A deep neural network to find Nash equilibria of normal-form stage games. The network can be trained for a specific number of players and game shapes (symmetric and asymmetric).

NashNet is a supervised deep neural network that is trained with normal-form stage games and their Nash equilibria to predict the equilibria in new games. The network can be trained for a specific game shape. The shape of the game, however, can be symmetric or asymmetric. The games can also have any number of players. The number of generated equilibria can be one or any desired number based on the settings in the training time.

The loss function and the network architecture are designed in a way that if more than one equilibrium is being generated, they do not replicate each other and try to cover all the true Nash equilibria of the input game. The loss function is following a max-min strategy and the architecture has multiple heads. Because there can be fewer number of Nash equilibria for a game than the generated ones, to combine possibly redundant predictions, the predictions of the neural network are clustered through the DBSCAN method.

More detailed descriptions are added after the pending papers are published.

NashNet is written in Python, using the Tensorflow 2.1, Keras, and Scikit-learn libraries. To generate the datasets, the Gambit library is used to find the true output values (Nash equilibria) of the regressor network.

The source code can be found under the src directory. To start the training and subsequent testing, run the Run.py. It uses the configurations stored in the Config folder. The trained models are stored in the Model directory, with the model snapshots during the training inside the Model/Interim folder. At the end of the training and testing, the respective report files are saved in the Reports folder.

The file run.sh is designed to run the Run.py multiple times with different training and testing configurations, for which they are stored under the Configs directory. When running the run.sh, the trained models and final test and training reports, with their directory structure, are all saved under the Results folder.

Pourya Hoseini, Dustin Barnes, and Tapadhir Das

Copyright 2019 - 2020, Pourya Hoseini, Dustin Barnes, Tapadhir Das, and the NashNet contributors. Any usage must be with the permission of the authors.

We can be reached at the following email addresses:

• Pourya Hoseini: hoseini@nevada.unr.edu
• Dustin Barnes: dkbarnes@nevada.unr.edu
• Tapadhir Das: tapadhird@nevada.unr.edu