Multilevel Hidden Markov Models for Behavioral Data: A Hawk-and-Dove Experiment

Motivated by the analysis of behavioral data taken from an economic experiment based on the Hawk-and-Dove game, this article describes a multilevel hidden Markov model, that includes covariates, autoregression, and endogenous initial conditions under a unified framework. The data at hand are affected by multiple sources of latent heterogeneity, due to multilevel unobserved factors that operate in conjunction with observed covariates at all the levels of the data hierarchy. We fit a multilevel logistic regression model for repeated measurements of player behaviors, nested within groups of interacting players. The model integrates discrete random effects at the group level and Markovian sequences of discrete random effects at the player level. Parameters are estimated by a computationally feasible expectation-maximization algorithm. We model the probability of playing the Hawk strategy, which implies fighting aggressively for controlling an asset, and test the role played by initial possession, property, and other player-specific characteristics in driving hawkish behaviors. The results from our study suggest that crucial factors in determining hawkish behavior are both the way possession is achieved - which depends on our treatment manipulation- and possession itself. Furthermore, a clear time-dependence is observed in the data at the player level as accounted for by the Markovian random effects.