Muhammad Najib - "From Polyhedron to Verification: Geometrical Reasoning in Cooperative Multi-Player Mean-Payoff Games"

Concurrent multi-player mean-payoff games serve as important models for multi-agent systems with quantitative individual goals. These games have been extensively studied in non-cooperative settings, for example, using Nash equilibrium. This talk, however, explores an alternative setting: what happens if cooperation is possible? This setting is particularly relevant for cooperative AI systems, as it allows for the modelling of cooperation among agents, even when their goals do not fully align. First, we present a characterisation of cooperative game solution concept called the core using discrete geometry techniques and establish a necessary and sufficient condition for its non-emptiness. Second, we utilise this characterisation to demonstrate the existence of polynomial witnesses in the core. Finally, we leverage this existence to address key decision problems in rational verification.


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