The Game of Life

Let's dive into some theory with Math again. Why? Because it is universally applicable! (If you are able to see beyond)

I remember studying Game theory at university years ago. Of course, it had to do little with models and applications and much to do with 50% of the class scared of getting a bad grade and screwing their stipend, 10% of the people being into some hardcore theoretical mathematics and the rest of us (~40%), just ditching the class in order to actually do some real world projects.

I remember reading up the textbook (cover-to-cover, this is the only way I can read anything) and the only thing which particularly interested me were the Markov chains (though, Hidden Markov Models were not mentioned) and the Nash equilibrium. This was back then when John Nash was still alive. He has a led a truly spectacular scientific live, including first being diagnosed with Paranoid schizophrenia and then winning the Nobel prize for Economics. Now, that's something literally crazy, ain't it?

Anyways, from scientific point of view, the works of Nash are equally amazing. Formally defined, the Nash equilibrium can be summarized as:

A "Nash equilibrium" is a set of strategies, one for each player, such that no player would benefit if they change their own strategy, provided that the opponents' strategy remains known to them.

Basically, it's an optimal state where everyone is doing well and everyone is happy. Examples for "Nash equilibrium" cases would be the traffic rules: Everyone has interest to abide by the rules, because doing so guarantees that you will be safe at the road, because others also respect the rules.

Sounds simple but it's so hard to do.

The nature of life is, we are always competing to achieve the best result (most money, highest social status, best relationships with others) in as little time as possible. Supposedly, one is able to rob a bank and get rich quickly, however the same person can quickly realize that has reduced greatly his ability to live a normal life (due to hiding and enormous efforts to launder the money) and he can even get jailed! Considering the other alternative of becoming an entrepreneur, going through the same amount of risky situations in order to get almost the same amount of money. Or an "equilibrium" version in which one is to get a stable job and stack their savings with stocks and bonds while slowly becoming affluent. Which of these scenarios would be most beneficial to the individual? Which one would benefit the society the most?

Good thing is, the Game theory (branch of Mathematics which deals with modeling competitive situations between adversaries) is great at modeling similar situations.
If you are dealing with management and people, this can sometimes come in handy. I am not talking about creating formulas for your life but rather getting inspiration from proven mathematical - and as we will see later - evolutionary biology models.

Prisoner's dilemma:
The Prisoner's dilemma is one of the classical competitive game models.

The rules are simple: two prisoners, who have escaped from the prison are captured and tortured with the following possible scenarios:
1. Cooperation: If both admit, that they are guilty, they receive a very reduced sentence.
2. Non-cooperation: If both blame the other person for the crime, they both receive a much harsher sentence.
3. Ratting out the other person: If one blames the other, and the other admits, the first prisoner is released and the second serves a sentence.

I will call them "players", rather than prisoners. We can model the above scenarios the following scores for Player A and Player B:


















NoStrategyScore
1Cooperation between between player A and player B+5 points for both players
2Cheating: Player A screws Player B+10 points for Player A and -10 points for Player B
3Cheating: Player B screws Player A-10 points for Player A and +10 points for Player B
4Non-cooperation between players-20 points for both players

Basically, you get the most points if you screw the other person. You get some mediocre results if you decide to play it nice. You both lose some points if you rat each other. And if you end up being taken advantage of, you lose greatly. We're often taught that this it's sort of "impossible" to come up with a good strategy for Prisoner's dilemma. I've just recently found that there are very easy and practical strategies for doing well if someone is to face the Prisoner's dilemma.

Robert Sapolsky who teaches neurology at Stanford University suggests that after an extensive study has been carried out on different strategies between players facing the dilemma, one winning strategy to win the most points in long term is the "Tit for tat" strategy.

Tit for tat strategy:
In this strategy, every round the action of the player reflects the action of the opponent. If the opponent cooperates, the player cooperates. If the opponent screws the player, the player also screws the opponent. And if the opponent goes back to being cooperative, the player does the same thing.
This strategy prevents the player of losing the game, because it implies instant retaliation upon detection that the opponent attempts to cheat the player.

Forgiving tit for tat strategy:
This is an improved version of the previous strategy, which attempts to establish a "buffer" with which one of players can forgive X amount of bad rounds of the opponent, in order to prevent the overall game resulting in total non-cooperation (in which case both players would be worse off). The idea of "forgiving" the opponent is actually an attempt to avoid "noise" signals (e.g. events which were not hostile but were interpreted as such mistakenly). Historically, it's usually worth it to re-assure yourself before you proceed to going fully MAD.
This strategy ensures even higher overall score than the previous one, however, there is a hole which can be exploited. If the opponent is malicious, he can learn and abuse the "buffer" step of the player. So, if Player A has a "buffer" of 3 rounds (meaning that he will switch to non-cooperation after 3 consecutive cheats), Player B can always cheat 2 times and go back to cooperative strategy. This is why even a better strategy exists.

Pavlovian strategy:
When I first heard it, I thought it was a reference to the Balkan's mentality, but nope, it was not. Actually it turns out it's in relation to the Pavlovian psychology. The approach in this strategy is very simple: If the player does something and gets any points, he will simply do the same thing again. And again. And again. Basically, with this approach the player will be able to abuse the opponent, if he is vulnerable to it, maintain cooperation - if the opponent provides the means to do so, and retaliate if there's nothing else to do. It's basically the strategy of all criminals, manipulators and dirty little schemers.

Balanced gradual escalation:
The original and "forgiving" Tit for that would fail when the opponent does not have a "forgiving" mechanism and is plain malicious while the "Pavlov strategy" is too abusive (or should I rephrase - too successful?). A balanced approach is to first start with a "Tit for tat strategy", so you cannot be exploited. After X amount of rounds then the player switches to "Forgiving tit for tat" strategy. If you think about it, this is also the way great managers lead their companies. At first they are harsh with the new employees and after they prove themselves, they start trusting them more.

My whole point with this post is simple. Using these strategies, you can avoid a lot of emotional and managerial equivocations in your life and maximize your relationships with people with a clear and trustworthy model.

Remember: You can never play a good game without a good opponent.
This is why I hope, in the Game of Life, for you to meet some good partners and opponents.

Au revoir!

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