Table 1 

Meaning of symbols  
Symbol  Meaning 
M  Number of groups 
θ  Probability that a donor and recipient in a oneshot game are in the same group 
r∈{G, B}^{M}  Reputation vector of a player in the eyes of M observers 
p_{k}(r)  Probability that a player in group k has reputation vector r 
p_{−k}(r)  Probability that a player outside group k has reputation vector r 
σ(r)∈{C, D}  Donor’s action to a recipient having reputation r∈{G, B} 
Φ_{r}(a,r^{′})  Probability that an observer assigns reputation r∈{G, B} to a donor selecting action a∈{C, D} to a recipient having reputation r^{′}∈{C, D} 
p_{in}(r)  Probability that a player in the eyes of an ingroup observer has reputation r 
p_{out}(r)  Probability that a player in the eyes of an outgroup observer has reputation r 
Nakamura and Masuda
Nakamura and Masuda BMC Evolutionary Biology 2012 12:213 doi:10.1186/1471214812213