• Daniel Ooi

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All human interactions are games. Ok that sounds really terrible. I don’t mean that people manipulate, mislead and trap others all the time like Game of Thrones (although this does happen, and chaos can be a ladder). But suppose you meet someone walking towards you on a narrow sidewalk. You can swerve either right or left, and so can they. What are you going to do, and why? This study of human interaction is called game theory.


Games are often hidden in plain sight. But before we go into real-life games, let’s look at a stylized example - the Prisoner’s Dilemma. Suppose Bonnie and Clyde are arrested for robbery and are held in separate rooms. They are being questioned simultaneously and have no means of communication. But suppose this is neither Sherlock nor CSI - there is no proof to conclusively nail them. Now, if they both lawyer up, the police can only lock them up for a year each. But suppose there is a plea deal: if Bonnie lawyers up, but Clyde confesses to incriminate Bonnie, Bonnie goes away for 10 years but Clyde gets off scot-free, and vice-versa. If both confess, the police then use their confessions to lock them up for 7 years each. This may seem a bit trivial, but assume that both Bonnie and Clyde know all these, and that they only care about how long their jail term is.


Suppose you are Bonnie - what would you do? If Clyde confesses, Bonnie does better to confess - if she lawyers up she goes away for 10 years, whereas if she confesses she goes away for 7. If Clyde lawyers up, Bonnie also does better to confess - she gets away scot-free, while lawyering up lands her in jail for a year. So, regardless of what Clyde does, Bonnie does better to confess. But what prevents Clyde from thinking in exactly the same way? He too would confess no matter what Bonnie does. Thus, confessing is a dominant strategy for both Bonnie and Clyde - it does better than all other strategies. And thus the outcome is both confessing, and both going away for 7 years.


This is what economists call the Nash equilibrium - the set of choices where neither player wants to change their action on their own. Now in total there are 4 possible sets of choices, denoted as (Bonnie’s choice, Clyde’s choice): (Confess, Confess), (Confess, Lawyer Up), (Lawyer Up, Confess) and (Lawyer Up, Lawyer Up). And consider the corresponding jail terms - why would they not agree on (Lawyer Up, Lawyer Up)? That’s better for both of them. Recall that they can’t communicate since they are held separately - no telepathy please. Suppose both Bonnie and Clyde were intending to lawyer up - if all Clyde cares about is his own jail term, he has an incentive to switch to confessing, since he gets no jail term compared to 1 year in the scenario both lawyered up. And remember if Clyde was thinking about this, Bonnie would too. And so, both players lawyering up is not a Nash equilibrium.


And now notice this: the Nash equilibrium does not guarantee the outcome that is best for everyone, which in this case would be both Bonnie and Clyde lawyering up, and then going to jail for a year. This is because of our assumption that Bonnie and Clyde only care about their jail terms. In economic-speak, Bonnie and Clyde are self-interested - you do what is best for yourself. Now, self-interest does not imply selfishness - there are economic models that capture altruism and fairness. But in the Prisoner’s Dilemma, it is rational to be selfish, since anything else would give you a worse outcome.


Now in case you think people are not rational and do not play Nash equilibrium strategies, consider a real-life example: the mad dash for toilet paper. Suppose you and I think that there is going to be a shortage of toilet paper. In response to that information, I can either just buy them as usual, or try to hoard them by buying loads. Given you and I have the same information, it is likely that you are thinking exactly the same thing. If you buy as usual, there’s more for me, so I am going to hoard. If you hoard and I don’t, I won’t have any left in the toilet paper apocalypse. So, hoarding is the dominant strategy for you and I - everyone hoarding is a Nash equilibrium. Thus, toilet paper hoarding is effectively a Prisoner’s Dilemma. And when that happens, a shortage is the result. This is a self-fulfilling prophecy - I fear a toilet paper apocalypse, and by my actions I cause what I fear to happen. And again, the Nash equilibrium is worse for everyone than if everyone had restrained themselves.


Hopefully by now you see we have a conundrum. Socially-optimal outcomes are never guaranteed because of how incentives work. In this game, doing what is best for myself is mutually exclusive with getting what is best for everyone. Are we stuck then? Do we give up rationality or socially-optimal outcomes? Something seemingly irrational is the key to this problem.


"But to those of you who will listen, I say: Love your enemies, do good to those who hate you, bless those who curse you, pray for those who mistreat you. If someone strikes you on one cheek, turn to him the other also. And if someone takes your cloak, do not withhold your tunic as well. Give to everyone who asks you, and if anyone takes what is yours, do not demand it back. Do to others as you would have them do to you." Luke 6:27-31


In today’s context, if someone didn’t manage to get any toilet paper, give it to them. If someone steals a pack of flour from your trolley while you’re queuing to pay, let them take it. But this means less for me - and that’s precisely the point of what Jesus said. Retaliating would give you the Prisoner’s Dilemma problem, where everyone is worse-off. Let yourself be deprived, return evil with good - do not do what is in your best interest, and that benefits everyone.


But this makes no sense! Why should I suffer a loss because someone else was nasty? Surely this is irrational, since there is no incentive to do so. Or is there?


Jesus said,

"But love your enemies, do good to them, and lend to them, expecting nothing in return. Then your reward will be great, and you will be sons of the Most High; for He is kind to the ungrateful and wicked. Be merciful, just as your Father is merciful." Luke 6:35-36


My incentive to suffer loss in loving is blessing in eternity. Returning to our toilet paper game, this means even though people may act selfishly by hoarding toilet paper, it is better not to hoard - the payoffs have changed such that selflessness dominates selfishness. In exchange for a few toilet paper rolls, I am reminded of what eternal gain I have. In this sense, by not doing what is immediately best for myself, I am doing what is best for myself, not just now, but forever. If there is life forever, decisions in the present should consider gains and losses, both now and in the long run, in eternity.


Now, there is very real and present joy that is experienced in the act of loving now - who does not feel the warmth and gladness in seeing someone you love doing well in life? Who does not feel the satisfaction and fulfilment in caring for their friends? The present joy is undeniable, but crucially for me, this is neither the only nor the ultimate motivation behind love:


We love because He (God) loved us first. 1 John 4:19 (text in parenthesis mine)


There is something wondrously profound in this - I choose to love because God has loved us, not in order for God to love me. In Jesus I have new life, and with new life comes new desires, new preferences, new perception. Having experienced the greatness of God’s love, I can love freely and unconditionally as God does. And in His love, God enables me, more and more, to love as He does. It all comes from God.


But what about our discussion about eternal rewards?


God is my ultimate desire and joy - C.S. Lewis describes God as the All-Satisfying Object. Psalm 16 says of God,


In Your presence there is fullness of joy; at Your right hand are pleasures forevermore. Psalm 16:11


My love flows from my love for God, and being the ultimate fountain of joy and delight, God is the best reward that anyone could ask for. In giving us new birth, God enables us to see and treasure Him as we rightly should. This sounds paradoxical, but love does not earn me the reward of God - rather, because God has graciously promised us Himself as the Reward, I am enabled to love. In the cost-benefit analysis of love, with God in mind, love is never a net loss but an infinite gain. In this sense, choosing to love unconditionally is rational!


Sometimes I take this for granted and forget just how amazing this is, that God calls us to love, and even makes it worthwhile for us to do so! He invites us to live radical lives - to love ridiculously, to play irrationally, to incur costs, to suffer loss - and yet, in the light of God’s promise, it is rational, it is reasonable, it is gain of eternal proportions.


The game is on.

A Game of Toilet Paper Hoarding

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