Abstract
A usual assumption in the hedonic games literature is that of complete information; however, in the real world this is almost never the case. As such, in this work we assume that the players’ preference relations are hidden: players interact within an unknown hedonic game, of which they can observe a small number of game instances. We adopt probabilistic topic modeling as a learning tool to extract valuable information from the sampled game instances. Specifically, we employ the online Latent Dirichlet Allocation (LDA) algorithm in order to learn the latent preference relations in Hedonic Games with Dichotomous preferences. Our simulation results confirm the effectiveness of our approach.
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Notes
- 1.
We have preliminary results showing our approach can be quite effective in even more complex settings.
- 2.
The number of agents participating in each \(\varvec{\phi }_i\), along with the total number of formulae per agent within each level of complexity environment were chosen so that the required dataset could be generated within a reasonable time frame; these numbers do not impose any burden on the LDA algorithm itself.
- 3.
For practical reasons, the logged information is repeated more than once within a document. That is, we boost the term frequency of the agents’ indicative words, and the characterization’s ‘gain’/‘loss’, to avoid misleading words with low frequencies.
- 4.
As we have already mentioned, there is no stochasticity during the dataset creation. However, by employing this repetition of the learning procedure per game, we ensure the robustness of our results.
- 5.
A larger number of topics allows for more preferences sub-formulae to be learned, but it naturally increases complexity.
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We thank Michalis Mamakos for code sharing.
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A Appendix: Detailed Results
A Appendix: Detailed Results
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Georgara, A., Ntiniakou, T., Chalkiadakis, G. (2019). Learning Hedonic Games via Probabilistic Topic Modeling. In: Slavkovik, M. (eds) Multi-Agent Systems. EUMAS 2018. Lecture Notes in Computer Science(), vol 11450. Springer, Cham. https://doi.org/10.1007/978-3-030-14174-5_5
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