Anya Zhang and Galen Lee
Launched in 2012, Tinder is a location-based dating app with an estimated 50 million users. Users are shown the profiles of other users who match certain criteria (eg. gender, age range, location) and are given the option to either swipe right to indicate interest or left otherwise. If two users swipe on each other, a "match" occurs, and they are able to enter into conversation. Although users are able to display many types of information, such as occupation, a bio, top Spotify artists, and social media accounts, Tinder users empirically base the majority of the decision whether or not to swipe based on the appeal of displayed photos, which also take up the majority of real estate onscreen.
Although Tinder exhibits several features linked to concepts we’ve studied this semester, such as information elicitation and recommender systems, we decided it was best modeled as an example of a reputation system where users essentially give feedback about the quality of each other’s profiles, which the app uses to suggest new matches in the manner of a centralized rather than decentralized market. The app thus broadly satisfies the three requirements of a well-functioning reputation system: 1. Useful reports from participants, and a centralized system that 2. interprets others’ reputation information to help participants make decisions and 3. changes the action set of participants based on their own reputation.
Before defining the reputation game, we begin with assumptions used to create our model. First and most importantly, we define each user by two variables: The first is their physical attractiveness or “rating" = (r) on a scale from 0.0 to 5.0, inspired by Tinder’s underlying mechanism. The second which we introduce ourselves is the notion of “pickiness" = (p), or the minimum rating needed by any other user to merit a right swipe. These two factors are not entirely independent - we assume in addition that (p) is within the range ([r - 1.5, r + 1.5]). These values are taken as immutable truths for each user. Thus, given an interaction between any pair of users (i,j), we only need to compare (i)’s pickiness and (j)’s rating to determine (i)’s swipe behavior, and vice versa. For example, if (i) has a pickiness of 3.4, (i) will swipe right on (j) if and only if (j) has a minimum rating of 3.4. Whether (j) also swipes right on (i) is determined independently (with the above caveat) by (j)’s pickiness and (i)’s rating.
Based on these assumptions, we can fit Tinder nicely into the reputation game model based on the repeated Prisoner’s Dilemma for peer-to-peer markets. Payoffs to each user (i) for an interaction with user (j) depend on whether each of them cooperate (swipe right) or defect (swipe left). The normal-form representation of this utility function is shown in the table below:
Importantly, utility is also affected by the actual values of (r) and (p). If (i) and (j) match, (i)’s utility begins at 1 and is improved by the amount by which (j)’s rating exceeds (i)’s expectations. Similarly, if (i) matches (j) but (j) doesn’t match (i) back, (i)’s utility begins at -1 and is improved by the same amount up to 0. If (j) matches (i) but (i) doesn’t match back, we assume that this boosts (i)’s ego by a small amount and increases his/her utility by 0.5 [1]. If neither swipes on each other, utility is 0 for both.
Thus, our goal for this project was to create a model of Tinder that would simulate real-world user behavior based on the two variables, accurately predict values for those variables from an app perspective, and create a "deck" of candidates for users in a way that would maximize their utility. Ideally, we would also want to show that our mechanism incentivized truthful behavior.
For the sake of simplicity, rather than having a simulation that calculated utilities and updated predictions simultaneously as Tinder likely does for new users, we split the process into two distinct section - one to train predictions, and one to use the results of our predictions to calculate utilities.
We ran the training section in “rounds", randomly assigning each user a single candidate for matching so that all user’s predictions would update at more or less the same speed. The only constraint was that each candidate could only be assigned to a user at most once (which we maintained using the “seen" set), to avoid overfitting effects, although the same candidate could be assigned to multiple users during a single round. (Thus, the number of prediction rounds was by necessity limited to the number of users). Using the results of swipes based on comparing true values for ratings and pickiness in each round, we trained our predictions for user rating and pickiness with the following code:
def train(self, other, discount):
diff = abs(self.p_hat - other.r_hat)
self_diff = max(diff, 1) * self.delta
other_diff = max(diff, 1) * other.delta
if self.p <= other.r and self.p_hat > other.r_hat:
self.p_hat = round(max(self.p_hat - self_diff, 0.0), 2)
other.r_hat = round(min(other.r_hat + other_diff, 5.0), 2)
elif self.p > other.r and self.p_hat <= other.r_hat:
self.p_hat = round(min(self.p_hat + self_diff, 5.0), 2)
other.r_hat = round(max(other.r_hat - other_diff, 0.0), 2)
self.delta = self.delta * discount
other.delta = other.delta * discount
return
In other words, if our prediction matched the expected outcome, we
changed nothing. However, if (i) swiped right on (j)
((p_i \leq r_j)) but we’d predicted that (i) would swipe left on
(j) ((\hat{p_i} > \hat{r_j})), we would decrease (\hat{p_i}) by a
small amount and increase (\hat{r_j}) by a small amount. small amount
was determined by the magnitude of difference (
(|\hat{p_i} > \hat{r_j}|)), multiplied by delta, a factor that began
at 1.0 and slowly decreased by a factor of discount every round that
the parameter was used. We defined discount in tinder.py by
calculating the necessary value for it to begin at 1.0 and get to 0.1 by
the time we had finished predictions, leading it to converge at a
reasonable value. Since the expected number of times for a user’s
predictions to be adjusted was twice the number of rounds (any user
would show up once per round by default and another expected one time as
a candidate for another user), this was defined as discount =
(0.1^{1/(2 \times \text{rounds})}).
In the second section, we showed each user only the filtered candidates who, by our predictions, would create stable matches with them (where intuitively, a stable match between two users is one where each user has a rating that is higher than the other user’s pickiness). As before, each user’s real-world swipe behavior and utility was still computed using true values - predictions were used only to create the candidate list. In addition, we limited each user to 50 right swipes (similar to Tinder’s daily limit) in order to incentivize better matches (which gives more utility per match) in addition to raw number of matches. Finally, we ranked the results in order of increasing user utility.
Importantly, as can be seen from the equations, a user’s behavior cannot change her own rating, only her pickiness. Her pickiness is used to determine which users to display to her, while her rating is used to determine whether she should be displayed to others. Thus, in a consideration of the strategy-proofness of the mechanism, it suffices to show that pickiness is strategy-proof.
To test the accuracy of predictions, we ran this algorithm ten times and took the average RMSE over the trials. By adjusting the following values in addition to the algorithm outlined above, we managed to get RMSE for 300 users to a consistent (\sim 0.12) for both (\hat{p}) and (\hat{r}):
-
initial value of
delta(1.0) -
value for
discountto converge to (0.1) -
number of prediction rounds (250)
Additionally, we observed that the type of user that tended to do well under our mechanism had high enough ratings to get many right swipes from other users, but not so high that they were too picky. However, the less picky they were, the more utility they would also get from having their expectations exceeded most of the time. Thus, typical high-ranking users had ratings near 3.8-4.1 and minimum pickinesses for their ratings, around 3.3-3.6. By adjusting the values for number of right swipes and utility, the results could easily be manipulated to prioritize any type of strategy, suggesting that more testing would help determine an optimal approach from an app perspective. Given more time, we’d also want to test to see whether reporting a different pickiness (i.e. behaving in accordance to a different reported (p), but calculating utilities using a true (p)) would benefit users and attempt to design a mechanism to incentivize truthful behavior.
- Although normally a user who swipes left on another user can’t tell what their response is, under conditions like “superlikes", a user can see up front whether the other has liked them and can still choose to swipe left, presumably increasing their utility by a small amount