All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Many scholars held that the basic principle is that it is permissible for young children to play with toys and that this is excluded from the prohibited image-making. It has been narrated that ʻAa'ishah said, "I used to play with dolls in the presence of the Prophet, and my girlfriends also used to play with me. When the Messenger of Allaah used to enter (my house), they would hide from him, but he would call them to come and play with me." [Al-Bukhari and Muslim]
You asked whether it is allowed for the children themselves to enact it without toys so that they joust or run away and catch each other; perhaps you mean that they act these roles out. If this is what you mean, then you should know that some scholars deemed it impermissible for the Muslim to enact the role of a disbeliever (kaafir) or a dissolute (faasiq). Shaykh Ibn ʻUthaymeen wrote, "Some examples on the prohibitions as far as acting is concerned are: depicting the role of a non-Muslim or a dissolute sinner because it is feared that this would negatively impact his heart; he may recall someday that he had depicted the role of a non-Muslim and Satan would exploit this to whisper to him..."
The Muslim is responsible for the people under his care; he is obliged to take good care of those under his guardianship and shield them against harms. Allaah, The Exalted, says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones...} [Quran 66:6]
Ibn ʻUmar narrated that the Prophet said, "...man is a guardian and responsible for his family..." [Al-Bukhari and Muslim]
Al-Qaadhi Abu Bakr ibn Al-ʻArabi wrote:
"A child is a trust in his parents' hands and his pure heart is a priceless, raw, unpolished gem ready to be shaped and formed. Children are born as blank slates, ready to absorb whatever is given to them. If good is instilled in the child’s heart and he is accustomed to doing good things during his upbringing, then he will attain happiness in this worldly life and the Hereafter. His parents, teachers, and mentors share the rewards of the child’s righteousness. On the contrary, when the child is imbued with evil and becomes accustomed to it and is neglected, he will be one of the wretched and will be ruined. In this case, the parents and those responsible for him bear the sin for that. Just as parents would guard their child against worldly fire, they should guard him against the Hellfire in the Hereafter for a greater reason. This can be achieved through giving children a good education, disciplining them, and teaching them good manners as well as protecting them from evil of bad friends…"
Allaah knows best.