Algorithms

Ramo currently contains more than 10 different algorithms capable of computing or learning (approximate) equilibria in multi-objective games. The following tables give an overview of our current algorithms, the equilibria they aim to find and the utility functions they support.

Computing Equilibria

The following table gives an overview of the current algorithms for computing equilibria from a given MONFG and utility functions.

Algorithm	Equilibrium	Utility functions
MOSE	Pure-strategy Nash equilibria	All
MOQUPS	Pure-strategy Nash equilibria	Quasiconvex

Learning Algorithms

This table show the learning algorithms currently included in Ramo. Please note that only the iterated best-response and fictitious play algorithms get access to their full individual payoff matrices. All other algorithms have to learn the payoffs together with an optimal strategy.

Algorithm	Equilibrium	Utility functions
Iterated best-response	Nash equilibrium	All
Fictitious play	Nash equilibrium	All
Independent Q-learners	Nash equilibrium	All
Independent actor-critic learners	Nash equilibrium	All
Joint-action Q-learners	Nash equilibrium	All
Joint-action actor-critic learners	Nash equilibrium	All
Cooperative action communication	Nash equilibrium	All
Self-interested action communication	Nash equilibrium	All
Cooperative policy communication	Nash equilibrium	All
Hierarchical communication	Nash equilibrium	All
Non-stationary agent	Leadership equilibrium	All
Best-response agent	Leadership equilibrium	All