Jane Austen as a Game Theorist: Reconsidering Pride and Prejudice

Jane Austen’s characters may first conjure up images of joyous young ladies and gentlemen in a countra-dance ballroom. Whilst this was my original impression shaped by fictions including Pride and Prejudice, I soon became further intrigued by the potential for interdisciplinary learning. This Exploration Project marries my passions for Literature and Mathematics, and triggers my interest in using statistics to solve real-life conundrums as I am determined to continue my application of Mathematics in other academic subjects.

Last summer, I was fortunate to attend a summer program that focused on History, Political Philosophy, Economics and Law, at Yale University. There, I discovered my profound interest in all those disciplines, and met fantastic intellectuals including PBS News Hour host Paul Solman. As I embarked on my Exploration Project, I spent days at the Hong Kong University Library until I came across the title, ‘Jane Austen, Game Theorist’. I was exhilarated to find that Mr. Solman interviewed the author, Professor Michael Suk Young Chwe only a few months ago, and immediately fell in love with Professor Chwe’s discussion of various aspects of Game Theory in Austen’s novels, including her foundation of Game Theory, Competing Models, Strategic Thinking, Innovations, Criticisms, Intensions, ‘and Cluelessness’. I discovered the book’s incredible scope of influence in the academia since its publication earlier this year [2013].

Having always adored the intelligently arranged marital networks between Austen’s characters, I base this investigation on my favourite Austen novel, Pride and Prejudice, in which the initially conflicting pride of Mr. Darcy and scathing prejudice of Elizabeth (‘Lizzy’) Bennet becomes conciliated as the two become overruled by the power of love. This novel provides a myriad of aspects worthy of investigation using Game Theory, since its plot involves several key characters whose apparently complex relationships can be mapped out clearly using tools I acquired in my Mathematics course, including tree diagrams, Bayes’ Theorem, and matrices.

Austen’s Application of Game Theory in Pride and Prejudice

Bayes’ Theorem is a method to determine the probability of an event occurring. Applying Bayes' theorem often involves the use of tree diagrams, a link to Game Theory. I will apply Game Theory as a model that involves both Bayes’ Theorem and tree diagrams to guide me in analyzing the probability of the outcome of Pride and Prejudice (that Elizabeth and Mr. Darcy marry).

As a starting point, I tried to brainstorm the explicit and implicit aspects of interpersonal relationships in Pride and Prejudice, that can be modeled by Game Theory—

EXPLICIT: love triangles; marriage proposals; gossip triangle

IMPLICIT: Elizabeth and Darcy’s respective relationship with Caroline Bingley sacrifices original perceptions; Mr. Darcy’s Pride and Elizabeth’s Prejudice change over time

The model of game theory is used to visually present the probabilities involved in the situations.  Later, based on further research on cooperative and non-cooperative models, I narrowed down my topic. Initially, the marital relationship between Elizabeth and Mr. Darcy seems impossible: Darcy fancies Elizabeth, surely, but is too proud to propose, while Elizabeth is so blinded by prejudice that she could not see any positive attributes of Darcy. At this point, Caroline Bingly serves as a competitor for Elizabeth who sets the ‘game’ as a zero-sum, non-cooperative game. Caroline gossips about Elizabeth and her family in front of Darcy, and tries to win Darcy’s affection.

*The heavily mathematics-related parts of this project will be omitted in this blog post.

As the plot progresses, the game interestingly becomes a cooperative game whether the characters intentionally cooperate or not. Mrs. Bennet, the matchmaker, first helps Mr. Collins win Elizabeth, but fails; then, Mrs. Bennet cooperates with Jane’s natural beauty to win Mr. Bingley, but fails once again. Nevertheless, the Bennet’s do famously turn out quite well, i.e. wins ‘the game’ in some ways. How? In terms of Elizabeth and Jane, the pair of affectionate, loving sisters, they cooperate to ensure that each other feels happy no matter what the circumstance of suitors are. More significantly, somewhat unwittingly, Elizabeth cooperates with Darcy to eventually accept his proposal. When Elizabeth rejects Darcy’s first haughty proposal, she clearly stated the reasons for denying him. Unintentionally, Lizzy turns the game into a ‘two-person cooperative game’, which John Nash discusses in his ‘Essays on Game Theory’.

Nash’s work is beyond my Mathematics Syllabus, but the geometrical representation, especially the intersection, inspired me to consider that the novel has reached a turning point where a non-cooperative game has transformed into a cooperative one, as Darcy, enlightened, is then determined to clarify those accusations to his advantage, and takes actions including paying for Lydia’s marriage to secure Elizabeth’s trust. Without this cooperation, the game would have ended up failing. There are thus so many cooperations and non-cooperations that enables Austen’s Pride and Prejudice to conclude the way it does. This makes me wonder, mathematically, what is the probability that Elizabeth and Darcy do win the game by overcoming all the implicit and explicit, internal and external obstacles to their marriage, their pride and prejudice, to enter into the holy estate of matrimony? Bayes’ Theorem and decision trees come in here. A tree diagram that represents all the possibilities that the marriage would or would not have been possible is used in this project. 

