Tissue pack here, tissue pack there, tissue pack everywhere...

This is a summary of a project that I did with my friends Kenneth, Kenvia, James, Grace, and Geri for our Game Theory Class taken in Fall 2007.

By now, I think many of us are pretty familiar with the phenomenon of using tissue packs to reserve seats at crowded food centres during lunch hours. This phenomeon sprung up only recently and is especially pervasive in the central business district. I'm also pretty sure it's unique to us Singaporeans. In fact, my friend Kenneth notified me that the Coxford Singlish Dictionary has listed this behaviour as one of the things that make us uniquely Singaporean.

At the start of the term when we first got together as a group, we were not sure if this topic was worth exploring, but what made up our minds was a group of office workers (presumably from nearby NTUC) who dropped by our basement Kopitiam for lunch. They came to the table next to ours, and all 6 of them each dropped a pack a tissue paper on the table, forming a beautiful formation of tissue packs, and then proceeded to order their food. When we saw that, that was it for us! We were gonna try and explain this uniquely Singaporean behaviour using a game-theoretic approach.

My group and I thought that this social behaviour can be explained by what ethologists call the Hawk-Dove game. This is a variation of the game of chicken in game theory. Hawks are aggresive individuals who will always fight for a valuable resource and Doves will never fight but display itself in a conflict. A Hawk meeting another Hawk will fight for the resource and the winner will get the resource, whereas a Hawk meeting a Dove will always win the resource. A Dove meeting another Dove will have a one-half probability of getting the resource.
One important assumption must be highlighted here, i.e.
1) The value of the resource is less than the cost of fighting
This means that it will be much better to give up the resource than to fight and risk injury.

Back to our tissue pack scenario, imagine an instance whereby 2 strangers in a crowded food centre, who happen to arrive at an empty table at the same time. Each believes the she has a right to the table. Ignoring altruism, how do we decide who gets the table? If both individuals are Hawks, we will have a fight on our hands. In the absence of a social mechanism to assign property rights to individuals, this is exactly what happens.

In any population, we cannot have a single type of individual i.e. only Hawk or Dove. Dixit and Skeath (2004) explains this rather amusingly with their example. If a population were to be populated with Wimps (Doves) only, then a Macho (Hawk) newcomer will successfully invade bcos he can impress the girls. On the other hand, if a population were to consist only of Machos (Hawks), then they are gonna be in the hospital all the time and the girls will as a result have to go for the healthy Wimps (Doves). Therefore we should expect to see a mixture of both types in the population with each playing a pure strategy Hawk or Dove. This mixture is known as an evolutionary stable strategy (ESS).

Problem is, despite being stable, this outcome is not exactly efficient, because instances of conflicts still arise when Hawks meet Hawks or when Hawks meet Doves. But consider if someone starts to use something (in this case a tissue pack) as a symbol of territory ownership and others slowly start to acknowledge this symbol. Then we have what is called a labelling asymmetry where individuals can be seen as possessor or non-possessor of a resource. The person who puts a tissue pack at the table is marking her territory! With this labelling asymmetry, possessors will gravitate towards playing Hawk invariably and non-possessors will gravitate towards playing Dove invariably. It makes intuitive sense, since if you believe you are the possessor, you will more likely play Hawk to defend your resource. We now have a different game where people tell themselves "If possessor, play Hawk; if non-possessor play Dove" This new strategy now becomes the ESS. According to economist Robert Sugden, this is also called a spontaneous order/convention.

Interested readers on related topics of social evolution can check out Sugden's book: "The Economics of Rights, Cooperation and Welfare". I got most of the material from there.