Do incremental game have to have exponential growth ?

Costs to the player increase exponentially so that the game slows down over time rather than speed up or stay constant. Here are some examples of how idle games would play out with flat costs. The bottom line is that it doesn't work very well.

Flat costs, no upgrades:

Generators cost 100.
Generators give 1 per second.
Example:
*Player clicks and plays up to 10 generators. It takes 100 clicks, then about 5 more minutes of clicking slowly.
*From this point on, the player checks back every 5 minutes, and spends all money, quadroupling the amount of generators owned.
*At 10 minutes, the player has 40 generators.
*At 30 minutes, the player has 5000 generators.
*At 1 hour, the player has 20 million generators.
*At 2 hours, the player has 330 trillion generators.
*It only takes the player about 20 minutes to realize this pattern, get bored, and quit.
*Conclusion: Flat costs mean exponential growth. Also, no depth is super boring.

Flat costs, weak (linear) upgrades:

Generators cost 100
Generators give 1 per second Upgrades unlock every 10 generators
Upgrades increase revenue by 50% of their base. Upgrades are balanced to have identical price performance to generators as they unlock.
Example:
*Player clicks and plays up to 10 generators. It takes 100 clicks, then about 5 more minute of clicking slowly.
*T = 6m. We'll assume no more clicking from this point onward.
*Player saves for and gets upgrade. 10 generators, 1 upgrades, 15 income, 6 minutes.
*Player saves for and buys 10 more generators. Takes 1.2 minutes. 20 gens, 1 upg, 30 income, 7.2 minutes. *Player saves for and buys upgrade. Takes .4 minutes. 20g 2u 40i, 7.6 minutes.
*Player saves and gets 10 gens and 1 upg. Takes .8 minutes. 30g 3u 75i, 8.4 minutes.
*Player saves and gets 10 gens and 1 upg. Takes .4 minutes. 40g 4u 120i, 8.8 minutes. *Player saves and doubles gens and upgrades. Takes 1.2 minutes. 80g 8u 400i, 10 minutes.
*Player saves for 2 minutes and spends half on gens and half on upgrades. 320g 32u 5400i, 12 minutes.
*Player saves for 2 minutes, spends half on each. 3500g 350u 600000i, 14 minutes. *Player saves for 2 minutes, spends half on each. 360000g 3600u, 650 million income, 16 minutes.
*Player saves for 2 minutes, spends half on each, generators and upgrades multiply by 10,000. 18 minutes.
*Again, generators and upgrades multiply by 100 million. 20 minutes. *Again, multiply by 10 quadrillion. 22 minutes.
*Continues another 8-12 minutes until the player has exceeded the maximum number javascript can handle. 35-40 minutes in, the game has exploded,and the player quits.
*Conclusion: Flat costs plus linear upgrades means accelerating exponential growth. The game remains interesting, but explodes quickly.

Flat costs, strong (exponential) upgrades:

Generators cost 100
Generators give 1 per second
Upgrades unlock every 10 generators
Upgrades multiply revenue by 1.5. Upgrades are balanced to have identical price performance to generators as they unlock.
Example:
*Player clicks and plays up to 10 generators. It takes 100 clicks, then about 5 more minute of clicking slowly.
*T = 6m. We'll assume no more clicking from this point onward.
*Player saves for and gets upgrade. 10 gens, 1 upg, 15 income, 6 minutes.
*Player saves for and buys 10 more generators. 20g, 1u, 30i, 7.2 minutes.
*Player saves for and buys upgrade. 20g 2u 45i 8.1 minutes.
*Player saves to get 10 more gens and another upgrade. Takes 1.7 minutes. 30g 3u 100i 9.8 minutes.
*10 more gens, 1 more upg. Takes 1.3 minutes. 40g 4u 200i 11.1 minutes.
*10 more gens, 1 more upg. Takes 1.1 minutes. 50g 5u 375i 12.2 minutes.
*Again. Takes 1 minute. 60g 6u 675i 13.2 minutes.
*Again. Takes 1 minute. 70g 7u ~1200i. 14.2 minutes.
*Again. Takes 1 minute. 80g 8u ~2050i. 15.2 minutes.
*Player gets wise, buys more gens than upgs because the upgs cost a lot to save for. Buys 25% of total generators each second, increasing generators 1000 fold every 31 seconds. Does this for 2 minutes. 34 trillion generators, 8 upgrades, 87 trillion income, 17.2 minutes.
*Player also starts buying upgrades to supplement this, and within 3 minutes has exceeded the maximum numbers that javascript can handle. 20 minutes in, the game has completely exploded, and the player quits.
*Conclusion: Flat costs with exponential upgrades goes completely bananas. The game is short and exploded quickly without optimal play.

Someone else can explain, or if people are really interested, I can play out some scenarios for linear and/or exponential cost.

/r/incremental_games Thread