Charting the Shapes of Stories with Game Theory

TL;DR

The paper proposes a framework to convert narratives into extensive-form games by extracting decisions and payoffs with AI, allowing formal game-theoretic analysis of the plot. It introduces the idea of a 'rationalizes' relationship between a story path and a game equilibrium, and demonstrates this on Romeo and Juliet using LLM-assisted construction and Gambit solving to compare alternative game trees. The work connects narrative dynamics to equilibrium-based fortune, suspense, and counterfactuals, and discusses potential real-world applications and limitations. It lays out a scalable pipeline for analyzing stories and other narratives, with future work aimed at broader genres and more robust evaluation.

Abstract

Stories are records of our experiences and their analysis reveals insights into the nature of being human. Successful analyses are often interdisciplinary, leveraging mathematical tools to extract structure from stories and insights from structure. Historically, these tools have been restricted to one dimensional charts and dynamic social networks; however, modern AI offers the possibility of identifying more fully the plot structure, character incentives, and, importantly, counterfactual plot lines that the story could have taken but did not take. In this work, we use AI to model the structure of stories as game-theoretic objects, amenable to quantitative analysis. This allows us to not only interrogate each character's decision making, but also possibly peer into the original author's conception of the characters' world. We demonstrate our proposed technique on Shakespeare's famous Romeo and Juliet. We conclude with a discussion of how our analysis could be replicated in broader contexts, including real-life scenarios.

Figures (2)

• Figure 1: The game trees constructed with the assistance of Gemini for the final plot twists at the end of Romeo and Juliet. We consider both Game i@ rooted to the right of the purple boundary (the red node (B) highlighted in green) and Game ii@ rooted just left of it (the chance node (A) highlighted in yellow). The Nash equilibrium (specifically, limiting logit equilibrium) of Game ii@ is denoted by the yellow arrows at decision nodes; all strategies at each decision node are deterministic except for Juliet's first decision which flips a fair coin when determining whether to marry Paris or fake her own death. For Game i@, the equilibrium strategies are all deterministic and denoted by green arrows. The loop encircling the three blue nodes indicates that these states (histories) appear exactly the same to Romeo; Romeo cannot differentiate between whether or not Juliet has actually died.
• Figure 2: Shape of a Game: The design of the game tree can have a dramatic impact on the shape of the resulting story. (\ref{['fig:shape:small']}) Game i@ has zero surprise (fluctuations in value function) and zero suspense (variance of value function) as it always results in a happy ending (I/J). (\ref{['fig:shape:big']}) Adding a chance node and decision node to Game i@ results in Game ii@ and gives the story shape; the martingale of the Romeo and Juliet plot under Game ii@ has both high surprise (large changes in both characters' values after Juliet is overcome with grief at the root node and when the message fails to reach Romeo) and high suspense (high variance of the character's value functions at Juliet's decision to fake her death as well as nature's choice of whether the message successfully reaches Romeo). (\ref{['fig:shape:big_b']}) Contrast this with the lack of shape of the story given by the alternate ending where Juliet randomly selects to marry Paris. Shakespeare selects the most interesting story from the behaviors that are rationalizable.