Table 1.

Meaning of symbols

Symbol	Meaning
M	Number of groups
θ	Probability that a donor and recipient in a one-shot game are in the same group
r∈{G, B}M	Reputation vector of a player in the eyes of M observers
pk(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}
Φr(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}
pin(r)	Probability that a player in the eyes of an ingroup observer has reputation r
pout(r)	Probability that a player in the eyes of an outgroup observer has reputation r