The Evolution of Coercive Institutional Punishment

Dynamic Games and Applications, Forthcoming

16 Pages Posted: 7 May 2011 Last revised: 16 May 2011

See all articles by Alexander Isakov

Alexander Isakov

affiliation not provided to SSRN

David G. Rand

Massachusetts Institute of Technology (MIT)

Date Written: March 29, 2011


Institutional punishment plays a central role in human societies. Yet research in evolutionary game theory has focused almost exclusively on peer punishment. Here we present a model for the evolution of institutional punishment. We consider a set of states ('kingdoms'), each consisting of a number of individuals ('subjects') and a single leader ('king'). Subjects choose how much to pay to the king as tribute. The king chooses how much to punish his subjects based on their tribute payment level, in an effort to exact as much tribute as possible. We find the existence of both coercive Nash equilibria with punishment and high tribute payments, and non-coercive Nash equilibria with no punishment and no tribute payments. We also examine stochastic co-evolutionary dynamics using agent based simulations. We find that within a single state, the more intensely kings punish, the more subjects evolve to pay in tribute. The king earns the most when punishment is strong and subjects are accurate in their learning. When we consider evolution occurring at the level of the king as well as the subject, we see that kings evolve to punish heavily, as long as subjects are sufficiently accurate and frequent in their learning. If citizens have error-prone learning and/or are slow to update their strategies, however, selection leads to kings who punish little. Thus confusion is collectively beneficial for subjects. In sum, we show circumstances under which natural selection can favor the emergence of institutional punishment as a tool of coercion.

Keywords: Institutional punishment, Evolutionary game theory, Coercion, Cooperation, group selection

Suggested Citation

Isakov, Alexander and Rand, David G., The Evolution of Coercive Institutional Punishment (March 29, 2011). Dynamic Games and Applications, Forthcoming. Available at SSRN:

Alexander Isakov

affiliation not provided to SSRN

David G. Rand (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States


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