Davide Legacci | Research Blog

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A Potential Zero Sum Game

An example of a game which is at the same time zero-sum and potential.

➡️ A Potential Zero Sum Game

# game-theory, learning-in-games

A Quick Note On Orthogonal Projections

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 Regular Level Sets

An exercise on submanifolds arising as regular level sets of smooth maps1.

  1. 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

Slope Strategies And Nash Equilibria Folk Results

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

Iterative Elimination Of Dominated Strategies And Nash Equilibrium

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

Shahshahani Volume Of The Probability Simplex

Let’s compute the volume of the probability simplex with respect to the Shahshahani metric.

➡️ Shahshahani Volume Of The Probability Simplex

# geometry

Hamiltonian Riemannian Game Dynamics

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

Geometric Aspects Of Learning 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 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