Social dilemmas describe conflict situations between immediate self-interest and longer-term collective interests. In these situations, it is better that all players work together to attain a common goal, but individuals may threaten the best payoff of the group by free-riding. Human behavior in a pandemic is one example of a social dilemma but wait-and-see games and relying on herd immunity to get a free ride generates a threat of continuing the pandemic. This study aims to use probabilistic incentives given by a third party as a mechanism to inhibit free-riding behavior by promoting cooperation in the volunteer dilemma game. For more realistic human behavior simulation, we use an agent-based model of network topology. When the parameters of the problem change gradually, an abrupt jump in the cooperation rate may happen and lead to a significant shift in the outcome. Catastrophe theory is a valuable approach to survey these nonlinear changes. This study tries to give some managerial insights to the decision-makers to find the minimum level of necessary effort in which the cooperation dominates the defection.