  A $d$-defective $k$-painting game on a graph $G$ is played by two players:
Lister and Painter. Initially, each vertex is uncolored and has $k$ tokens. In
each round, Lister marks a chosen set $M$ of uncolored vertices and removes one
token from each marked vertex. In response, Painter colors vertices in a subset
$X$ of $M$ which induce a subgraph $G[X]$ of maximum degree at most $d$. Lister
wins the game if at the end of some round there is an uncolored vertex that has
no more tokens left. Otherwise, all vertices eventually get colored and Painter
wins the game. We say that $G$ is $d$-defective $k$-paintable if Painter has a
winning strategy in this game. In this paper we show that every planar graph is
3-defective 3-paintable and give a construction of a planar graph that is not
2-defective 3-paintable.
