Endogenous Energy Reactive Modules Games: Modelling Side Payments among Resource-Bounded Agents

We introduce Energy Reactive Modules Games (ERMGs), an extension of Reactive Modules Games (RMGs) in which actions incur an energy cost (which may be positive or negative), and the choices that players make are restricted by the energy available to them. In ERMGs, each action is associated with an energy level update, which determines how their energy level is affected by the performance of the action. In addition, agents are provided with an initial energy allowance. This allowance plays a crucial role in shaping an agent’s behaviour, as it must be taken into consideration when one is determining their strategy: agents may only perform actions if they have the requisite energy. We begin by studying rational verification for ERMGs and then introduce Endogenous ERMGs, where agents can choose to transfer their energy to other agents. This exchange may enable equilibria that are impossible to achieve without such transfers. We study the decision problem of whether a stable outcome exists under both the Nash equilibrium and Core solution concepts.