This paper investigates the relationship between market overconfidence and occurrence of stock-price bubbles. Sixty participants traded stocks in ten experimental asset markets. Markets were constructed on the basis of subjects' overconfidence, measured in pre-experimental sessions. The most overconfident subjects form 'overconfident markets', and the least overconfident subjects 'rational markets'. Prices in rational markets tend to track the fundamental asset value more accurately than prices in overconfident markets and are significantly lower and less volatile. Additionally we observe significantly higher bubble measures and trading volume on overconfident markets. Altogether, our data provide evidence that overconfidence has strong effects on prices and trading behavior in experimental asset markets.