Prisoner’s Dilemma in Long Term Games

Is it better to be loved or feared?

“It is better to be feared than loved, if you cannot be both” – Niccolo Machiavelli

Here is the Game Theory approach to this age long question, as exemplified by the Prisoner’s Dilemma

silhouette of a man in window
Photo by Donald Tong on Pexels.com

So the mathematical answer didn’t convince you that snitching was the best approach? Perhaps it was because you inherently understood that long term games have an effect on player behavior.

If you haven’t read my article on the basics you should check out the article first, as it is the foundation for the analysis on this one.

Basics of Game Theory

If you’ve read it, or have a general idea of the prisoner’s dilemma in general you should be able to understand what I’m talking about.

In the previous article, I mentioned two lovable criminals (Bubba and Bert) both arrested and facing charges. Their sentence would depend on their decision to either betray their partners and snitch to the police or to remain quiet. The sentences are as follows.

IF they both keep quiet, they each face a year in prison

IF they both snitch, they each face two years in prison

IF one snitches and the other doesn’t, the betraying party walks free, and their partner gets 3 years instead.

Bubba and Burt Prisioner Dilemma Image

For reasons explained in the other article the conclusion was that both of them snitching was an equilibrium, as it is both of their dominant strategy to snitch on each other, to avoid the worst fate, and have a chance at walking free.

Here is where it gets complicated.

For years, cops taking this approach noticed it was futile against organized crime.

Was the math wrong? No, but the equation was incomplete. It overlooked one major factor when it comes to criminal endeavors, and basic human behavior. That these interactions weren’t isolated incidents, but instead, part of a longer set of interconnected games.

This leads to three possible and realistic scenarios with various degrees of complexity but with two identifiable drivers of behavior.

  1. The Strangers Scenario
  2. The Lovers Scenario
  3. The Mobster Scenario

I’m going to explain the scenarios and how they may affect overall outcome of the games.

The Strangers Scenario

black and white people bar men
Photo by Gratisography on Pexels.com

Let’s pretend that Bubba and Bert did not know each other well prior to their criminal endeavor that lead to this situation. Perhaps, they were strangers at a bar that got to talking over a few beers and decided it would be a good idea to commit a crime together.

This scenario with all else being equal results in the previously mentioned solution unless the following modifiers are applied.

  • Fear of Retribution

If one of them could make a believable threat to the other, they could influence the outcome of the game.

Threats might include being part of a hardened criminal gang that will kill the other person for snitching on their members, taking personal revenge if they both end up in the same jail, threatening their families, etc.

This would allow for a strategic advantage, where one player decides to give up this game, in exchange for something greater. He might go to prison, but he’d rather be alive.

Now the player with the advantage has a choice to make, either snitch and walk free, or stay quiet for their own long term advantage. For example, maintaining their reputation in the criminal community. Two years in jail might be nothing compared to the possibility of losing all their business contacts, by which they hope to continue their way of life when they get out. i.e. their own fear of retribution.

The Lovers Scenario

affection afterglow backlit blur
Photo by luizclas on Pexels.com

Let’s suppose now that Bubba and Bert, are instead Bubba and Berta, a criminal power couple that got caught over a slight slip up on their latest adventure, and are now in police custody. Their long standing love and connection to each other affects their decision making skills for this particular scenario.

  • Love, Loyalty, and Long Hauls

This particular modifier is quite opposite of the Fear of Retribution, in the sense that each of the players are willing to cooperate with each other despite temporary setbacks to themselves. The willingness to do something at a personal expense is another known factor that affects games, as they are exclusively related to more important long term games. This effect might also be recognized in strong friendships, brand loyalties, and missionary causes.

This scenario can be seen by many types of people with strong ideals and belief systems, as they are necessary to overcome the short term setbacks for their greater cause, whether it’s love for their partner, or love for their cause, it is more important to them that they stick to their beliefs even if it means playing a non-dominant strategy. If the other player feels the same, they both win, if they don’t they are at peace with themselves anyways.

Coincidentally if one player is unsure but knows with absolute certainty that the other will not betray their own belief system, it might be reciprocated in kind to achieve the best mutual solution, and gain further long term benefits from the partnership.

The Mobster Scenario

man lights legs silhouette
Photo by Tookapic on Pexels.com

In this next scenario, let’s imagine that Bubba and Bert are in fact both members of a prominent Mafia in town. In this scenario we’re looking at the traditional mafia organization such as those in the late 19th, early 20th century, leading up to the RICO act in the early 1980s. Consequently a similar modern alternative scenario would be a modern day gang under similar country sociopolitical landscape as the United States during that era.

Feared AND Loved

Take a child in a low-income environment with no education, and little support from their society and step into their shoes for a second. Imagine the poverty, the hardships, and the relative helplessness as it may appear from their eyes. Imagine this scenario during the Great Depression, a violence ridden society, a desperately crumbling government etc.

Now at a certain age, you get approach by a close knit group that treat each other like family, provide support, resources, and opportunities previously inaccessible to you.

They treat you with the love previously unknown to you, they provide for you and your loved ones, and they accept you for who you are, instead of looking down at you like the rest of society. The trade off is only to live in accordance to their rules and contribute to their businesses.

These are the benefits that organized crime provides. Undeniably this creates a love and loyalty to the organization that most people don’t experience during their entire lives. The love and loyalty that comes from belonging to something greater than yourself.

As these gangs and mafias inevitably violently clash against the greater society, a virtue of violence gets elevated as a desirable quality, elevating the entire organization as a whole to adapt a violent culture. This creates the last piece of the puzzle. Whatever punishment they meet at the mercy of the greater society, the punishment will never be as great as the punishment they’ll receive for betraying their family.

This creates an Iron Clad incentive to never betray other players based on both willingness to cooperate to continue to reap the benefits of the organization and unwillingness to defect out of fear of the extreme punishments that will be inevitably follow.

  • The Lesser of Both Evils

Given the particulars of the situation it might be possible to overcome this Iron Clad incentive, by reversing the balance of power and modifying the payoffs.

IF by circumstance, it can be proven (or implied) that a certain member of the gang has ALREADY betrayed their family and will face extreme punishment (reversing the balance of power from a positive to a negative) and offer protections against the greater punishment (modifying the payoffs) can reverse the incentives of cooperation from Non-cooperative to Cooperative (Snitch instead of keeping quiet).

This is in fact the spirit of the Witness Protection Program, as a legislative strategy to combat and remove these criminal incentives to the benefit of the greater society as a whole.

Conclusion

The long term nature of games vastly modifies the mathematical nature of them, and should be examined not only in the context of payoffs, players, and moves, but also on time, and context. As we have seen in the article above, it is mandatory to understand these games in those context if we hope to utilize them for practical concepts.

Similarly to the Mobsters and their long term games, it is particularly important to take a look at other topics such as geopolitics, not in the context of simple games, but long term games with unchanging players, in changing environments.

In reference to the quote at the beginning of the article

“It is better to be feared than loved, if you cannot be both” – Niccolo Machiavelli

The focus of the quote for any game theorist needs to be the latter part “IF you cannot be both” which implies the ultimate goals NEEDS to be both, and only secondarily look at the other options, which would be defined by the nuances of the contexts in which the game is being played.

For questions or comments please feel free to reach out to me at Hugo@DailyGameTheory.com

%d bloggers like this:
search previous next tag category expand menu location phone mail time cart zoom edit close