diff --git a/python/tests/test_5_simulation.py b/python/tests/test_5_simulation.py
new file mode 100644
index 000000000..c23636c8c
--- /dev/null
+++ b/python/tests/test_5_simulation.py
@@ -0,0 +1,140 @@
+import pytest
+
+
+@pytest.fixture
+def relay():
+    return Relay()
+
+
+def repr_peers(peers):
+    return ",".join(p.id for p in peers)
+
+
+class Relay:
+    def __init__(self):
+        self.peers = []
+
+    def make_peers(self, num):
+        newpeers = [Peer(relay, i) for i in range(num)]
+        self.peers.extend(newpeers)
+        return newpeers
+
+    def receive_all(self):
+        for peer in self.peers:
+            drain_mailbox(peer)
+
+    def assert_same_members(self):
+        peers = list(self.peers)
+        for peer1, peer2 in zip(peers, peers[1:]):
+            print(f"checking {peer1.id}.members == {peer2.id}.members")
+            assert peer1.members == peer2.members
+            nums = repr_peers(peer1.members)
+            print(f"{peer1.id} and {peer2.id} have same members {nums}")
+
+
+class Message:
+    def __init__(self, sender, recipients, msgtype, payload):
+        self.sender = sender
+        self.recipients = recipients
+        self.msgtype = msgtype
+        self.payload = payload
+
+    def __repr__(self):
+        nums = repr_peers(self.recipients)
+        return f"<Message {self.sender.id}->{nums} {self.msgtype} {self.payload}"
+
+
+class Peer:
+    """A peer in a group"""
+
+    def __init__(self, relay, num):
+        self.relay = relay
+        self.id = f"p{num}"
+        self.members = set()
+        self.mailbox = []
+
+    def __eq__(self, other):
+        return self.id == other.id
+
+    def __hash__(self):
+        return int(self.id[1:])
+
+    def add_member(self, newmember):
+        self.members.add(newmember)
+        send_message(sender=self, msgtype="addmember", newmember=newmember)
+
+    def del_member(self, member):
+        send_message(sender=self, msgtype="delmember", member=member)
+        self.members.remove(member)
+
+    def send_chatmessage(self):
+        send_message(sender=self, msgtype="chatmessage")
+
+    def __repr__(self):
+        return f"<Peer {self.id} members={repr_peers(self.members)}>"
+
+
+def send_message(sender, msgtype, **payload):
+    msg = Message(sender, list(sender.members), msgtype, payload)
+    for peer in sender.members:
+        peer.mailbox.append(msg)
+
+
+def create_group(peers):
+    for peer in peers:
+        peer.members.update(peers)
+
+
+### Naive Algorithm for processing group membership message
+
+
+def drain_mailbox(peer):
+    while peer.mailbox:
+        msg = peer.mailbox.pop(0)
+        if msg.msgtype == "addmember":
+            peer.members.add(msg.payload["newmember"])
+            peer.members.update(msg.recipients)
+        elif msg.msgtype == "delmember":
+            member = msg.payload["member"]
+            if member in peer.members:
+                peer.members.remove(member)
+        elif msg.msgtype == "chatmessage":
+            peer.members.update(msg.recipients)
+
+
+### Tests
+
+
+def test_add_and_remove(relay):
+    p0, p1, p2, p3 = relay.make_peers(4)
+
+    create_group([p0, p1])
+    assert p0.members == p1.members
+    assert not p2.members and not p3.members
+
+    p0.add_member(p2)
+    p0.add_member(p3)
+    relay.receive_all()
+    relay.assert_same_members()
+
+    p3.del_member(p0)
+    relay.receive_all()
+    relay.assert_same_members()
+
+
+def test_concurrent_add(relay):
+    p0, p1, p2, p3 = relay.make_peers(4)
+
+    create_group([p0, p1])
+    assert not p2.members and not p3.members
+    # concurrent adding and then let base set send a chat message
+    p1.add_member(p2)
+    p0.add_member(p3)
+
+    # now p0 and p1 send a regular message
+    p0.send_chatmessage()
+    p1.send_chatmessage()
+    relay.receive_all()
+    p0.send_chatmessage()
+    relay.receive_all()
+    relay.assert_same_members()