Prisoners of Prisoner's Dilemma

Prisoner's dilemma is the Achilles heel of intelligence. It leads to intelligent agents act in a way that is suboptimal for each agent. To avoid suboptimal (sometimes disastrous) outcomes, the agents need to have a coordination authority, which is resource consuming at best and tyrannical at worst.

We are all prisoners of prisoner's dilemma.

Primer on Prisoner's Dilemma

Two persons, A and B, commit a crime together. They are kept in solitary confinement, and are not allowed to communicate to each other.

A is asked whether or not B has committed the crime, and vice versa. Thus, both A and B have an option to betray the other (by claiming that the other person has committed the crime), or to be loyal to the other (by claiming that the other person has not committed the crime). Following rules are set for deciding punishment to them:

  1. If both A and B are loyal to each other, they both get 1 year of jail.
  2. If both A and B betray each other, they both get 5 years in jail.
  3. If A betrays but B is loyal, A is set free and B gets 7 years in jail.
  4. If B betrays but A is loyal, B is set free and A gets 7 years in jail.

(Photo credit: geeksforgeeks.com)

Note that A and B are assumed to be selfish agents: they only try to maximize their individual payoffs.

Given above payoff conditions, and assuming that there are no further implications of decisions taken by A or B, it is rational for A and B to betray each other. Why? Consider from the point of view of A: A cannot control B's actions. B will either be loyal or not, and A's actions do not affect that.

Thus, it makes sense for A to betray. By same logic, it makes sense for B to betray. Thus, both A and B will betray each other, and thus end up serving 5 years in jail. Overall this is a suboptimal outcome for both of them, since by being loyal, they could have served only 1 year in jail.

In other words, in some situations, non collaborative behavior leads to inferior outcomes for each participant, but each participant is invcentized to pursue that inferior outcome.

Examples of Prisoner's dilemma in real life

Prisoner's dilemma show itself in various situations, leading to smart people being weighed down by their smartness.

Traffic jams on Indian roads

Following is a typical scene played out daily across the Indian roads:

(Photo credit: Hindustan Times)

Why does this happen? In the absence of traffic signal or signal policeman, each participant's movement is to minimize his or her own travel time. Assuming everyone else's behavior as independent of your actions, it is optimal to "betray" in the sense of pushing through your vehicle at every possibility and move forward. This leads to poor outcomes for everybody.

Should I carpool or not

I user Uber everyday to commute to office and I face a decision everyday: should I carpool or not? My objective is to minimize travel time, thus I end up not pooling.

If all the Uber users were forced to use pool, there would be lesser traffic on the roads, reducing my travel time to values lower that what it is now, despite the overhead associated with picking up and dropping off the co-passenger. But given that behavior of others is fixed for me, the optimal strategy for me is to not pool.

Arms race

Given two enemy countries, since they cannot control each other's behavior, it is optimal for each of them to spend resources in building up arms. Thus, they cannot achieve the configuration where they both are unarmed despite that being beneficial to both of them.

Is there a way out of Prisoner's dilemma?

The way to avoid prisoner's dilemma is to have superior authority with a stick: the government in most cases.

Thus the government may put traffic lights and if you disobey that, you will be fined. Government may also force me to carpool: Delhi's odd even rule was supposed to curb pollution.

The cost of maintaining such a superior authority is high: you need to have all the government apparatus and policemen and judges and regulators, and need to pay for their upkeep. They may turn corrupt and extract more than stipulated fee for their duties. In some corrupt countries, exceess of 10% of country's GDP goes to the pockets of the royal family.

But there is no way out of it: even a very corrupt government is preferable to no government at all. Thus, the way out of prisoner's dilemma is costly, and there is no choice.

Prisoner's dilemma is not something specific to Human Nature

It may be tempting from above examples to think that prisoner's dilemma is the result of human being's selfish nature: If only we were all altruistic and thought about everyone's interest rather than just our own, there would be no prisoner's dilemma.

This is not true: prisoner's dilemma is observed in other species as well. Species other than humans, which have lower intelligence, are too bound by prisoner's dilemma in their evolution path. If members of a species initially play nicely with each other, sooner or later a mutation that changes the behaviour to betrayal will emerge. That mutation will spread since it will provide survival advantage to the carrying host, and the nice members of the species will be wiped out because of lack of resources.

Prisoner's dilemma is inherent in the logic of our universe.

Is there an alternative intelligence that avoids Prisoner's dilemma?

Can there be an alien species laughing out at us as countries develop nuclear arsenals and companies engage in mutually destructive competition and Indian commuters get jammed on the roads?

Can there be an alternative universe where rules of logic do not land us in the predicament of prisoner's dilemma? Like Euclidean geometry was found to be not the only geometry possible (and thus parallel postulate need not be true), can there be an alternative logic where agents do not act to maximize their payoffs?

I have not studied logic enough to be able to answer these questions. If you know of some studies related to this, let me know in the comments.

An enjoy your stay in the prison that the world is.