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EDIT: There is no known way to determine the source of an RKV launch, as even determining the path of an RKV launch would still force you to retaliate against every star system in the path of that RKV as a likely candidate.
EDIT #2: If an RKV is a blackbody, the only way to detect an incoming RKV would be by the gravity well it creates as it passes. It wouldn't show up on a telescope.
EDIT #3: If you want to be a peaceful civilization, the single most critical invention you will need is faster than light communication. Without it, liberal, humanistic values as we know them would simply not work on a galactic scale.
EDIT #4: Even if hitting a planet with an RKV is hard, then you have to imagine that, by the same logic, reaching it by a manned spacecraft or robotic probe is even harder, because not only do you have all the same guidance and fueling problems of an RKV, you'd also have life support problems, communications, etc. etc. Hence an RKV is still the most likely form in which we will encounter alien life.
EDIT #5: A better idea from Cascade:
+ Show Spoiler [Relativistic Kill Probes] +
The idea is a funny thought experiment, and I agree that if interstellar war works the way you describe (essentially insta-gib on first contact), evolution will favour kill-first behaviour.
why 50% of light speed though? If the civilization is very advanced, I think it is safe to assume that they can shoot at 100% light speed.
Just take a big asteroid or a chunk of a big planet or whatever, transform 1% into a laser beam and you will hit before the target can see anything.
You assume that there is no way for another civilization to defend themselves from this kind of attacks, on the basis that they wont see it coming. This is not true. The problem the killer has is that the information they have about their target is old (depending on distance, but from a few years for neighbouring stars to billions of years on the other side of the universe), and they wont hit until later in the future. ( in the rest-frame of the killer for example). You can calculate the orbit of the planet if you are good at gravity calculations, sure. But a planet can regularly manually change it's orbit randomly, for example by shooting out some ray in some direction, giving recoil. If the killer just calculates the orbit assuming the planet stays as it is, it will miss. This would completely change the picture of accurate instant kill snipes, into a picture of wild shooting and crossed fingers.
What a killer CAN do however, is to shoot a killing device, that takes up information about the target as it moves, and uses this information to adjust trajectory. This would return the picture the one originally described in the OP.
BUT: then the first civilization can do the same. This first message doesn't have to be just a "hi". It can be a killing device programmed to identify other civilizations, and kill them if they find them a threat. Then the original guys will get a report (a million years later) that the probe found this civilization and didn't trust it, so it killed it. In this way, the optimal strategy seems to be to send out a lot of almost-speed-of light probes in all direction, programmed to identify and kill threats, or if they find an empty system, to stop there, multiply, and send out 1000 new identical probes at almost speed of light. Maybe set up a warning beacon to warn the "home planet", if there even is such a planet, in case it sees a threat. Then the picture would be that of civilizations expanding like spheres in space at close to speed of light, killing (absorbing, multiplying, consuming, whatever) everything it passes. I can see the queen of blades doing this.
The winning civilizations would be the one that expands the fastest, and that can beat other probes when they encounter them. If there is such a thing as a home-planet, they will sit in the centre and get more and more delayed reports from the front as it moves out. until one day you will get a message from a beacon 25 000 light years away: "unidentified probe spotted. moving at 0.9999c. Activate defensive measures." then 3 seconds later "ERROR: DEFENCE BREACHED" then silence. Then you know that you have 2.5 more years to live, and that's the end of that civilization.
This assumes that there will be no faster-than-light BS, or workarounds like wormholes etc, but that advanced civilizations will get very close to the limit of light speed in terms of warfare.
Then what would the winning strategy be? What if a drone from a successful civilization came to earth? How will the drone do to best make sure that we don't kill them, and to as soon as possible send out new drones, and maximise defence from other incoming drones?
Answer is: I have no idea. But I doubt that we will enjoy it.
why 50% of light speed though? If the civilization is very advanced, I think it is safe to assume that they can shoot at 100% light speed.

You assume that there is no way for another civilization to defend themselves from this kind of attacks, on the basis that they wont see it coming. This is not true. The problem the killer has is that the information they have about their target is old (depending on distance, but from a few years for neighbouring stars to billions of years on the other side of the universe), and they wont hit until later in the future. ( in the rest-frame of the killer for example). You can calculate the orbit of the planet if you are good at gravity calculations, sure. But a planet can regularly manually change it's orbit randomly, for example by shooting out some ray in some direction, giving recoil. If the killer just calculates the orbit assuming the planet stays as it is, it will miss. This would completely change the picture of accurate instant kill snipes, into a picture of wild shooting and crossed fingers.
What a killer CAN do however, is to shoot a killing device, that takes up information about the target as it moves, and uses this information to adjust trajectory. This would return the picture the one originally described in the OP.
