Assuming a single server, IMHO, the performance is gonna suck. This is a scenario where you need to have a big pipe to the server, and for games, probably a whompin' server as well.
Since you have 160 machines pretty much aimed at one place, through one pipe, the final aggregating segment should be as large as possible. If all of the stations are at 10, and the server-link segment is 100, you're 16 times oversubscribed on the link to the server. If each stations are 10 meg, and the server-link is a gigabit, you are only 1.6 times oversubscribed, and much more likely of getting packets through smoothly.
The next issue, in a similar vein, relates to the peripheral switches. Same scenario, 23/24 (or 47/48) ports aimed at the same exit. A gig uplink would do wunnerful things for the rapid egrees of your data. And though a switch with gig uplinks is more expensive, you could easily go to 48 port switches and not oversubscribe the uplink (assuming 10 meg stations).
Put single gig switch as a concentrator feed to the server, and you got a pretty decent setup.
Many-to-one is bad for a switch, unless the gozoutta is much bigger then the collective gozintas.
And...a collision is NOT a dropped packet. The collision occurs as the packet is transmitted, the conflicting transmitters fall back for a short (standards-defined random) time, then they give it another shot. That's why the spec syas you can only have so many hops, and limits the segment length, so the collision can be sensed in time to kill the transmission and fall back. Too many hops, or excessive segment length would allow the packet to be completely transmitted before the collision is sensed (a "Late Collision" usually shown on an analyzer as a series of A's or 5's in the captured packet).
Dropped packets are purely a phenominon of the switched or routed environment. The packet is sent, buffered, and due to (usually) high latency (like slow/busy switches, slow/busy routers, satellite transit times, etc), the packet times-out or gets dumped for priority traffic. Then the higher-level protocol (which usually takes longer than collision-fallback-retransmit) has to decide things are taking too long and crank out another packet (which is subject to the same path latencies or policies)...and hope this one gets through.
If you put a switch in the wrong place, or implement it improperly, it will amplify everything bad about your network.
FWIW / .02
Scott