Davide Legacci - Research

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Hamiltonian Riemannian Game Dynamics

Riemannian game dynamics1 are dynamics for one-population games induced by the payoff vector field. Under some circumstances, such dynamics display Hamiltonian properties2.

➡️ Hamiltonian Riemannian Game Dynamics

Geometric Aspects of Learning and Evolution in Games

The space of finite normal form games admits a non-canonical direct sum decomposition into the subspaces of non-strategic, potenti, and harmonic games3, closely related to the discrete Hodhe decomposition for simplicial complexes. I am interested in an analogue decomposition for games with continuous strategy space (concave games), and continuous population space (population games)

➡️ Geometric Aspects of Learning and Evolution in Games

  1. Mertikopoulos P, Sandholm WH (2018) Riemannian game dynamics. Journal of Economic Theory 177:315–364. 

  2. Alishah HN, Duarte P (2014) Hamiltonian evolutionary games. arXiv preprint arXiv:1404.5900

  3. Candogan O, Menache I, Ozdaglar A, Parrilo PA (2011) Flows and Decompositions of Games: Harmonic and Potential Games. Mathematics of Operations Research 36(3):474–503.