J Stat Phys (2018) 172:279–292
https://doi.org/10.1007/s10955-017-1873-0
Risk and Interaction Aversion: Screening Mechanisms
in the Prisoner’s Dilemma Game
Gabriel A. Canova
1
· Jeferson J. Arenzon
1
Received: 2 August 2017 / Accepted: 29 August 2017 / Published online: 4 September 2017
© Springer Science+Business Media, LLC 2017
Abstract When the interactions between cooperators (C) and defectors (D) can be partially
avoided within a population, there may be an overall enhancement of cooperation. One
example of such screening mechanism occurs in the presence of risk-averse agents (loners,
L) that are neutral towards others, i.e., both L and its opponent, whatever its strategy, receive
the same payoff. Their presence in the Prisoner’s Dilemma (PD) game sustains the coexistence
of cooperators and defectors far beyond the level attained in their absence. Another screening
mechanism is a heterogeneous landscape obtained, for example, by site diluting the lattice. In
this case, cooperation is enhanced with some fraction of such inactive, interaction-averse sites.
By considering the interplay of both mechanisms, we show that there is an explosive increase
in the range of densities, just above the percolation threshold, where neutrality is prevented
and loners become extinct, the behavior reverting to the pure PD game. Interestingly, this
occurs despite defectors being usually abundant in that region. This has to be compared with
the corresponding loner-free region in the undiluted case that, besides being very small, is
dominated by cooperators.
Keywords Game theory · Prisoner’s Dilemma · Voluntary participation
1 Introduction
Risk-sensing is a useful resource [20,28,29,66] while foraging in changing environments
or when deciding the best strategy during a dispute. When participation is not compulsory,
withdrawing from a conflict may have several purposes [29], like an easy way out, the imposi-
tion of some punishment to the opponent or just avoiding a costly situation [3]. Evolutionary
B
Jeferson J. Arenzon
arenzon@if.ufrgs.br
Gabriel A. Canova
gabrielcauz@gmail.com
1
Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051,
Porto Alegre, RS 91501-970, Brazil
123
@Phil_Robichaud
@deepthiw
@JoseServera