Verification and Dynamics of Group-Based Potential Games

A class of potential-type games, called the group-based potential game, is investigated in this paper. First, the verification of the (strongly) group-based potential game is studied. Using the semitensor product, the verification can be solved by checking whether a linear equation has a solution. Second, profile dynamics are considered when the strongly group-based potential game is played on a hypergraph. It is proved that the strategies of a strongly group-based potential hyper-networked evolutionary game converge to a pure Nash equilibrium under the group-based cascading myopic best response adjustment rule. Finally, an example is provided and discussed in detail to demonstrate the theoretical result.