  In this paper, we study distributionally risk-receptive and distributionally
robust (or risk-averse) multistage stochastic mixed-integer programs (denoted
by DRR- and DRA-MSIPs). These frameworks are useful for optimization problems
under uncertainty where the focus is on analyzing outcomes based on multiple
decision-makers' differing perspectives, such as interdiction problems that are
attacker-defender games having non-cooperative players. We present cutting
plane-based and reformulation-based approaches for solving DRR- and DRA-MSIPs
without and with decision-dependent uncertainty to optimality. We show that
these approaches are finitely convergent with probability one. Furthermore, we
introduce generalizations of DRR- and DRA-MSIPs by presenting multistage
stochastic disjunctive programs and algorithms for solving them. To assess the
performance of the algorithms for DRR- and DRA-MSIPs, we consider instances of
distributionally ambiguous multistage maximum flow and facility location
interdiction problems that are important in their own right. Based on our
computational results, we observe that the cutting plane-based approaches are
2800% and 2410% (on average) faster than the reformulation-based approaches for
the foregoing instances with distributional risk-aversion and
risk-receptiveness, respectively. Additionally, we conducted out-of-sample
tests to showcase the significance of the DRR framework in revealing network
vulnerabilities and also in mitigating the impact of data corruption.
