Strategic Interaction in Trend-Driven Dynamics
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We propose a discrete-time stochastic dynamics for a system of many interacting agents. At each time step agents aim at maximizing their individual payoff, depending on their action, on the global trend of the system and on a random noise; frictions are also taken into account. The equilibrium of the resulting sequence of games gives rise to a stochastic evolution. In the limit of infinitely many agents, a law of large numbers is obtained; the limit dynamics consist in an implicit dynamical system, possibly multiple valued. For a special model, we determine the phase diagram for the long time behavior of these limit dynamics and we show the existence of a phase, where a locally stable fixed point coexists with a locally stable periodic orbit.
KeywordsMean-field interaction Multi-agent models Phase transition Strategic games
Special thanks go to Fulvio Fontini for the fruitful discussions. The authors, also, thank Roberto Casarin, Gustav Feichtinger, Marco LiCalzi, Antonio Nicolò and Paolo Pellizzari. The authors acknowledge the financial support of the Research Grant of the Ministero dell’Istruzione, dell’Università e della Ricerca: PRIN 2008, Probability and Finance, and PRIN 2009, Complex Stochastic Models and their Applications in Physics and Social Sciences. We are responsible for all the remaining errors.
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