This can be modelled as a game theoretic problem, namely the multiplayer Prisoner's Dilemma. The Prisoners Dilemma is named after a fictional story where two suspects are interrogated regarding a major crime. The police have insufficient evidence for a conviction, so they offer the prisoners separately a deal: if one confesses (defects), he goes free (temptation payoff) and the other one gets a high conviction (sucker payoff). However, if both confess, both get punished (punishment payoff). If no one confesses, both get a less severe verdict, in overall the best for everyone (reward payoff).
The following table shows the possible strategies and payoffs (exemplified with the payoffs 0,1,2,3, the higher the better):
|Prisoner B stays silent (cooperate)||Prisoner B tells (defect)|
|Prisoner A stays silent (cooperate)||(2,2) both get off with small sentence||(0,3) Player A gets punished for everything, Player B goes free|
|Prisoner A tells (defect)||(3,0) Player A goes free, Player B gets punished for everything||(1,1) both get punished|
At the pool, we have the case of a multiplayer Prisoner's Dilemma with the options to reserve a beach chair in the morning or to refrain from this behavior.
|Most others do not reserve chairs (cooperate)||Most others do reserve chairs (defect)|
|Player does not reserve chair (cooperate)||(2,2) all get a fair chance for a beach chair when needed||(0,3) player must sit on the ground, some others enjoy their reserved chairs|
|Player does reserve chair (defect)||(3,0) player has guaranteed beach chair, others are suffering slightly||(1,1) only chance to get a chair is reserving in the morning, worse situation than in upper left case|
Unfortunately, with a sufficient number of defecting players (people who reserve a beach chair early in the morning) there is no merit in not reserving - you will go without a pool chair then (sucker payoff). So the only feasible strategy is to struggle for any free one in the morning and probably get one chair reserved for your family of 4 people. Another problem is that the people are constantly changing. So even if a cooperative behavior could be agreed on, there might be the arrival of a new bunch of defectors the next day, who would then feel themselves lucky to get all the chairs they desire so easily. There is certainly a tempation to reserve if nobody reserves, because then you have your beach chair guaranteed (otherwise there is still the chance that you get none, if already more than 20 people are at the pool). So, defecting is a stable strategy, although it is in overall worse for the whole group - this a tragedy of the commons.