BUT: then the first civilization can do the same. This first message doesn't have to be just a "hi". It can be a killing device programmed to identify other civilizations, and kill them if they find them a threat. Then the original guys will get a report (a million years later) that the probe found this civilization and didn't trust it, so it killed it. In this way, the optimal strategy seems to be to send out a lot of almost-speed-of light probes in all direction, programmed to identify and kill threats, or if they find an empty system, to stop there, multiply, and send out 1000 new identical probes at almost speed of light. Maybe set up a warning beacon to warn the "home planet", if there even is such a planet, in case it sees a threat. Then the picture would be that of civilizations expanding like spheres in space at close to speed of light, killing (absorbing, multiplying, consuming, whatever) everything it passes. I can see the queen of blades doing this.

The winning civilizations would be the one that expands the fastest, and that can beat other probes when they encounter them. If there is such a thing as a home-planet, they will sit in the centre and get more and more delayed reports from the front as it moves out. until one day you will get a message from a beacon 25 000 light years away: "unidentified probe spotted. moving at 0.9999c. Activate defensive measures." then 3 seconds later "ERROR: DEFENCE BREACHED" then silence. Then you know that you have 2.5 more years to live, and that's the end of that civilization.
This assumes that there will be no faster-than-light BS, or workarounds like wormholes etc, but that advanced civilizations will get very close to the limit of light speed in terms of warfare.
Then what would the winning strategy be? What if a drone from a successful civilization came to earth? How will the drone do to best make sure that we don't kill them, and to as soon as possible send out new drones, and maximise defence from other incoming drones?
Answer is: I have no idea. But I doubt that we will enjoy it.
EDIT #6: People keep trying to use traditional methods of game theory and int'l relations theory to think about this. The core problem here is that all these theories rest upon the assumptions of instantaneous communication and easy identification of who is responsible for the killing. Unfortunately, across interstellar distances, both are untrue, and especially compared with how fast weapon systems themselves can move, and also especially compared with how technologically hard it is to see who is doing the killing versus breaking the agreement yourself. This is why I've avoided using math in describing this post, as any game theoretic analysis I ran here would immediately be invalid because every freaking game theory principle out there rests on people being able to talk to one another..
EDIT #7: People also talk about the "pacifist" civilizations banding together against a hostile civ. Putting aside the idea that pacifism automatically will make different intergalactic species set aside their differences to go on a mutual witch hunt, there's also the more mundane problem of how the fuck to establish an alliance or even communicate peaceful intentions when each conversation could take thousands of years, time in which the "pacifist" civilization could easily just blow you up.
EDIT #8: Please see below for a more rigorous explanation of this scenario:
+ Show Spoiler +
Your comments reflect a lack of understanding of game theory, so I offer this model based on information sets and extensive form sequential games.
Consider:
1.) Player 1 chooses to broadcast or not broadcast.
2.) Player 2 receives message and chooses whether or not to broadcast or launch a RKV.
3.) Player 1 either receives broadcast or detects RKV and decides whether to launch RKV. (this stage is a 3-fold branching. Detect response first, detect RKV first, or detect nothing)
That fully specifies an extended form game (tree structure) with all the necessary components to establish information sets given some strongly negative payoff for being dead and some presumably slightly negative payoff for having to launch an RKV, with broadcasting information being basically free. Information sets come into play in stage 3, since player 1 does not know if an RKV has been sent or not and has to make a decision based on the possibility of both situations.
The OP suggests that a SPNE is for 1 not to broadcast and launch RKV on detection of traceable communication. This is trivally a SPNE since the payoffs are 0 for both parties and we have not formulated any positive payoffs in this game. Thus, since we cannot do better (period), we cannot do better by deviating. (simple argument from weakening)
Later on, the OP suggests a peaceful outcome if the game is extended into
1.) Player 1 chooses to broadcast location, not broadcast, or to broadcast that player possesses advanced first strike and broadly decentralized second strike capabilities.
2.) Player 2 receives message and chooses whether or not to broadcast or to broadcast in turn the possession of advanced first strike and broadly decentralized second strike capabilities or to launch a RKV.
3.) Player 1 either receives broadcast or detects RKV and decides whether to launch RKV.
In this game, we see that broadcasting advanced first strike capabilities with broadly decentralized second strike capabilities while committing to launch RKV on detection of incoming RKV is also a SPNE. Given the payoffs we described earlier, there is a strongly negative payoff for player 2 to launch RKV, since they will be greeted in turn with an RKV in response.
A point that was somewhat unclear to me after the somewhat confusingly ordered edits in the OP was whether or not the origin of an RKV could be successfully traced for MAD. If RKVs are traceable then as I said in the previous paragraph, communication can still be an RKV. Otherwise, the only SPNEs are those where the first player does not broadcast.
