Cash Equilibrium
or the game theory of gender equity
March 2023
In modern dating, there's a fine line between chivalry and equality.
Long gone are the days where men are obliged to pay for everything.
Although it's still commonplace to offer, it can come off anywhere from generously courteous, to offensively
antiquated.
The rules are even less clear for women; should you accept? Or offer to split? Or pay for everything entirely?
Every option comes intertwined with considerations about one's morals, financial circumstances, or just how much
you even like the other person.
In Australia, the gender pay gap currently sits at 11.5%.
This begs the question: should women be expected to pay an equal share on an unequal wage?
Here we explore strategies for tackling an abstraction of the above problem with the use of Game Theory.
And of course, what kind of blog post would this be without a background story...
~Meet Cute~
Alice and Bob matched on 'Hinder'. After a few days of chatting, Bob asked Alice out for a brunch date.
Alice agreed; out of many suitors Bob seemed to be the most interesting,
and based on their insofar conversations they had a fair amount in common.
Bob and Alice both attended the local university and studied the same commerce degree.
Bob is a year older and was a semester off graduating. Alice was in her penultimate year, although the two did
share some courses.
The pair met up at a trendy cafe near campus on Sunday morning. Bob ordered a batch brew and eggs benedict with
bacon.
Alice ordered a soy latte and an outrageously priced smashed avocado toast. She joked about how their generation
could never afford to buy houses.
Amidst all the frivolities and flirtatiousness of a first date, Bob learnt that Alice is vegetarian, and went to
town's private school.
Alice, on the other hand, discovered that Bob hailed from a farm in the countryside and was on a rural equity
scholarship.
In spite of their differences in upbringings, their mutual interests prevailed, and both students had a great
time.
In each of their minds both Alice and Bob wanted to get to know each other better.
Although they coyishly hid their attraction to avoid coming off as too keen.
At last the time came to settle the bill.
Bob instinctively reached for his wallet as the cashier brought up the total.
It was he who asked for the date, it's the least he could do. That's how his mother raised him, right?
Alice noticed and suddenly her mind went into overdrive. Bob was the spitting image of a cash-strapped student.
Coming from an upper-middle-class family, she lived at home and had allowances for expenses like these.
Would it be cruel to have him pay? Could he not afford to see me again? Or, is he trying to make me feel
like I owe him something?
In the moment Alice asked the cashier if they did split-bills. The cashier nodded.
Now thoughts ran amok through Bob's mind; maybe Alice is the strong, independent type that don't-need-no-man?
What does it mean if she's trying to get square with me already? Does she pity me? Am I some charity case?
Bob, determined to save his pride, cheerfully made an excuse to pay for everything:
"No need, this one's on me. I ate more anyway!"
Alice, moved by his confidence, gladly relented. As they left the cafe and parted ways for the day Alice
whispered softly with a wink:
"You know, you didn't have to. I'll shout us next time!"
| Meet Cute | Alice Pays | Alice Abstains |
|---|---|---|
| Bob Pays | 1,1 | 2,3 |
| Bob Abstains | -3,0 | -2,-2 |
The above matrix models the payoffs for each action Alice and Bob can make in their fictional first date
scenario.
This is an asymmetrical cooporative game where both people want to make the best impression. Minimising
financial cost is secondary.
If both Alice and Bob pay, they leave a reasonable impression of one another and split the fiscal burden.
This result leaves some questions unanswered and their future is up in the air.
If Bob pays he makes a strong impression, although this is somewhat offset by the cost incurred.
Alice saves money at no reputational loss as she had no expectation to pay, and gains the power to determine the
future of the relationship.
If Alice has to pay (an immaterial sum), Bob makes a terrible impression and Alice just wastes time for nothing.
If neither Bob nor Alice pays, both of them get into an equal amount of trouble.
Bob has only one logical action - to offer to pay - abstaining is absolutely negative.
Alice's two options are equally viable with an average payoff of 0.5 for herself.
By considering Bob's (lack of) strategy, she can maximise the overall payout for both parties - and thus the
chances of another date.
~Moving In~
Alice was the one to ask Bob out on their second date, and she made good on her promise to return the
favour and pay.
The couple continued dating over the coming year, following the spirit of: "I'll shout us next time! ;)"
They shared countless magical moments with their friends and family,
and were there for each other at core moments in each others' lives.
