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On Agent Failures in Totally Balanced Cooperative Games

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Cooperative game theory is used to analyze how selfish agents, who must cooperate to achieve their goals, might work together and share the resulting gains. One prominent solution concept, known as the core, requires that no subset of agents should have any incentive to defect and work on its own. Existential and computational questions regarding the core are widely studied in the literature. However, most models assume that all the agents would always be able to fill their role and that there are no failures. This is hardly the case in reality. The recent model of the reliability extension formalizes the notion of independent agent failures in cooperative games.

In this talk, I will use this model to demonstrate the effect of such failures on the class of totally balanced games and the more specific subclass of convex games. Totally balanced games are games where the core is non-empty in every subgame. I will show that totally balanced games remain totally balanced even under failures. I will then present an algorithm to compute such a core solution. These results lead to some interesting discoveries regarding the effect of failures on existence of the core.

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