Consider:
1.) Player 1 chooses to broadcast or not broadcast.
2.) Player 2 receives message and chooses whether or not to broadcast or launch a RKV.
3.) Player 1 either receives broadcast or detects RKV and decides whether to launch RKV. (this stage is a 3-fold branching. Detect response first, detect RKV first, or detect nothing)
That fully specifies an extended form game (tree structure) with all the necessary components to establish information sets given some strongly negative payoff for being dead and some presumably slightly negative payoff for having to launch an RKV, with broadcasting information being basically free. Information sets come into play in stage 3, since player 1 does not know if an RKV has been sent or not and has to make a decision based on the possibility of both situations.
The OP suggests that a SPNE is for 1 not to broadcast and launch RKV on detection of traceable communication. This is trivally a SPNE since the payoffs are 0 for both parties and we have not formulated any positive payoffs in this game. Thus, since we cannot do better (period), we cannot do better by deviating. (simple argument from weakening)
Later on, the OP suggests a peaceful outcome if the game is extended into
1.) Player 1 chooses to broadcast location, not broadcast, or to broadcast that player possesses advanced first strike and broadly decentralized second strike capabilities.
2.) Player 2 receives message and chooses whether or not to broadcast or to broadcast in turn the possession of advanced first strike and broadly decentralized second strike capabilities or to launch a RKV.
3.) Player 1 either receives broadcast or detects RKV and decides whether to launch RKV.
In this game, we see that broadcasting advanced first strike capabilities with broadly decentralized second strike capabilities while committing to launch RKV on detection of incoming RKV is also a SPNE. Given the payoffs we described earlier, there is a strongly negative payoff for player 2 to launch RKV, since they will be greeted in turn with an RKV in response.
A point that was somewhat unclear to me after the somewhat confusingly ordered edits in the OP was whether or not the origin of an RKV could be successfully traced for MAD. If RKVs are traceable then as I said in the previous paragraph, communication can still be an RKV. Otherwise, the only SPNEs are those where the first player does not broadcast.
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Had a long chat with a friend while drinking about what would happen if aliens ever knew we existed. Probably freaked the hell out of him, sorry about that, but we didn't get to the really scary stuff (see the last paragraph for that). But anyhow, with all the hubbub about finding habitable planets lately--maybe cooked up by a clever NASA spokesperson, or maybe not--human beings should understand that if aliens behave according to game theory, the most probable way that Earth will encounter alien life will be in the form of a relativistic kill vehicle (RKV) that instantly and without warning sterilizes the planet. We will not see any cute spaceships or wise aliens--it will simply be a 130 MT to 200 GT explosion happening somewhere on the earth's surface. (The latter explosion would turn us into Alderaan.) This is because across interstellar distances, talking is slow (bound by lightspeed), while RKVs and interstellar weapons are, relatively speaking, fast, so it makes sense to kill everything and ask questions later.
What is an RKV? An RKV is a simply a lump of matter accelerated to a significant fraction of lightspeed and sent on its merry way to a target. The faster it travels, the less warning time it gives for the recipient (if we put sensors in a spherical grid along the edge of the solar system, for example, an RKV traveling at 50% of the speed of light would give Earth approximately 2 hours to react). The effects of an RKV impact on earth would vary with mass and speed of target; a 1000 kg object traveling at 50% of the speed of light would result in a 3.3 gigaton energy release, or the equivalent of 66 copies of the largest nuclear bomb ever detonated going off at once.
In theory, there is no upper limit to the size of an RKV, and speed is limited only by the length of distance between us and the aliens. The longer the distance, the more space there is to accelerate, so the bigger a fraction of lightspeed can be reached. As for size, they could even decide upon overkill and launch entire asteroids at us (which would shatter earth), or guarantee some amount of destruction by placing a thermonuclear warhead in the asteroid to break it up into hundreds of chunks before it gets within range of earth, giving a sort of interstellar shotgun effect, where each pellet of buckshot can recreate the dinosaur extinction event.
A few other things to note: the RKV can be propelled with any sort of technology. It can even be propelled with current human technology. I always thought that if world peace were achieved, the first order of business for a unified human government would be to strap all preexisting nuclear warheads in a long daisy chain to one of the smaller asteroids between Mars and Jupiter, and then keep it ready to launch at the first alien civilization we detect. The slow pulse detonation of all 23000 nuclear warheads would be a cheap and effective way to propel the rock to a good fraction of lightspeed. Hell, we could even split those up amongst ten or twelve smaller rocks, and use solar mirrors and gravitational slingshots to get the first couple of speed boosts.
