Tag: game theory

Posted in Philosophy

Zero-Sum Game

Posted on by Jinavie

Game theory is the study of using mathematical models to understand how rational decision-makers would strategically act in a given environment. One concept from game theory is that of the zero-sum game, where there is a finite amount of utility shared between players, meaning that if one person gains something, another must lose something to balance it out.

A classic example is a game of competitive sports, where there can be only one winner. For you to win, someone else must lose. A zero-sum game can have as few as two players (such as a singles tennis match) or many players (such as a game of poker, where every dollar you win is a dollar taken away from the other players).

From a young age, we see many examples of zero-sum games. We play sports and board games where there is a clear winner. We are marked on curve and compared to our classmates in exams. We compete for jobs and romantic partners. Competitiveness is driven into us and is sold as a survival skill.

This leads us to be prone to zero-sum thinking which can lead to many biases. Some studies show students acting more competitively and less inclined to help their peers if they were graded on a curve (e.g. percentiles), rather than grade categories (e.g. A, B, C). We think that if someone is a jack of all trades, they are masters of none, because surely no one can “have it all”. Many people oppose immigration because they believe that immigrants will take the finite number of jobs and houses. Some people negotiate aggressively in a deal, thinking that “your loss is my gain”. In severe cases, people may even sabotage others to increase their gains.

However, life is not always a zero-sum game. Game theory also describes non-zero-sum games, where the net balance of utility between all participants can be higher (or lesser) than zero. Simply put, in a non-zero-sum game, there can be more than one winner and sometimes, everyone can be a winner.

The best example of this is the mutual benefit born from cooperation. Zero-sum thinking may dictate that you must conquer your neighbouring tribe because they are your competition, but throughout history, cooperation, peace and harmony have prevailed as the winning strategy, because it results in greater net gain.

Happiness is also a non-zero-sum game, where just because someone else is happy, it does not take away from your happiness. But for some reason, some people cannot stand to watch others happy, or feel they must be happier than those around them. These people constantly try to “one-up” others, not recognising others’ happiness, or even sabotaging others and making them feel bad because they can’t stand to see other people be happier than them. This is an extremely toxic, unnecessary behaviour, that should be unacceptable in any kind of relationship, particularly between friends or family.

The far healthier behaviour is to be happy for others’ happiness, regardless of your life situation. This is why compassion is one of the keys for happiness. Realising that we can all find our own joy and contentness and help each other find happiness is a key step in being sustainably happy.

1 + 1 = 3

Posted in Psychology & Medicine

Tit For Tat

Posted on by Jinavie

In human society, there are many ways for a person to interact with others when in a group setting. Some may choose to be selfish and only be out for their best interests, while others may choose altruism and cooperate with each other. The mathematical model that tries to predict human behaviour and outcome in these settings is the Prisoner’s Dilemma – the core of game theory. Tit for tat is one strategy that can be employed in such a setting.

The basis of tit for tat is equivalent exchange. A tit for tat player always chooses to cooperate unless provoked. As seen in the Prisoner’s Dilemma, if both players cooperate, both benefit (let us say 3 points each); if one player defects, that person gains more than from cooperation (5 points) while the tit for tat player gains 0 points.
If a tit for tat player is provoked, that player will retaliate. However, the player is also quick to forgive. Ergo, if the other player chose to cooperate, the tit for tat player (following the principle of equivalent exchange), will also cooperate. If the other player defected, the tit for tat player loses the first round and then chooses to defect from then on.
Note that tit for tat strategy only works when there is more than one game so that the player has a chance to retaliate.

Let us use an example to illustrate why tit for tat strategy works. In this scenario, two tit for tat players and two defectors all play six games each, using the above point system (if both defect, they each receive 1 point). The results are as follows:
  • Tit for tat vs defector: Tit for tat loses first round, both defect for next 5 rounds (5 vs 10)
  • Tit for tat vs tit for tat: Both cooperate on every round (18 vs 18)
  • Defector vs defector: Both defect on every round (6 vs 6)

When the points are added up, a tit for tat player gains 28 points (5 + 5 + 18) while a defector only gains 26 points (6 + 10 + 10). This is a surprising turn of events, as the defectors never lost a round and tit for tat players never “won” a round. This goes to show how cooperation leads to better long-term results while selfishness prevails.

