  Cooperative games model the allocation of profit from joint actions,
following considerations such as stability and fairness. We propose the
reliability extension of such games, where agents may fail to participate in
the game. In the reliability extension, each agent only "survives" with a
certain probability, and a coalition's value is the probability that its
surviving members would be a winning coalition in the base game. We study
prominent solution concepts in such games, showing how to approximate the
Shapley value and how to compute the core in games with few agent types. We
also show that applying the reliability extension may stabilize the game,
making the core non-empty even when the base game has an empty core.
