## 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 maps^{1}.

➡️ 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