  We consider decentralized stochastic multi-armed bandit problem with multiple
players in the case of different communication probabilities between players.
Each player makes a decision of pulling an arm without cooperation while aiming
to maximize his or her reward but informs his or her neighbors in the end of
every turn about the arm he or she pulled and the reward he or she got.
Neighbors of players are determined according to an Erdos-Renyi graph with
which is reproduced in the beginning of every turn. We consider i.i.d. rewards
generated by a Bernoulli distribution and assume that players are unaware about
the arms' probability distributions and their mean values. In case of a
collision, we assume that only one of the players who is randomly chosen gets
the reward where the others get zero reward. We study the effects of
connectivity, the degree of communication between players, on the cumulative
regret using well-known algorithms UCB1, epsilon-Greedy and Thompson Sampling.
