An example of hierarchical conditional-logistic Bayesian estimation, applied to punishment choice in a public goods game.

Conditional-logistic regression and softmax regression (a.k.a. multinomial logit regression) are covered in Chapter 22 of DBDA2E, but no examples of hierarchical versions are given in that chapter. An example of hierarchical conditional-logistic Bayesian estimation, applied to punishment choice in a public goods game, is provided in a new article. The appendix of the article (linked below) provides complete details of the model.

Abstract: Punishment is an important method for discouraging uncooperative behavior. We use a novel design for a public goods game in which players have explicit intended contributions with accidentally changed actual contributions, and in which players can apply costly fines or ostracism. Moreover, all players except the subject are automated, whereby we control the intended contributions, actual contributions, costly fines, and ostracisms experienced by the subject. We assess subject’s utilization of other players’ intended and actual contributions when making decisions to fine or ostracize. Hierarchical Bayesian logistic regression provides robust estimates. We find that subjects emphasize actual contribution more than intended contribution when deciding to fine, but emphasize intended contribution more than actual contribution when deciding to ostracize. We also find that the efficacy of past punishment, in terms of changing the contributions of the punished player, influences the type of punishment selected. Finally, we find that the punishment norms of the automated players affect the punishments performed by the subject. These novel paradigms and analyses indicate that punishment is flexible and adaptive, contrary to some evolutionary theories that predict inflexible punishments that emphasize outcomes. Keywords: punishment, public goods game, ostracism, trembling-hand, intention, outcome bias.

Liddell, T. M., and Kruschke, J. K. (2014). Ostracism and fines in a public goods game with accidental contributions: The importance of punishment type. Judgment and Decision Making, 9(6), 523-547. The article is here (http://journal.sjdm.org/14/14721a/jdm14721a.pdf).