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Tit for Tat with Forgiveness: Rosh Hashanah Day II


When I was in college, I was a double major in Psychology and Jewish Studies (the former often being even more relevant to my work as a rabbi than the latter!) and to this day I remain an avid reader of psychology literature in the popular press.  In particular, I have always been fascinated by game theory and especially by the prisoner’s dilemma – the social experiment in which two players may either cooperate with or betray one another in order to maximize their own payoff.  Those of us familiar with the prisoner’s dilemma will remember its classic formulation:  Two suspects are arrested. The police separate the prisoners, privately offering each the same deal.  If both testify, each receives a five-year sentence, commuted in acknowledgement of his cooperation.  If both remain silent, there is insufficient evidence to convict and each is held for six months on a minor charge.  However, if one testifies while the other remains silent, the betrayer goes free and the silent accomplice receives a full sentence of ten years. Not knowing the choice his partner will make, each prisoner must decide whether to betray his colleague or to remain silent.  How should he act?

 

The great irony of the prisoner’s dilemma lies in the fact that rationality will lead both players to defect even though their joint outcome would be far better if they cooperated.  Unable to predict what his colleague is planning, each prisoner reasons that he would do better to confess than remain silent – if his partner also confesses he will get five years (as opposed to ten); if his partner does not confess he will go free (as opposed to being jailed for six months).  On the basis of this strategy, both prisoners ultimately confess, resulting in a five-year jail term for each rather than the six months they could have served with cooperation.  Rational thinking leads to a suboptimal solution for both parties.

 

There is, however, an element that can tip the equilibrium of the prisoner’s dilemma from competition to cooperation and that element is repeated play.  In what’s known as an iterated prisoner’s dilemma where the game is enacted continuously between two individuals (generally via computer and with the premise of the situation recast so that it is financial incentives rather than jail time that is ultimately at stake), each player has an opportunity to “punish” his colleague for previous defection, and fear of retaliation often leads to a cooperative outcome.  In fact, one of the most effective strategies for the iterated prisoner’s dilemma is something called Tit-for-Tat in which the individual will initially cooperate and then respond in kind to an opponent’s previous move.  If the opponent was cooperative, the individual is cooperative.  If the opponent was competitive, the individual responds in kind.  Tit-for-Tat allows a player to adopt an optimistic and helpful stance without becoming a martyr.  It is a strategy that balances cooperation and self-protection.

 

While the prisoner’s dilemma was formally introduced in the early 1950’s, one could say that it was invented almost 6,000 years ago when God first created the universe.  For essentially life is one big prisoner’s dilemma – a complex, multi-layered environment in which we must constantly decide whether to compete or cooperate, love or fight, look after our own self-interest or work towards the common good.  And while with life, as in psychology experiments, our greatest profits in both the financial and the spiritual realm often stand to be made when we are work together, there are many powerful incentives luring us to betray, from self-protection and fear, to selfishness, ambition, and greed.  Sometimes we have been burned in the past and are loathe to trust again.  Often our memories are longer for the times we’ve been aggrieved than for the times we’ve been treated with kindness.    Indeed, balancing cooperation and self-interest remains one of the essential dilemmas not only of game theory but perhaps of human existence as a whole.  It is one of the themes very much on our mind as we make our way through the High Holiday season.

 

The balance between cooperation and self-protection is not only a human quandary, but this dilemma extends even to the Divine.  Pesikta Rabbati, a collection of rabbinic midrashim from the late 1st century C.E., explores God’s creation of the world using the parable of a king who had two cups made of delicate glass.  The king said: “If I pour hot water into these vessels, they will expand and burst; if I pour cold water into them, they will contract and shatter.”  What did the king do?  He combined hot and cold water together and poured this mixture into the glasses so that they remained intact.  Likewise, argue the rabbis, the Holy One said: “If I create the world with mercy alone its sins will be too many.  If I create it with justice alone, how could the world endure?  So I will create it with both justice and mercy.  In that way, humanity can survive.”

 

God, like us, is torn between a desire to be trusting and gracious and a desire to be rational and fair.  And this tension, far from being resolved when the world was formed, extends throughout the course of human history.  The rabbis explain that the two opposing attributes of God captured in the above midrash – din and rahamim (justice and mercy) are also reflected in the two names we most commonly use for the Divine – Adonai and Elohim.  While Adonai indicates God’s compassion and preference for kindness, Elohim captures God’s sense of justice and fair play where deeds must necessarily carry consequences in order to ensure a safe and ethical society.  As the midrash reminds us, ruling the world through either justice or mercy alone can lead only to brokenness – be it broken relationships, broken hearts, broken laws, or broken faith.  The dilemma for God, as for us, is in balancing measures of cooperation, love, and trust with measures of rationality, caution, and self-interest.