Within a few months, Bob graduated and landed an associate position at 'Big Firm'.
Alice continued her studies into her final year, and scored an internship at 'Rival Corporation'.
The two mused that one day they'd face each other on the business battlefield.
On their first anniversary Bob asked Alice to move in together.
Alice gladly accepted, knowing very well that she had overstayed her welcome at her parents' home and would have to move out after she had graduated.
At this stage it only felt natural to live with the man she loved.
With Bob spending long hours at the firm it was the easiest way for them to spend more quality time together.
Over the following weekends they inspected rental properties.
City apartments were smaller than either of them were accustomed to, but demand was insane.
Beggars can't be choosers.
For the first time in her life Alice realised how tough it could be to struggle in the real world.
After weeks of searching Bob and Alice signed a lease for a tiny one bedroom apartment.
The rent was reasonable given the current state of affairs, ridiculous for a single occupant, but within their
means as a couple.
They moved in straight away.
In the beginning Alice and Bob were happy to split the rent 50/50.
But nothing lasts forever, and it wasn't long until their honeymoon period came to an end.
Alice, facing the newfound struggle of having to pay for housing on her allowance and casual job, suggested to
Bob that she pay less rent.
She justified her proposal by claiming that her income as a student is insufficient, but eventually she will
graduate and work full-time too.
Bob was stuck between a rock and a hard place. He feared that by complying he could spoil the future of their
relationship.
Yet now he was the breadwinner of the couple, and perhaps he had a duty to placate his partner...
Then for whatever unfathomable reason, Bob retorted that Alice spent more time at home, had far more things, and
took up more space in bed - so if anything she should pay more rent!
These were the words of a soon-to-be dead man.
Naturally an argument erupted as Alice and Bob aired their grievances and screamed at one another.
It was the first time they had fought so badly, was this a symptom of living together?
The quarrel went on well into the evening, reaching a fever pitch as each of them threatened to move out and
break up...
Eventually, the adrenaline ran out and rationality returned to the room.
Through the fire and flames, both Bob and Alice came to realise that their lives were so intimately tied
together now.
Leaving each other over something as petty as a few dollars of rent would be such an anti-climactic end to all
the joy they had been through.
That night, as Bob and Alice made amends, both of them knew that they had entered a new chapter of their lives.
| Moving In | Alice Pays Rent | Alice Demands Less Rent | Alice Moves Out |
|---|---|---|---|
| Bob Pays Rent | 2,2 | 0,3 | -3,-1 |
| Bob Demands Less Rent | 3,0 | 1,1 | -3,-1 |
| Bob Moves Out | -1,-3 | -1,-3 | -2,-2 |
"Moving In" is modelled as a symmetrical non-cooporative game.
Scoring is based primarily on monetary cost, but also factors in relationship quality.
At this point in their lives, Alice and Bob are on a close enough playing field that each person has three
possible actions;
paying their share of rent, demanding a discount, or moving out (and breaking up).
But what is immediately clear is that moving out is not a credible threat.
Beyond the heat of the moment destruction, the absolute outcome is negative for both people.
Eliminating the option allows the payoff matrix to be simplified into a 2x2 form that resembles the well-known
Prisoners' Dilemma.
The optimal solution to which is always to "betray"; to fight fire with fire - i.e. to demand a discount from
the other party.
And so they came full circle, back to splitting the rent evenly. Albeit with some scars picked up along the way.
~Marriage, Mortgage, and Motherhood~
Alice and Bob continued to alternate paying for, or splitting everything evenly, over the life of their relationship.
It was the simplest solution, Bob and Alice valued each other as equals.
They knew that as a couple they would have spent roughly the same amount of money on each other over the years.
Ten years in, they had gotten married, and worked their way up through the corporate world.
They now shared a modern highrise with a view - a stark contrast from their beginnings in the run down one
bedder.
Then one day Alice awoke with dizzying nausea. She bolted to the bathroom and hugged the bowl for what seemed
like an age.
Bob rushed her to the doctor, fearing the worst.
He'd always known that Alice was a little bit anaemic, but had never seen her like this before.
The doctor took some blood and ran some tests. They anxiously awaited the results...
