Modeling participation behavior in repeated task allocations with fuzzy connectives

In task allocation problems one usually only considers a single round in which players participate. In practice, many allocation problems are of repeated nature, in which players can decide to keep participating or leave. Players' participation, or behavior, influences the outcome, or social welfare, of these problems. In this paper, we use a fuzzy connective to model agents' behavior in regard to their perception of the game, i.e., optimism level, based on their experiences thus far. We conduct simulations to investigate the interactions between the agents' participation behaviors and the outcomes of the task allocations in multiple rounds. We compare two task allocation algorithms, one merely focusing on costs, and the other focusing on both fairness in the allocation and costs. The results show that the fairer algorithm makes agents more optimistic, and in return, agents keep participating in the allocation game. This leads to a higher social welfare in the long run compared to the cost-minimization algorithm.

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