Parents can legally take things away

Can my parents take something away from me?

Yes, your parents are allowed to. If your parents bought the PSP, it is their property anyway. If you have bought the PSP, this is what you get from your pocket money:

The wording of ยง110 BGB

"A contract concluded by the minor without the consent of the legal representative is considered effective from the start if the minor carries out the contractual performance with means that have been made available to him for this purpose or at free disposal by the representative or with his consent by a third party are."

The pocket money paragraph regulates that children are free to use their pocket money and that they can do whatever they want with it - but only with the consent of their parents. The same applies to money given to children by relatives or acquaintances for their wallets with the consent of their parents.
Allowed and prohibited pocket money purchases

However, children are not allowed to buy everything with their pocket money. On the one hand, children under the age of seven are in principle not legally competent. So any purchases you make do not count. Your parents can bring back what you bought if they do not agree to the purchase.
Children and young people under the age of 18 have only limited legal capacity. This means that they are also not allowed to make certain purchases. That applies to
all purchases that require a written contract, including installment purchases.
all products that children and young people are not allowed to own by law, i.e. alcohol, cigarettes, weapons.
all things that are so expensive that a child / adolescent cannot pay for them with normal pocket money.
No determination of the height

Nowhere is it specified how much money children and young people can shop for. And since saving is allowed, elementary school students may also have higher amounts at their disposal.
The pocket money paragraph was not created so that parents can bring what they have bought back to the store after their children's major purchases - because they find the purchase senseless or because their child has changed his mind afterwards.
Thanks to the pocket money paragraph, it is easier for children to do small, everyday business and learn how to handle their money. In the case of expensive purchases, the seller can still require parental consent. Parents can also cancel the purchase later.
Incidentally, higher amounts of money won by a child are not covered by the pocket money paragraph. This money belongs to the minor. However, he may not freely dispose of it but only with the consent of his parents or the legal representative.