Alice was pregnant.
Miraculously, without a moment of hesitation, the couple were overcome with joy. They were going to be parents!
The news of the baby set in motion set forth a series of events.
Changes in lifesyle and mentality were in order - all to prepare them for their future family.
Most notably, Alice and Bob committed to purchasing a home in the suburbs.
With a mortgage and motherhood on the way, money was as tight as it had ever been.
They both had the same degree, worked in the same industry, with the same skills and experience;
but somehow Bob had broken into middle-management years ahead of Alice - and thus was earning more.
A mortgage is the largest financial decision a middle-class family can make.
So one night, Alice and Bob sat down and ran through the numbers.
It was a no-brainer for them to target making more than the minimum repayments so they'd save interest and
finish their loan earlier.
But the actual distribution of payments between the two was a much trickier equation.
There were really only two logical options. It all came down to whether they kept sharing the burdens of paying 50/50,
or adjusted their share based on their relative incomes:
| Mortgage | Alice Half Target | Alice Adjusted (Reduced) |
|---|---|---|
| Bob Half Target | 2,-2 | 1,-1 |
| Bob Adjusted (Increased) | 1,-1 | 0,0 |
Bob and Alice's mortgage is modelled as a one-sided zero-sum game.
Scores solely represent financial situation - Alice is at a disadvantage due to her lower salary.
From an equality point of view it appears reasonable for both Bob and Alice to make half of their target
repayment for half the utility of their house.
But when factoring in Alice's disadvantage, this strategy is less costly to Bob and leaves Alice with less money
to spare.
Over the course of several decades this difference compounds to significant sums of disposable/retirement
income.
I mean, how many baby boomer grandmas do you see buying boats and sports cars?
If Bob offers to pay more based on his salary, then he bears the cost. But both he and Alice benefit from the
reduced interest long-term.
Conversely, if Alice reduces her repayment she saves money, but the overall increase in interest negatively
impacts both of them.
The only perfectly equitable situation is when Bob and Alice both adjust.
Bob pays slightly more, and Alice slightly less, such that the proportional difference reflects their relative
incomes.
This, in theory, leaves each person with the same percentage of their income remaining.
A purely rational analysis of the payout game would dictate that Alice always adjusts for income, whilst Bob
should minimise his costs by only paying his half of the target.
However, let's say that in this fictional universe Bob also chose to adjust because he is not a soulless money
making robot, and values his wife and family's quality of life...
And they all lived happily ever after!
It is important to note that the absolute amounts of remaining income were not the same.
Alice still earned less than Bob, and Bob was not simply giving her half of all his extra earnings.
Alice was still motivated to work hard and maximise her income for her own personal gain.
Simply by being compassionate and considering the idea of compensatory adjustment, Alice and Bob were able to
achieve equity as a means of fostering long-term equality.
~Epilogue~
Historically, women earned practically zero income and were entirely dependent on their fathers and husbands to
survive - a 100% pay gap!
Over the centuries minority groups have fought hard for, and won, the right to equality, but only on paper.
In reality the world is still fraught with injustice around every corner.
In 2017 a Melbourne vegan cafe once tried to combat inequality by imposing (an optional) 18% "man tax".
Whilst the intention was good, their execution garnered them a lot of hate; and they closed up shop little over a year later.
Perhaps their fate might have been different if they had they marketed it as a "women's discount" instead?
Feelings of joy drive positive reinforcement and repeat business,
in contrast to shaming, guilting, and penalising half of the potential market.
Regardless, the actions of a single business at the microeconomic scale couldn't change the world.
Generalisations like Bob and Alice's story are never truly accurate, yet en-masse can they be powerful.
So in the absence of auditing everyone's individual financial situations (and the privacy issues that goes with
that), splitting the macroeconomic difference can be an efficient and equitable strategy for achieving long-term equality.
Doing mental arithmetic is hard; and when things are hard, people stop caring.
This is why I've created Libra - a simple pay gap calculator with a friendly UI.
Libra is a vision of what Big FinTech could do to help tackle gender pay inequality.
By all means, if you're reading, please take this ridiculously trivial idea and roll it into your product!
Technology has great potential for enacting positive social change.
By making it easy to pick responsible options, and normalising away the stigma, we can help to close the gap to zero.