  Two-player zero-sum games of infinite duration and their quantitative
versions are used in verification to model the interaction between a controller
(Eve) and its environment (Adam). The question usually addressed is that of the
existence (and computability) of a strategy for Eve that can maximize her
payoff against any strategy of Adam. In this work, we are interested in
strategies of Eve that minimize her regret, i.e. strategies that minimize the
difference between her actual payoff and the payoff she could have achieved if
she had known the strategy of Adam in advance. We give algorithms to compute
the strategies of Eve that ensure minimal regret against an adversary whose
choice of strategy is (i) unrestricted, (ii) limited to positional strategies,
or (iii) limited to word strategies. We also establish relations between the
latter version and other problems studied in the literature.
