Nash Equilibrium

Having finally defeated the Serpent King, John was just about to take a break when his phone began to buzz incessantly with new messages. Picking it up, he saw a flood of inquiries.

"How much for defeating the Planet Devourer? How long will it take? Does my character's stats work for this?"

"What's the price for taking down the Red Iron Beast?"

"How much to defeat the Avenger?"

These inquiries were all high-end tasks similar to the Serpent King. Overjoyed, John put aside his rest and started responding immediately. Based on the stats provided by the customers, he continued offering competitive rates.

Tasks that others wouldn't dare to take on, he would. Prices that others wouldn't dare to offer, he would give!

The Revival Game Studio's business boomed once again. To accommodate these high-paying jobs, John had to temporarily stop accepting some regular tasks. There was no other choice; business was just too good, and the four computers couldn't keep up.

However, John didn't dedicate all four computers to high-paying tasks. Even with a flood of high-end tasks, he would only allocate two computers to them, keeping the other two for regular tasks.

The reason was simple: his computing power was insufficient. The chip, which could barely reach a frequency of 30KHz when overclocked, couldn't handle the massive computational load. The more challenging the boss, the higher the technical requirements, and thus the higher the demand for computing power. Running two high-end tasks simultaneously was his limit.

Despite this, John's earnings skyrocketed. 

The two computers dedicated to high-end tasks now had an average hourly rate of $39. The other two computers, working on regular tasks, averaged $7.10 per hour. Combined, the four computers brought in about $2,200 a day, totaling over $60,000 a month!

While this income was impressive and enviable to others, John still wasn't satisfied.

It was too slow for his goals.

In his plan, the next-generation chip needed a substantial performance boost—at least a tenfold increase in computing power. This required higher precision in manufacturing and more expensive components. The cost of materials alone for the next chip was expected to be around $70,000 to $80,000.

Though his income had increased, so had his expenses. John was still financially stretched.

"It's time to change my business strategy to maximize profits," John thought.

With fixed computing power and four computers, he needed to find a way to maximize his income without changing his current setup. This required a strategic approach, often analyzed using Nash Equilibrium.

Nash Equilibrium, part of game theory, is about finding the optimal strategy. It applies to various aspects of life, including running a business. For instance, a bakery making 1000 buns daily might have leftovers, causing waste, while making 800 buns might not meet demand. Pricing higher might reduce sales, but pricing too low could decrease profits despite higher sales volume. Finding the right balance using Nash Equilibrium can optimize the baker's income.

John decided to use this theory to formulate his optimal pricing strategy.

Having moved past the initial phase of attracting customers with low prices, he could now afford to raise prices moderately.

For John, higher prices would reduce customer numbers, while lower prices would increase demand but overwhelm his capacity. Taking on too many high-end tasks would squeeze out regular ones, and his computing power was limited. His goal was to keep all four computers running at full capacity, maximizing computing power usage and ultimately, his earnings.

John quickly set up a complex equation incorporating various parameters: total computing power (30KHz), price parameters, time parameters, customer flow, conversion rates, and transaction rates—over twenty parameters in total. After a brief calculation, he reached a conclusion.

"Prices should directly correlate with computing power expenditure. The average pricing should be 8.5% below market rates to achieve maximum profitability."

This would maintain a slight surplus of tasks daily, preventing both backlog and downtime, keeping his computing power usage high but manageable, ultimately maximizing his income.

John updated his shop, adjusting prices accordingly. Predictably, the price increase led to some customer backlash, with many canceling their orders. But that was fine—it helped reduce the task backlog.

After a trial run for two days, things stabilized. Reviewing his earnings, John saw that the combined average hourly rate for the four computers had increased to approximately $120.

This meant daily earnings of $2,880, translating to about $86,000 a month.

This figure was satisfactory for now. John realized that with his current setup and computing power at its limit, further income growth was not feasible without upgrades.

"Let's maintain this for now," he thought. "I can start buying materials for the new chip gradually, not rushing to get everything at once. I can experiment with less critical parts first to gain some experience."

For the next month, John planned no significant changes, focusing on stability.

Meanwhile, the reputation of Revival Game Studio was quietly growing. With many satisfied customers spreading the word, more players stuck on difficult bosses sought out John's services.

"Boss, can you handle the Light Eater? Here are my stats. Can do? Great… What? I have to wait in line? Three days? What if I pay extra? Not even then? You're turning down money?"

"Boss, I confirmed the delivery and left a good review. Also, pre-booking for five days later to take down the Tree Demon."