Coalition Tolerance to Multiple Failures of Its Members

The paper deals with coalitions whose members are unselfish. Coalition members do their best to complete the arising tasks, and do not expect to receive a reward. A coalition member can be an entity such as a social or governmental organization, a military unit, or a complex technical device such as an autonomous robot, or any other entity that has the capabilities, willingness, and ability to cooperate. The paper considers the non-redundant coalitions, which have only those coalition members without whom they cannot perform the tasks. In the paper, we consider only the situations when substitution of failed coalition members is impossible. A coalition tolerates the failure of its members by using the surplus of coalition capabilities. In our research, coalition capabilities are understood as resources and services (e.g., materials, energy, power etc.). During the execution of tasks, one or more members of the coalition may fail. The paper uses the probability of the event that the coalition tolerates the failures of its members to evaluate the coalition fault tolerance. A method is proposed for determining the coalition fault tolerance in the case of multiple member failures. Complexity of the proposed method and its applicability are assessed.