The volunteers’ dilemma game models a situation in which each player can either make a small sacrifice that benefits everybody or instead wait in the hope of benefiting from someone else’s sacrifice.
An example could be: you see a person dying and can decide whether to call an ambulance or not. You prefer that someone else call but if no one else would, you would strongly prefer calling over not calling and the person being dead. So if it is just you watching the person die, you would call the ambulance given these payoffs.
There are as many pure strategy Nash equilibria in this game as there are players, a “player x calls ambulance, everyone else does not” for every x. There’s also a symmetric mixed strategy Nash equilibrium where every player has the same probability p of calling the police.
The fun part is that as the number of bystanders goes up, not only does your own probability of calling go down but also at equilibrium, the combined probability that anyone at all would call the ambulance also goes down. The person is more likely to die if there are more observers around, assuming everyone is playing optimally.
One implication of this is that if you have a team of people, unless you try to assign specific individuals to take charge of specific tasks, you might end up in situations where the probability of tasks happening at all decreases as you add more people (everyone feels like it’s less their responsibility to take care of any particular ball).
The volunteers’ dilemma game models a situation in which each player can either make a small sacrifice that benefits everybody or instead wait in the hope of benefiting from someone else’s sacrifice.
An example could be: you see a person dying and can decide whether to call an ambulance or not. You prefer that someone else call but if no one else would, you would strongly prefer calling over not calling and the person being dead. So if it is just you watching the person die, you would call the ambulance given these payoffs.
There are as many pure strategy Nash equilibria in this game as there are players, a “player x calls ambulance, everyone else does not” for every x. There’s also a symmetric mixed strategy Nash equilibrium where every player has the same probability p of calling the police.
The fun part is that as the number of bystanders goes up, not only does your own probability of calling go down but also at equilibrium, the combined probability that anyone at all would call the ambulance also goes down. The person is more likely to die if there are more observers around, assuming everyone is playing optimally.
One implication of this is that if you have a team of people, unless you try to assign specific individuals to take charge of specific tasks, you might end up in situations where the probability of tasks happening at all decreases as you add more people (everyone feels like it’s less their responsibility to take care of any particular ball).