This also means that RKVs, at least speaking with regards to any spacefaring civilization, are energy-efficient compared to other weapons systems. With a good interstellar map, Civilization A could not only launch RKVs at Civilization B's home planet, but launch smaller shotgun blasts at all the other stars within a 100 light-year box around Civilization B's home planet, just to make sure any colonies are severely damaged as well. This level of capability is reachable with an Earth-level civilization with just a few years of dedicated RKV production (making as many nukes as possible to hook up to as many asteroids as possible). Assuming that Civ A has full energy infrastructure over one planet and partial energy harvests over a few more planets, simply by diverting 1% of their annual energy production into charging up RKVs over a few dozen years would let them have thousands of relativistic weapons to launch, enabling saturation bombardment of every single alien civilization they encounter.
Also, since the RKV is going so fast, it will be impossible to get to it with a shutdown code once it has traveled far enough away. This means that an RKV is essentially an unrecallable weapon for use only against predictible targets like orbiting planets, which means that even unused, RKVs are one of the best forms of interstellar MAD against planet-based life possible.
Note, I say this is the most probable way, not necessarily with a >50% probability, but if you assume all aliens choose their initial actions upon finding other intelligent life from an equally likely basket of hostile and not-so-hostile actions, then eventually the aliens which choose the insta-kill, no-radio-broadcast action 100% of the time will outnumber the aliens who are actively broadcasting and announcing their home planet's location to the universe. Hence these aliens will be the more common type by evolution. There are still chances that we will encounter happy aliens or dumb aliens (preferably both happy and dumb, as any other combination would pose extreme threats to our survival as a species), but they will be outweighed by chances we will encounter aliens which are intelligent and violent.
This concept rests upon four basic assumptions: 1) communications will never evolve beyond lightspeed, 2) in any interstellar communication, the sender species reveals the exact coordinates of their planet, 3) the most lethal and reliable methods of long-range species elimination all operate at near-light-speeds, and 4) there is no way to show peaceful intent without actively communicating peaceful intent. Currently, all 4 assumptions hold true.
Drawing together these four assumptions, let's consider a thought experiment.
Civilization A detects the radio waves of Civilization B. If a second pulse comes shortly thereafter, Civilization A can triangulate a position in the sky. Civilization A has a choice: it can broadcast radio waves that travel at 100% lightspeed, or launch an RKV that travels at 50% lightspeed. Since it will take at least a back-and-forth to establish peaceful intent, in the time before both sides know each other is peaceful, RKVs could already annihilate the home planets of the other civilization. So Civilization A will essentially think: "why take the risk? What if they launch immediately upon hearing a reply from us?" and will launch first. Civs which do not think this way will be killed off by Civs that do, until the universe is truly silent.
If the universe is anarchic and civs are competing with each other, then a few trends emerge in politics. First and foremost is that the dominant form of government will be a centralized authority with totalitarian control over energy production. The main function of the central authority will be how to most efficiently convert produced energy into RKVs or other ways to perform interstellar first strikes. However, they will need to spread out their colonies as fast as they can to survive, which means their local political institutions have to become somewhat autonomous because lightspeed communications are slow the further out you get--their populations will need to not be coerced by a central authority into giving up all their energy production to the center, but be morally or spiritually compelled to do so. The third aspect is that the civilization will need to be dead silent and paranoid with regard to radio communications, as any comms can leak the position of population centers. Fourth is that the civ must kill without any warning any other civilization which it encounters. Civs which obey these four precepts will quite simply kill off all civs which don't. Basically, because of how slow communications and trade are compared to instant death when dealing with interstellar distances, the dominant form of government will resemble North Korea, except worse. And over time, that's all that will be left, and no civs will ever know how to stop as you will never know whether or not there is another civilization with more RKVs and more spread out colonies waiting to pounce on you.
There is, of course, one, small, faint glimmer of hope in this. One way out. And that is to make sure that in the initial communication pulse, a clear message of deterrence AND peace is recieved; that humankind is shown to already be spread out amongst thousands of planets with millions of RKVs and other first strike weapon systems ready to go, but we resolve conflict peacefully. Unfortunately, most of humankind's messages to space thus far have telling at least one of three messages: 1) we are confined to one planet, 2) we are violent amongst ourselves, and 3) we have not yet invested in interstellar weapons systems.
Maybe it's time we, as humans, got serious about colonizing other planets. After all, we have already sent out the Hitler TV broadcasts and the Arecibo message cheerfully broadcast to a star system chosen because it was likely to contain life, telling them exactly how to find Earth. After all, short of adopting a policy of active xenocide, how else are we going to defend ourselves if some other cosmic civilization is flinging white-hot spears of destiny at us just because their analysts used game theory to design their defense policy?