There are shortcomings of this strategy. If there is a failure in communication and one tit for tat player mistakes the other’s actions as an “attack”, they will retaliate. The other player then retaliates to this and a vicious cycle is formed. This is the basis of many conflicts ranging from schoolyard fights to wars (although interestingly, tit for tat strategy is also found during wars in the form of “live and let live”). One way to prevent this is tit for tat with forgiveness, where one player randomly cooperates to try break the cycle (a defector would respond negatively while a tit for tat player will accept the cooperation), or the tit for two tats, where the tit for tat player waits a turn before retaliating, giving the opponent a chance to “make up for their mistake”.

Computer simulations have all proven that tit for tat strategy (especially the other two types mentioned just before) are extremely effective in games. In fact, it is considered one of the most optimal strategies in overcoming the Prisoner’s Dilemma.

In human societies, there is usually a mix of “nice people” and “selfish people”. By cooperating and trusting each other, we can produce a much greater gain over time compared to being selfish. And since society still unfortunately has “defectors”, you can retaliate to those who refuse to cooperate by defecting on them also. Ergo, a good approach to life is to initially reach out your hand to whoever you meet and treat them from there on according to how they respond. If they take your hand and want to cooperate, treat them with altruism and help them out. If they swat your hand away and try to use you for their selfish gain, it is fine to shun them and not help them out.

Through cooperation, understanding and connection, we can build a far more productive and efficient society, just like the ants.

Posted in Science & Nature

Duel

Posted on by Jinavie

Three gunslingers called Good, Bad and Ugly duel to the death. They each stand an equal distance from each other and shoot at the same time. Good’s accuracy is 30%, Ugly’s accuracy is 70% and Bad’s accuracy is 100%. Who has the highest chance of survival?

Common sense dictates that Bad, with the highest accuracy, will have the highest survival rate. However, when the duel begins, the following scenario will occur.

Good’s most rational decision is to shoot Bad rather than Ugly. Reason being, shooting the person with the higher accuracy improves your survival rate in the next round. Ugly also chooses to shoot Bad instead of Good as it is the best choice. Lastly, Bad shoots Ugly instead of Good. This scenario can be explained by the following diagram:

Thus, the probability of Bad being alive after the first round is (1-0.3)(1-0.7)=0.21, or 21%. This is because Ugly is killed by Bad on the first shot. On the second round, the probability of Good dying is the same as Bad’s survival rate of the first round, which is 21%. Therefore, Good’s survival rate is 79%. On the other hand, Bad’s survival rate becomes 0.21(1-0.3)=0.147, or 14.7%. 

Ultimately, the survival rate of each shooter is: Ugly 0%, Bad 14.7%, Good 21%, making Good the most likely winner. This illustrates the fundamental principles of game theory – an extremely useful theory that helps predict the many choices we make in life.

Posted in Philosophy

Prisoner’s Dilemma

Posted on by Jinavie

The prisoner’s dilemma is a famous example of how game theory functions. It predicts the behaviour of two people when forced to cooperate. The story goes as follows:

Two accomplices in crime are arrested by the police. They are interrogated in separate rooms. As the police have insufficient information, they offer a deal to each prisoner to confess that the two committed a crime (or deny). The deal is:

  • If you confess and your partner denies taking part in the crime, you go free and your partner will serve ten years (and vice versa).
  • If you both confess you will go to prison for four years each.
  • If you both deny taking part in the crime, you both go to prison for two years.

Assuming the prisoners act rationally (i.e. for their best interest and minimising their jail time), the prisoner will obviously choose the “confess” option as this is hypothetically the best choice (minimum time = 0 years, compared to only 2 years minimum for denying). However, because both prisoners are thinking this, the result is almost always that both confess and end up with four years each. Therefore, because human beings are unable to trust another human being enough, people always end up acting irrationally (benefit not maximised).
If the two had been trusting (assuming the other would deny too) and cooperated, both would have served half the time. But people always assume (correctly) that the other person will betray them for their selfish gain and this win-win result is unattainable.

But what if the other prisoner was yourself? Let us assume that the prisoner’s dilemma game was played by you and an exact copy of you. A copy that thinks like you, acts like you and identical to you in every single way. Can you trust yourself? Do you trust yourself enough to deny the crime, when it is entirely possible that he or she rats you out to walk free while you suffer for 10 years? How do you know that he loves you more than himself? 

Your greatest enemy is you.