Part one: Queues?
Everyone hates waiting in line. Waiting in line is on of the most obnoxious process present in everyday life. Given the individual costs that waiting incurs in people, it is no surprise that one of the greatest public enemies in the world are queue cutters. However, what if I told you that, at least in theory, allowing queue cutting might improve the waiting experience of everyone involved in the line; not just the person cutting. The importance of the study is to improve the lives of every person who has to routinely wait in line in a cafeteria, food court, banks, and even public bathrooms by presenting a contrarian idea that refutes one of the most basic social systems present in society today.
My work builds upon Allon’s, and Hannay’s (2012) article “Cutting in Line: Social Norms in Queues” which is based on game theory and economical assumptions to create a hypothesis that rational consumers can accept a flexible queuing system that goes against common queuing etiquette. The main assumption of this research is that people will let others cut in line expecting that they will be able to do the same when they are presented with a rush. The purpose of this project is the analyse the central idea behind Allon and Hannay’s article in a real life scenario to see if the expected consumer behaviour matches the real life actions of people waiting in line. The goal of this paper is to test a theory that might improve the waiting experience of people, reduce the cognitive stress, and create a more comprehensive society where time is valued and time is allocated more efficiently.
What are Queues in the first place?
Waiting lines are multifaceted social phenomenons that reflect various priorities in society. On one side, queues are social contracts that reflects the societal compromise for fairness and order over efficiency. Upon a more empirical analysis, however, queues also represent an interesting type of market failure. From an economics perspective queues should not even exist in the first place. When there are supply or demand shocks, markets traditionally respond with an shift in prices. Still, when shocks are momentarily, society rejects such shifts in price on the bases of fairness.
Fun Fact: Humans secretly love waiting lines. Don’t believe me? Imagine you have to choose between 2 restaurants. One has a 45 minute waiting list with a lot of people waiting outside. The other empty, not a single soul inside. Most commonly people see queues as a sign of quality and of popular preference.
Part Two: Not All Queues are Created Equal
Lets be real. Improving the waiting experience by allowing line cutting is an idea so counter intuitive it is almost silly. Indeed, line cutting will not help all queues. Only a very specific queuing model could benefit from having a cutting flexible system. But which kind of lines? Here is where the Game Theory comes into play. According to Allon and Hanary (2012) only queues that have a Repeated Game characteristics could be benefited from queue cutting. Repreated games are games that players get to play a lot of times. What this means is that only queues that are done regularly by players can welcome a flexible system.
Waiting lines at Disney Land (Single-stage game)
Single-Stage Games Lines Vs. Repeated Game Lines
It is OK to be mad at someone who cuts in line for a Disney Land ride. That line is a once in a lifetime occurrence. One does not usually go to disneyland very often, lines are huge, and thus the cost of waiting is high. The same applies to lines for concert tickets or the new iPhone. One will not let others cut because it is a line that is done once or twice in a lifetime. However, one is more likely to let someone cut in line if it is a line one does regularly due to the expectation of being able to do the same if you are in a rush in the future.
Part 3: To cut or Not to Cut… That is the Queuestion
Now, lets build a model for a repeated game line that allows queue cutting.
Like in any game theory model we will asume certain things about the players. Here are some of the most important assumtions in this model:
- Players are rational. This means that players want to do whats best for them always.
- Players are altruistic to some extent. This means that under the right circumstances players can get utility by helping others.
- Players account for future scenarios in a repeated game structure. This means that people think strategically about the future in order to decide how to act in the present.
Now, onto the actual strategies. Player one is someone who is just arriving to a repeated game. Player one has to decide either to cut in line or not to cut in line. This decision is taken based on a couple of factors that overall weight either for or against cutting. This factors can all be broken down into include: Time constraints vs. Social Pressure. When cutting in line one has to decide weather the saved time is worth the awkward glance of people who just wasted more time of their life in line because of one’s intrusion.
Player 2 on the other hand has to decide weather to let the person cut in line or not. The factors that determine Player 2’s judgement are mainly Time constraint Vs. Future Expectation. Basically he (or she) has to decide if she has enough time to let the cutter in front, while being empathetic about how one might be in the same position in the future. Furthermore, we assume that being kind to others delivers some sort of satisfaction which can also be taken into account in the decision making process of Player 2.
Now lets see how this strategies look in a matrix.
The numbers represent utils. Utils are a (kind of ambigous) unit of measurement economists like to use to measure utility. Utility is a fancy Econ lingo that basically means satisfaction. The more utils one gets the more happy one is.
|Players||Player||Two||People in Line|
|Player||Strategies||Reject Cutters||Allow cutter|
|one||Cut in Line||(-2,0) Player one is faced with a very uncomfortable “defeat” P2 is left unaffected||(5,2) If Player one is allowed to cut, he will maximise his utility because he is basically saving all the cognitive stress and time lost caused by waiting. P2 gains some utility due to the expectation of being able to cut in the future|
|Person with a genuine rush||Join the Back of the line||(-1,0) P1 is affected since he is in a rush but did not cut in line. P2 is unaffected||(0.1) by not cutting in line P1 us unaffected. However, by having being able to let others cut in line, P2 has a consumer surplus of one caused by not having to let others cut when he could have afford it.|
The most important aspect of any game is equilibrium. Nash Equilibrium is a mix of strategies where no player has an incentive to deviate from their choice. Pareto’s optimality is an outcome where the most utility as an aggregate (not as individual players) is gained. In this case both Pareto’s optimality and the Nash equilibrium is achieved when someone in a rush cuts and when the person in line lets him cut.
Part 4: Enough Theory, Lets try it!
With the help of my high school cafeteria I was able to implement a cutting flexible queueing system during lunch. I placed a Surveying machine called a HappyOrNot Smiley terminal to see if the waiting experience improved from a week with normal fist come first served norms to a week with a cutting flexible system. The machine, like the one in the imaged below, asked students to rate their waiting experience.
From the control week to the cutting flexible week there was a slight improvement in the waiting experience. The following pie charts depict the distribution of responses. Dark green represented a mood of very happy, light green represented mild satisfaction, light red represented mildly disappointed, and dark red represented very disappointed.
Qualitative Observations:The cutting flexible queuing system was able to maintain a state of equilibria where norms and order of the mechanism was maintained. According to the staff of the cafeteria, the frequency of queue cutting did not increase even after several bright colour posters stating that queue cutting was allowed where placed all around the premise. An alternative hypothesis is that the social cost of cutting in front of known people is higher than the benefit gained from saving time while cutting. The social pressure inquired by cutting in front of acquaintances might prevent people from cutting in line even if queue cutting is allowed.
Part 5: In Conclusion:
While the observed improvement in waiting experience was very small, I believe that this opens the conversation into allowing queue cutting in places where a minority of people can be benefited from it. The fact that the experiment recorded a social equilibrium that maintained control shows that the cultural norms make enough pressure to allow for the implementation of this systems without fear of creating chaos. This systems are meant to help everyone who needs to cut in line for some reason or another, and while it is indeed the minority who ultimately decides to cut, that minority might include almost anyone.