We analyze a coordination game with information-constrained players. The players' actions are based on a noisy compressed representation of the game's payoffs in a particular case, where the compressed representation is a latent state learned by a variational autoencoder (VAE). The VAE is trained over a finite sample of past experiences, and is optimized to trade off the average payoff obtained over a distribution of possible games against the reconstruction error involved in predicting game payoffs on the basis of the latent state. Our use of the average payoff in the training objective requires us to generalize the basic VAE framework of Kingma and Welling (2014); we also compare our proposal to rationally inattentive decision making as modeled by Sims (2003) and Yang (2015). We apply our model to the coordination game in the experiment of Frydman and Nunnari (2022), and show that it offers an explanation for two salient features of the experimental evidence: both the gradual adjustment of the players' action probabilities with changes in the game payoffs, and the dependence of the degree of stochasticity of players' choices on the range of game payoffs encountered on different trials. Our approach also provides an account of the way in which play should gradually adjust to a change in the distribution of game payoffs that are encountered, offering an explanation for the history-dependent play documented by Arifovic et al. (2013). * We thank Francesco Grechi for help exploring the numerical properties of VAE models,