Aspiration Dynamics of Multi-player Games in Finite Populations

Studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer. In the latter case, individuals adjust their strategies based on a comparison of their payoffs from the evolutionary game to a value they aspire, called the level of aspiration. Unlike imitation processes of pairwise comparison, aspiration-driven updates do not require additional information about the strategic environment and can thus be interpreted as being more spontaneous. Recent work has mainly focused on understanding how aspiration dynamics alter the evolutionary outcome in structured populations. However, the baseline case for understanding strategy selection is the well-mixed population case, which is still lacking sufficient understanding. We explore how aspiration-driven strategy-update dynamics under imperfect rationality influence the average abundance of a strategy in multi-player evolutionary games with two strategies. We analytically derive a condition under which a strategy is more abundant than the other in the weak selection limiting case. This approach has a long standing history in evolutionary game and is mostly applied for its mathematical approachability. Hence, we also explore strong selection numerically, which shows that our weak selection condition is a robust predictor of the average abundance of a strategy. The condition turns out to differ from that of a wide class of imitation dynamics, as long as the game is not dyadic. Therefore a strategy favored under imitation dynamics can be disfavored under aspiration dynamics. This does not require any population structure thus highlights the intrinsic difference between imitation and aspiration dynamics

Semi-supervised Deep Generative Modelling of Incomplete Multi-Modality Emotional Data

There are threefold challenges in emotion recognition. First, it is difficult to recognize human's emotional states only considering a single modality. Second, it is expensive to manually annotate the emotional data. Third, emotional data often suffers from missing modalities due to unforeseeable sensor malfunction or configuration issues. In this paper, we address all these problems under a novel multi-view deep generative framework. Specifically, we propose to model the statistical relationships of multi-modality emotional data using multiple modality-specific generative networks with a shared latent space. By imposing a Gaussian mixture assumption on the posterior approximation of the shared latent variables, our framework can learn the joint deep representation from multiple modalities and evaluate the importance of each modality simultaneously. To solve the labeled-data-scarcity problem, we extend our multi-view model to semi-supervised learning scenario by casting the semi-supervised classification problem as a specialized missing data imputation task. To address the missing-modality problem, we further extend our semi-supervised multi-view model to deal with incomplete data, where a missing view is treated as a latent variable and integrated out during inference. This way, the proposed overall framework can utilize all available (both labeled and unlabeled, as well as both complete and incomplete) data to improve its generalization ability. The experiments conducted on two real multi-modal emotion datasets demonstrated the superiority of our framework.Comment: arXiv admin note: text overlap with arXiv:1704.07548, 2018 ACM Multimedia Conference (MM'18