Based on a quantitative analysis of the times that key words, such as ‘propose’ and ‘not propose’ are mentioned, I have refined the diagram with probability values.

From this point, I begin to apply Bayes’ theorem step by step, to find out the possibility that the final outcome is, mathematically, as it is known to the world.

To analyse literature in a more comprehensive way, I composed a mathematical problem that involve ‘given-that’ situations as extensions to this exploration. These types of analysis rely heavily on Bayes’ Theorem. Undertaking this project has enabled me to further my realization of the function of Bayes’ Theorem across academic disciplines.

Question: On the premise that Darcy does propose and Elizabeth does reject him in the first place, use Bayes theorem to calculate the probability that,

a. Mr. Darcy will change his behaviours that Elizabeth loathes;

b. Elizabeth has clarified the situation given that Mr. Darcy will change his behaviours that Elizabeth loathes;

c. Draw a conclusion that relates back to Jane Austen as a game theorist.

SOLUTION:

a. Omitted in this blog post.

b. Omitted in this blog post.

c. Clearly, if Elizabeth clarifies the reasons for discarding Mr. Darcy’s proposal, then the probability that Darcy changes will be much greater, as Austen arranges the plot in Pride and Prejudice. By applying Bayes’ theorem, we are clearly convinced of such a point, and potentially would believe in Jane Austen’s game-theoretic arrangements in the novel.

Reflection

In conclusion, Pride and Prejudice is abundant of evidence that its interpersonal relationships closely relate to a game-theoretical mathematical model that can be calculated and analysed.

This project has enabled me to experience the usefulness of Mathematics in relation to another academic discipline (Literature) that involve a different historical period, and cultural context. Amid the debate surrounding Michael Chwe’s nonfiction, I have, through research, mathematical exploration, and evaluation, made up my mind that Jane Austen is a game theorist, although it is not certain to what extent she was intentional. 

This is a very exciting finding for me, because Austen, although from such a different academic field and historical context long before mathematicians like John Nash and von Neumann formalised Game Theory in Mathematics, had already applied the basic principles of Game Theory. The conclusion triggers many Theory of Knowledge-related thoughts, such as ‘is a mathematical principle, truth or knowledge in the broader sense, found or invented?’, and ‘How can we label some writings a work of ‘Literature’, and others, mainly ‘General Fiction’?’ My response to the former, after I undertook this project, would be ‘found’, because some principles seem to exist subconsciously inside our minds for centuries, until mathematicians formally listed them as principles and used Mathematics to form equations; to the latter question, my reason that is specific to Austen would be the careful crafting that could resemble a game-theoretical model.

When applying Bayes’ Theorem, I found that while it is certainly useful, the theory also has potential drawbacks / limitations, and so does the project as a whole. Here are some major points,

A pre-condition for applying Bayes’ Theorem is an informal estimation of prior probabilities;

The conclusions may thus be mathematically inaccurate and unreliable to a certain extent, since the pre-conditions may not be perfectly quantised or modelled;

Literature may not be quantised perfectly, demonstrating that Mathematics is not a fully omnipotent tool that can analyse all cross-discipline subject matters;

Our informal rationality is relied upon when using Bayes’ theorem to solve mathematical problems or to analyse circumstances.

My project has inspired me to apply Mathematical theories and principles to real life situations more. It has been a very enjoyable learning process, within which I have overcome many difficulties, such as the scarcity of sources on my specific topic. This exploration has triggered me to initiate more projects that link my interest for different subjects together.

BIBLIOGRAPHY

Chwe, Michael. "Gaming Mr. Darcy: What Jane Austen Teaches Us About Economics." PBS. PBS, 10 July 2013. Web. 2 Jan. 2014. <>.

Chwe, Michael Suk. Jane Austen, game theorist. New Jersey and Oxford: Princeton University Press, 2013. Print.

"Economics, Game Theory and Jane Austen." PBS. PBS, n.d. Web. 2 Jan. 2014. <>.

Hodgson, David. Rationality + consciousness = free will. New York: Oxford University Press, 2012. Print.

Kolokolʹt︠s︡ov, V. N., and O. A. Malafeev. Understanding game theory: introduction to the analysis of many agent systems with competition and cooperation. Singapore: World Scientific, 2010. Print.

Mullan, John. "Jane Austen, Game Theorist by Michael Suk-Young Chwe – review." The Guardian. Guardian News and Media, 15 June 2013. Web. 2 Jan. 2014. <>.

Nash, John F.. Essays on game theory. Cheltenham [England: E. Elgar, 1996. Print.

Owen, John. Mathematics for the international student: mathematics HL (Core). Adelaide: Haese & Harris, 2004. Print.

Sprinz, Detlef F., and Yael Nahmias. Models, numbers, and cases: methods for studying international relations. Ann Arbor: University of Michigan Press, 2004. Print.

Freakonomics RSS. N.p., n.d. Web. 2 Jan. 2014. <>.

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