, imagine two students deciding whether to work on a group project together or separately. The players are the two students. The actions are “collaborate” and “work alone.” The outcomes depend on both students’ choices. If both collaborate, the project may improve. If one works hard and the other does not, the payoff may be uneven.

A key skill is separating the role from the person. In a model, “seller 1” and “seller 2” are roles. In real life, those roles might be two different stores, but the model focuses on their strategic positions, not their names.

Mapping Real-World Roles to Model Components

Many stories contain extra details that are not part of the game model. Your job is to map the important parts of the story to the correct model component.

Here is a simple way to do that:

| Narrative element | Game theory component |

|---|---|

| Person, company, group, country | Player |

| Choice available | Action |

| Result of choices | Outcome |

| Value of result | Payoff |

| What someone knows before choosing | Information |

| Real-world rule or limit | Assumption or constraint |

Let’s use a classic example: two coffee shops on the same street ☕. Each shop can set a high price or a low price.

The players are the two coffee shops.
The actions are high price and low price.
The outcomes are all possible price combinations.
The payoffs could be profits for each shop.
The information might be that each shop knows the other exists, but not the exact choice before deciding.

Now suppose the story says one coffee shop has a loyalty program, and the other does not. That could matter, but only if it changes the strategic choice or the payoff. If it does, include it in the model. If it does not, leave it out.

This is an important lesson in modeling: not every detail belongs in the formal game. A model is supposed to be useful, not cluttered.

Another example is a school election. Two students are running for class president. Each can campaign hard or campaign lightly. The players are the candidates, the actions are campaign levels, and the payoffs may include the chance of winning, time spent, and reputation. The voters are not necessarily players in the simplest model unless the story focuses on their strategic choices too.

Writing a Simple Formal Game Description

Once you identify the players and actions, you should write the game in a clear format. A simple description often includes:

The players
The available actions for each player
The payoff structure
Any assumptions

For example, consider this narrative:

“Two bakeries in town must choose whether to advertise heavily or advertise lightly. If both advertise heavily, they spend more money but attract more customers. If only one advertises heavily, that bakery gains more attention. If neither advertises heavily, both save money but may sell fewer items.”

A formal description could be:

Players: Bakery A and Bakery B
Actions: Heavy advertising, light advertising
Payoffs: Profit depends on the advertising choices of both bakeries
Assumptions: Each bakery chooses at the same time and cares only about profit

You can also write the action sets mathematically. If each bakery has actions $A_i = \{H, L\}$, where $H$ means heavy advertising and $L$ means light advertising, then the strategic choices can be represented compactly.

If you want to describe the payoff for Bakery A, you might write $u_A(H,L)$ to mean Bakery A’s payoff when Bakery A chooses $H$ and Bakery B chooses $L$. The symbol $u_A$ is just a label for Bakery A’s payoff function.

This kind of notation helps you move from a story to a precise model. It also makes it easier to compare different situations using the same framework.

Stating Assumptions Clearly

Assumptions are the rules and simplifications that make the model workable. In game theory, assumptions are not guesses. They are explicit statements about how the model works.

Common assumptions include:

Players are rational and try to choose the best action for themselves.
Players know the rules of the game.
Choices are made simultaneously or in a specific order.
Payoffs are based on the modeled outcomes.
Only the important strategic factors are included.

For example, if you model a price war between two stores, you might assume each store knows the possible prices and cares about profit. You might also assume the stores choose prices at the same time. If the story says one store secretly gets extra information, then the model should reflect that if the information affects decisions.

When writing assumptions, use simple and direct language. A good assumption statement is clear enough that another student can understand the model without reading the original story.

A strong assumption section might say:

Both firms choose simultaneously.
Each firm has two actions: enter or stay out.
Each firm wants to maximize expected profit.
The market demand is fixed during the decision period.

This tells the reader exactly what is included and what is left out.

Worked Example: A Team Project Choice

Let’s build a game from a story.

Story: “Two classmates, Alex and Jordan, must decide whether to divide the work evenly on a project or let one person do most of the work. If both share the work, the project is high quality and both spend moderate effort. If one person does most of the work while the other relaxes, the project may still be good, but the relaxed student benefits more. If both relax, the project is poor.”

Now translate it:

Players: Alex and Jordan
Actions: Share work evenly, relax
Outcomes: Four possible action combinations
Payoffs: Based on project quality and effort saved
Assumption: Both choose without knowing the other’s choice beforehand

We can summarize the action combinations like this:

$($Share, Share$)$: high-quality project, moderate effort for both
$($Share, Relax$)$: one student works more, the other saves effort
$($Relax, Share$)$: the reverse of the previous case
$($Relax, Relax$)$: low-quality project, little effort from both

Notice that the story does not give exact numbers. That is okay. A model can still be useful without exact numerical payoffs, as long as the ranking of outcomes is clear.

If needed, you can assign simple payoff numbers later, such as $u_A(\text{Share},\text{Share}) = 3$ and $u_A(\text{Relax},\text{Relax}) = 1$, but only if those numbers reflect the story accurately.

How to Check Your Translation

Before moving on, ask these questions:

Did I identify all the real decision-makers?
Did I leave out details that do not affect the strategic choice?
Are the actions clear and realistic?
Do the payoffs match the story?
Did I state my assumptions openly?

If the answer to any of these is no, the model may need revision.

A useful test is to explain your game to someone who has not read the story. If they can understand who the players are, what each can do, and what each wants, then your translation is probably strong.

Conclusion

students, translating narratives into games is a core skill in game theory 🔍. It helps you move from a confusing real-world story to a structured model you can analyze. The most important steps are to identify the players, list their actions, describe the payoffs, and state your assumptions clearly.

Remember that a good model is simple but not oversimplified. It keeps the strategic heart of the story and removes details that do not matter for the decision. With practice, you will get faster at seeing the game hidden inside the narrative.

Study Notes

A narrative is a story; a game is a structured model of strategic choices.
Players are the decision-makers, such as people, firms, teams, or countries.
Actions are the choices available to each player.
Payoffs measure how each player values the outcomes.
Information tells us what each player knows before choosing.
Assumptions must be stated clearly and should match the story.
Not every detail from a story belongs in the model.
A strong translation keeps the key strategic conflict and removes irrelevant details.
Use simple language first, then add notation like $A_i = \{H, L\}$ or $u_i(a_i, a_j)$ when needed.
Practice by asking: who chooses, what are the options, what happens next, and who gets what? ✅