An example of a game which is at the same time zero-sum and potential.
# game-theory, learning-in-games
Just some quick notes on orthogonal projections onto regular level sets from a linear-algebraic and a differential point of view.
➡️ A Quick Note On Orthogonal Projections
# geometry
An exercise on submanifolds arising as regular level sets of smooth maps1.
J. M. Lee, Introduction to Smooth Manifolds, 2nd ed. in Graduate Texts in Mathematics. Springer-Verlag New York, 2012. ↩
➡️ An Exercise On Regular Level Sets
# geometry
A key property of Nash equilibria in normal form games is that all players are indifferent among all of their supported choices.
➡️ Slope Strategies And Nash Equilibria Folk Results
# game-theory
In a finite game in normal form, if iterative elimination of weakly dominated strategies leads to a unique pure actions profile, then such action profile is a Nash equilibrium.
➡️ Iterative Elimination Of Dominated Strategies And Nash Equilibrium
# game-theory
Let’s compute the volume of the probability simplex with respect to the Shahshahani metric.
➡️ Shahshahani Volume Of The Probability Simplex
# geometry
Riemannian game dynamics are dynamics for one-population games induced by the payoff vector field. Under some circumstances, such dynamics display Hamiltonian properties.
➡️ Hamiltonian Riemannian Game Dynamics
# project
The space of finite normal form games admits a non-canonical direct sum decomposition into the subspaces of non-strategic, potenti, and harmonic games, closely related to the discrete Hodge 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 In Games
# project