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- Working Paper
We introduce a new game-theoretic framework for modelling dynamic interactions in a large population of anonymous agents. The behavior of an agent in an interaction depends on a time-homogeneous type and a time-varying state, which characterize the agent's available actions and motifs. We consider finite type, state, and action spaces. On the individual agent level, the state evolves in discrete time as the agent participates in interactions, in which the state transitions are affected by the agent's individual action and the distribution of other agents' states and actions. On the societal level, we consider that the agents form a continuum of mass and that the interactions occur asynchronously, and derive a continuous time model for the evolution of the societal state distribution. We characterize the stationary equilibrium as the solution concept in our games, which is a condition where all agents are playing their best response, and further the societal state distribution is stationary. A stationary equilibrium is guaranteed to exist in every dynamic population game. Our framework intersects with previous works on anonymous sequential games, mean-field games and Markov decision evolutionary games, but is novel in how we relate our dynamic setting to classical, static population games. In particular, we show a reduction of stationary equilibria in dynamic population games to standard Nash equilibria in classical population games. This inspires us to formulate an evolutionary model for the coupled dynamics of both the agents' actions and states Show more
Organisational unit02650 - Institut für Automatik / Automatic Control Laboratory
02619 - Inst. Dynam. Syst. u. Regelungstechnik / Inst. Dynamic Systems and Control
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