 

As game theorists followed the Tit-for-Tat strategy described earlier, they noticed something interesting.  On occasion, a one-time accidental error on the part of either player created a most troubling situation.  Because each agent was responding in kind to his partner’s prior “move,” any failure to cooperate – even one made by mistake – would be met with the same, quickly leading to a never-ending “death spiral.”  To overcome the dangers of this uncompromising strategy, a minor adjustment was made.  In a small percentage of cases (generally somewhere between 1-5%), an agent faced with competitive play would ignore his opponent’s move and cooperate anyway – thereby preventing the plummet of defection that would otherwise have been launched.  This new strategy was able to break cycles of non-cooperation, ultimately becoming more effective than its relentlessly retaliating predecessor.  It was called, quite aptly, Tit-for-Tat with Forgiveness.

How often does this occur in real life too – that small, often unintended, acts quickly escalate into something far larger!   An email is read in the wrong tone of voice.   A friend doesn’t call to check in, though later we learn she didn’t know times were so tough.  A fellow congregant passes us by at Kiddush, distracted by other things, and we take it personally.  We misinterpret our husband’s smile for a smirk, our child’s disorganization as obstinacy, our mother’s forgetfulness as not caring or listening hard enough.  Often but the tiniest things can move us from a posture of cooperation to one of competition.  And once we have become locked in that new perspective, it can be exceedingly difficult to return.

 

It is striking to me that the strategy designed to foster cooperative behavior, the one which even bears the name Tit-for-Tat with Forgiveness, ordains not continuous clemency but rather forgiving behavior used judiciously – in only 1-5% of the time to be exact!  Tit-for-Tat does not ask us to become martyrs, constantly sacrificing our own well-being and advancement for the sake of preserving the peace.  Rather it asks us – every once in a while – to reconsider our relationships, imagining the possibility of change.

 

The High Holiday season is, in its very essence, about transforming the kinds of patterns modeled by the prisoner’s dilemma, those long standing cycles of resentment in which we sometimes come to be trapped.  Forgiveness that comes easily, the minor indiscretions that happen between us and the people we most love, happens continuously throughout the year; we do not necessarily need the Yamim Noraim (Days of Awe) to strengthen our resolve in these areas.  Rather, it is for our most difficult and complicated relationships that the High Holiday season is made.  It is our once a year trigger to “randomly forgive.”

I would venture to guess that most of us have at one time or another been trapped in a pattern of animosity, and for many of us that painful dynamic is still alive and well.  Perhaps it is an estranged friend whose hurtful comments continue to echo in our ears, a sibling who always demands more than her fair share, a former spouse who seems more focused on causing pain than on arriving at amicable compromise.  Perhaps it is someone we see everyday or a person that we have come to avoid.  Perhaps it is someone who has genuinely and repeatedly treated us with malice; perhaps it is someone with whom we have simply gotten into the habit of being angry.  I believe that the lesson of Tit-for-Tat, the lesson of the High Holiday season in general, is not to ignore a long history of mistreatment and put oneself at emotional risk (this is especially true when grievances are of more than the garden variety and opting for reconciliation could possibly put a person in serious harm).  Rather, the message here is to temper justice with mercy – din with rahamim – and to use this period as the 1-5% of the year in which we randomly forgive, reset, and opt for cooperation – hoping, sometimes against hope, that this will be returned.

 

The Nobel-prize winning scientist Niels Bohr once said that the complimentarity theory that he designed in quantum physics – the principle that you cannot chart simultaneously the position and the velocity of a particle – came to him when his son confessed to having stolen an item from a local shop.  In that moment, Bohr found, he could think of his boy with love as a father or with justice as a judge but not both at the same time.  This same idea is captured in the Avinu Malkenu prayer that we recite each High Holiday season, invoking God as both a loving Father and a powerful King.  We hope that, ultimately, the Divine will look upon our deeds as a gentle parent and grant us pardon rather than viewing us with the dispassionate eye of a monarch.  In turn, we must extend that same generosity of spirit to those around us.

And so, as we continue through this High Holiday season, I wish for us the strength to break old patterns and to opt for forgiveness, to reset our personal Tit-for-Tat counters and instead look towards the possibility of repaired relationship.  We do not need to make ourselves martyrs, allowing those who have hurt us deeply simply to have their way.  But we do perhaps need to try – just one more time – to extend a white flag of friendship, hoping that it might spark the other to respond in kind.

May the coming year be one of second chances, cooperative choices, and old hostilities laid to rest.  Shana Tova!

 

 

 

Date Posted Title Author
Oct 6, 2016 Tit for Tat with Forgiveness: Rosh Hashanah Day II Rabbi Annie Tucker