SI: Nax and Perc on the replication of coalitionally beneficial behaviour by individual mistakes

In this paper published in Scientific Reports, Heinrich Nax and Matjaz Perc discuss naive learning in public goods games. They examine a situation in which simultaneous mistakes by multiple players can end up benefiting the mistake making players. For example, it could be the case that 3 players make mistakes and play a myopically suboptimal action, but that because they make mistakes simultaneously they gain payoff from these mistakes.

Hence, profitable coalitional moves are replicated by the mistakes of individuals. To replicate coalitional moves by larger numbers of players will require a larger number of mistakes and so such moves will be relatively less likely. This is similar to the assumption made in Newton (2012, paper, web), although in the cited paper it is an assumption, whereas in Nax and Perc it emerges endogeneously as described above.

A Nash equilibrium is k-strong if there exists no profitable coalitional deviation for a coalition of any size up to and including k  (see the paper under discussion or Newton & Angus, 2013). The authors show that behaviour under naive learning depends on the k-strength of the equilibria in their model (i.e. on the value of for which equilibria are k-strong).

Read the full paper here.