This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS(F) generated by a finite family of Lipschitz maps on a compact ball of Rn with the weak average contraction condition and show that it admits a quasi-attractor satisfying the deterministic chaos game. In particular, these properties are preserved under small perturbations of the iterated function system IFS(F) with respect to the Lipschitz topology.

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