  Iterated regret minimization has been introduced recently by J.Y. Halpern and
R. Pass in classical strategic games. For many games of interest, this new
solution concept provides solutions that are judged more reasonable than
solutions offered by traditional game concepts -- such as Nash equilibrium --.
Although computing iterated regret on explicit matrix game is conceptually and
computationally easy, nothing is known about computing the iterated regret on
games whose matrices are defined implicitly using game tree, game DAG or, more
generally game graphs. In this paper, we investigate iterated regret
minimization for infinite duration two-player quantitative non-zero sum games
played on graphs.
  We consider reachability objectives that are not necessarily antagonist.
Edges are weighted by integers -- one for each player --, and the payoffs are
defined by the sum of the weights along the paths. Depending on the class of
graphs, we give either polynomial or pseudo-polynomial time algorithms to
compute a strategy that minimizes the regret for a fixed player. We finally
give algorithms to compute the strategies of the two players that minimize the
iterated regret for trees, and for graphs with strictly positive weights only.
