Finding the Nash Equilibria of games

Provides classes for describing Normal Form Games and Polymatrix Games and provides many useful methods on them.

Implements the ADIDAS algorithm proposed by the paper: Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent https://doi.org/10.48550/arXiv.2106.01285

Implements Howson's algorithm for finding equilibrium in a Polymatrix Game by solving a LCP. Utilizes methods from QuantEcon. All other Python implementations so far seem to only support Bimatrix Games. GameTracer has an implementation in C.

Howson's paper: Equilibria of Polymatrix Games https://www.jstor.org/stable/2634798

Makes our LCP solver compatible with JAX so that we can try to use automatic differentiation on it. We then use the solver as a layer in a neural network.

Converts our LCP into QP form but games in general do not lead to nice QPs. We try a couple of QP solvers.

Uses InferOpt to wrap our LCP solver and puts it into a Neural Network where we combine it with our own loss estimater and loss gradients to optimise the Neural Network to predict Polymatrix approximations of Normal Form Games. This is novel