  We show that infinite divisibility of a trading commodity leads to a
self-sustained price bubble when traders use adaptive investment strategies.
The adaptive strategy can be viewed as a psychological response of a trader to
the situation when the trader's estimation of future prices does not match the
actual, realized price. We use a multi-agent model to illustrate the price
bubble formation and to quantify its main statistical properties such as the
return, the volatility, and the systematic risk of the price bubble to crash.
We discuss the plausibility for bubbles to drive prices of digital currencies.
