Love Games: A Game-Theory Approach To Compatibility

Abstract

In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's "zerodeterminant payoff strategies" to this setting and explore the existence of such strategies and the corresponding implications for relationship dynamics.

The Level Sets of Typical Games

“…Based on his work in game theory, differential geometry, and algebraic geometry, we can be pretty sure that Nash was the first to recognize this result and therefore acknowledge it to him. 1 …”

“…It may seem counterintuitive to apply noncooperative game theory to evaluate a relationship, but many everyday decisions are made quickly according to self-interest, without cooperative discussion. In [1] we used noncooperative game theory to design a new type of compatibility test to measure the balance and overall happiness of two people in a relationship. Our test may be customized to analyze the overall balance and satisfaction in any relationship between two people, romantic or otherwise; this is discussed in [1].…”

“…In [1] we used noncooperative game theory to design a new type of compatibility test to measure the balance and overall happiness of two people in a relationship. Our test may be customized to analyze the overall balance and satisfaction in any relationship between two people, romantic or otherwise; this is discussed in [1]. If you are in a relationship, we challenge you to take this test!…”

Endless Love: On the Termination of a Playground Number Game

“…We next seek to explain this by considering the game behaviour with initial strings that are likely to appear in real games. To this end, we use lists of the 50 most popular baby boys' and girls' first names in the UK in 2010 [4] (thus presumably populating playgrounds today) 3 . The initial number strings arising from all boy-girl, boy-boy, and girl-girl pairings of these names were computed, and the magnitudes of these 'realistic' strings were compared to our findings in the previous section.…”

“…The 'LOVES' game, variously known as the 'Love Calculator', 'crush compatibility test' and others, is played in various guises in playgrounds and classrooms across the world [1,2]. The game has given rise to websites and apps peppering the web (for example, http://www.lovecalculator.com); and its whimsical nature has been cited as motivation in developing more rigorous game-theoretical approaches to assess compatibility [3]. 'LOVES' is a word-and-number game which attempts to assign a two-digit number to two character strings, by applying an iterated rule to a initial set of numbers, derived from the occurrence counts of certain letters within the strings.…”