Game theoretical approach to dating applications

Index of Contents

1. Introduction

2. Definition ofthe Problem and Assumptions

3. Derivation ofthe Problem

4. Possible Solutions
4.1. Internalization of Costs
4.2. Introduce new "types" ofmen
4.3. Market Restriction
4.4. Market design

5. Conclusion

1. Introduction

The on-going process of technological innovation and expansion combined with a more and more fast-paced, dynamic and global world result in a slow take over of computers and artificial intelligence in fundamental human task areas. One example of how technological progress invades into our daily life is the invention of dating applications that enhance the search for a possible relationship partner by providing a distinct platform for people with similar purposes.

Since the interaction on these platforms are simultaneous actions of a group of human beings that yield a specific result - getting to know possible partners - the situation can be analysed from a game theoretic perspective. During this paper I will firstly elaborate on the underlying assumptions of my model. Afterwards I am developing a formal framework that allows to explore the phenomenon from a rather objective and rational perspective. The quintessence of this setup is that the problem at hand can be identified as a repeated collective prisoners' dilemma or an example of the tragedy of commons. In a final step I will provide several possible solutions to improve the efficiency of the analysed market / social interactions. Two of these approaches are very game theoretical, while I also included two more market-oriented approaches to provide a multidimensional perspective on the issue.

2. Definition ofthe Problem and Assumptions

At the very beginning of this paper I would like to clarify that although the analytical approach of the topic may cause a very pragmatic and unemotional use of language throughout this work, I do not want to sound sexist, objectifying or differentiating regarding different genders in any way, nor would I consider myself to represent any of such values in my regular life.

The problem at hand is of following nature: We analyse the male users' behaviour in a simple dating application. The application shows profiles of users that are of the gender you are interested in and then give you the option to "like" or "dislike" each of these profiles individually. If a player shows his personal interest to get into touch with a specific person and that user responds by signalling interest ("like") as well, the two individuals have a "match" and are thereby able to text each other. Furthermore, we assume the group of players (men) to be extremely huge and that they have no possibility to directly communicate with each other.

According to several researches (Fisman et al. 2004, p. 2; Grimes 2008; Bram 2016), the male population is overrepresented in applications ofthis form. Additionally, the average active man tends to invest more time into dating apps than the average female, which leads to a very unbalanced proportion: Women receive a lot of "likes" and messages, which decreases their interest in the application and eventually makes them turn it off. This issue gets even boosted by the kind of men giving "likes" to every woman in the first place and sort out "bad" matches later (since this is a dominant strategy compared to considering every single profile in detail; in depth analysis in the next chapter). This results in a heavily inefficient market.

We assume that every user using this application is heterosexual (probably there exist different applications for different sexual orientations). In the following I will treat women's attention as a "good" that can get consumed by sending "likes". Only the male part ofthe user base is analysed as actively acting in this game, since at the status quo men tend to extremely overuse the ability to show interest. I am aware that this analysis is one-sided and not all­embracing, but as we can see throughout this paper, these assumptions help us developing a rather realistic model of our problem and search for solutions.

Furthermore, one need to mention that I assume that this game is played an infinite amount oftimes, although this is not realistically. Normally, I would need to involve a certain probability of the ending of the game after each round (finding a relationship partner) and thereafter discount the future payoffs with a given discount factor. While I take this into consideration at the development of the dynamic model (chapter 3), I ignore these factors in the later analysis.

3. Derivation ofthe Problem

The following mathematical derivations will show that although rating every woman as a possible date is rational behaviour from an individual perspective, it's neither the social nor the individual maximum that could be achieved.

Most of economic goods can be broadly classified by using the following matrix:

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Based on the assumptions mentioned in chapter 2, women's attention therefore can be classified as a Common resource for our further analysis: When person A is receiving attention of a woman, this does not exclude any other man from receiving that woman's attention. However, as stated before, we assume that too many men striving for a woman's attention lead to less interest of that woman into all men on that platform - whether they are showing interest (yet) or not. This makes women's attention rivalrous.

In the next step we will build a model (based on Diekert 2012) to show how these features lead to a tragedy of the commons of women's attention, an excessive signalling of men's interest in women.

We define the relative amount of likes that men will give the women as a:

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The relative amount of acceptances induces costs that are determined by a function c(a). Moreover, a yields an amount of matches M (depending on a and the total amount of existing women's interest on that platform, W). The amount of matches can be translated to utility by multiplying with a factor q. Since time preferences are part of human's nature, we discount the complete personal benefit exponentially at a rate r.

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I assume the amount of womens' total existing interest to be driven by a dynamic equation. Women's attention is assumed to grow naturally (absolute value), g(W), since new women might discover the application and become users - depending on the current total amount of women's interest that "exists". Therefore, the maximization above is restricted by:

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This equation simply states that if more women's interest is "consumed" than what can naturally (expanding the user base) grow, the total amount of women's interest on the platform is decreasing and vice versa. To simplify this model, we assume costs to be proportional to relative amount of acceptances and the amount of matches to be proportional to effort times a function b(W) depending on the existing stock of the resource (women's attention).

In order to solve this dynamic optimization problem in continuous time, I use the Hamiltonian function (no detailed derivation here; source of Stanford university in footnote^[1] ):

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As we can see, the function is linear in the relative amount of likes sent by men. Therefore, in order to optimize the social overall value men should send out zero likes, as long as the term in the squared brackets is negative and 100% if the value is positive. We define the optimal value of Was W*. This state occurs, when the value in the squared brackets equals zero and therefore no further optimization is possible.

In the next step, we will do a similar calculation from the perspective of an individual man. Most of the factors stay the same. However, the development of the overall amount of women's interest that exist on the platform, depends on all men using the application.

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We assume that all men have the same costs, discount rate and utility factor. As we can see from the equation above the benefits of increasing the relative amount of interests send out are private, while the effect on the total amount of existing women's interest affects all men.

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^[1] http://web.stanford.edu/~pkurlat/teaching/14%20-%20Continuous%20Time.pdf