Gratitude-Trust-Reputation-Kindness;Repeat. Game Theory explains social capital building

WHEN JOHN NASH's THEORY applied over a A SIMPLE LIFE INCIDENT throws Life-changing perspective

The real-life story goes back over 2 decade. I had just learnt riding a bike, and used to borrow from brother to sneak out for a neighborhood round.

One such round, I had to fill petrol and, not so used to tank-filling , I went to close-by petrol bunk. and assuming i had cash - got it filled!!!

I realized i was not carrying any cash & was horrified at the prospect (15 yrs old) of managing the situation.

Not knowing anything better- I took out my watch -had a rather new Titan wrist watch, and went to the attendant- guilt laden, told him 'I dont have cash, but i will get it from home- you keep my watch till then'. For the record- he didn't know me or my home.

In an absolutely unforgettable experience- the lowly paid attendant (those days they had a trademark shoulder back to collect cash) in a grandfatherly stern tone- said this "This IS VERY BAD, DO NOT DO THIS AGAIN, WE KNOW WHO's WHO - GIVE ME CASH WHEN YOU COME NEXT".

Off course I rushed back home immediately and first gave cash to the 'Attendant Uncle'. This beautiful memory, encounter has remained itched in my mind since and i suspect guides me to take positive bets especially when it has positive impact on other and atleast non-negative or limited impact on me.

Recently while studying John Nash's Game Theory (Thanks to Prof Vimal Kumar, IIT Kanpur) , I thought of this encounter again and tried analyzing with this new found method.

Every player- in this case myself & petrol bunk attendant had some choices(strategies) & some playoffs.

Using Game Theory, particularly focusing on the concepts of trust, reciprocity, and equilibrium, we can breakdown the problem :

Players, Strategies, and Payoffs

Players:

Petrol Pump Attendant: Decides whether to "Fill Petrol" or "Decline to Fill."

Customer (I , in this case): Decides whether to "Pay Back" or "Not Pay Back" if the attendant fills petrol.

Strategies:

Attendant:

Fill Petrol: Trusts the customer will pay later.

Decline to Fill: Refuses service unless paid upfront.

Customer:

Pay Back: Repays as promised, upholding trust.

Not Pay Back: Does not repay, betraying trust.

Effectively this is what happens :

• (10, 10): If the attendant fills petrol and the customer pays back, both receive the maximum benefit.
• (-5, 5): If the attendant fills petrol but the customer does not pay back, the attendant incurs a loss (-5), while the customer benefits (5).
• (0, 0): If the attendant declines to fill, neither gains nor loses.

Analyzing Quantitatively - The Nash Equilibrium (NE)

Case 1: Attendant chooses "Decline to Fill"

• Payoffs: (0, 0), regardless of the customer's choice.
• Stable NE: Both players have no incentive to deviate, but this equilibrium is suboptimal as neither gains utility.

Case 2: Attendant chooses "Fill Petrol", Customer chooses "Pay Back"

• Payoffs: (10, 10).
• Optimal NE: Both players achieve their best outcomes by cooperating, leading to trust and long-term societal benefits.

Case 3: Attendant chooses "Fill Petrol", Customer chooses "Not Pay Back"

• Payoffs: (-5, 5).
• Unstable: The attendant incurs a loss and learns to switch to "Decline to Fill" in future, breaking the trust cycle.

What's happening here- when the customer doesn't pay back, the attendant has lowest payoff and stops to help anyone else. While when the customer pays back , both benefit in long term and they do so over repeated transaction.

In a repeated game (most transactions in life can be repeated , especially if they are win-win)

• Trust builds over time if both parties adopt cooperative strategies (Fill Petrol, Pay Back), leading to a stable equilibrium.
• Betrayal (Not Pay Back) disrupts the equilibrium and forces the attendant to switch strategies, harming long-term outcomes for all.

Let us see it over a simple graph, over time over repeated transactions-

This show, the long-term effects of trust and reputation (cooperation) versus betrayal in repeated interactions:

• Cooperative Strategy (Trust & Pay Back):

The cumulative payoff increases steadily over time, reaching the highest value because trust is consistently rewarded.

This demonstrates the benefits of fostering a virtuous cycle of trust and kindness.

• Non-Cooperative Strategy (Betrayal):

The payoff fluctuates between short-term gains (betrayal) and significant losses (loss of trust).

Over time, the cumulative payoff lags far behind the cooperative strategy due to recurring penalties for broken trust.

A simple analysis , a rather simple incident looked at from the right perspective gives a rather powerful conclusion.

In repeated interactions, over longer term: cooperation and trust yield the best long-term results for all parties involved, while betrayal results in volatile and suboptimal outcomes.

No Wonder, Trust-based strategies build social capital and create sustainable benefits for society as a whole