As an example, part of your military strength might be your ability to crash enemy systems with zero-day software exploits (or any other kind of secret weapon they don’t yet have counters for). At least naively, you can’t demonstrate you have such a weapon without rendering it useless. Though this does suggest a (unrealistically) high-coordination solution to at least this version of the problem: have both sides declare all their capabilities to a trusted third party who then figures out the likely costs and chances of winning for each side.
Though this does suggest a (unrealistically) high-coordination solution to at least this version of the problem: have both sides declare all their capabilities to a trusted third party who then figures out the likely costs and chances of winning for each side.
Is that enough?
Say Alice thinks her army is overwhelmingly stronger than Bob. (In fact Bob has a one-time exploit that allows Bob to have a decent chance to win.) The third party says that Bob has a 50% chance of winning. Alice can then update P(exploit), and go ‘uhoh’ and go back and scrub for exploits.
(So… the third-party scheme might still work, but only once I think.)
Good point, so continuing with the superhuman levels of coordination and simulation: instead of Alice and Bob saying “we’re thinking of having a war” and Simon saying “if you did, Bob would win with probability p”; Alice and Bob say “we’ve committed to simulating this war and have pre-signed treaties based on various outcomes”, and then Simon says “Bob wins with probability p by deploying secret weapon X, so Alice you have to pay up according to that if-you-lose treaty”. So Alice does learn about the weapon but also has to pay the price for losing, exactly like she would in an actual war (except without the associated real-world damage).
How does said binding treaty come about? I don’t see any reason for Alice to accept such a treaty in the first place.
Alice would instead propose (or counter-propose) a treaty that always takes the terms that would result from the simulation according to Alice’s estimate.
Alice is always at least indifferent to this, and the only case where Bob is not at least indifferent to this is if Bob is stronger than Alice’s estimate, in which case accepting said treaty would not be in Alice’s best interest. (Alice should instead stall and hunt for exploits, give or take.)
Simon’s services are only offered to those who submit a treaty over a full range of possible outcomes. Alice could try to bully Bob into accepting a bullshit treaty (“if I win you give me X; if I lose you still give me X”), but just like today Bob has the backup plan of refusing arbitration and actually waging war. (Refusing arbitration is allowed; it’s only going to arbitration and then not abiding by the result that is verboten.) And Alice could avoid committing to concessions-on-loss by herself refusing arbitration and waging war, but she wouldn’t actually be in a better position by doing so, since the real-world war also involves her paying a price in the (to her mind) unlikely event that Bob wins and can extract one. Basically the whole point is that, as long as the simulated war and the agreed-upon consequences of war (minus actual deaths and other stuff) match a potential real-world war closely enough, then accepting the simulation should be a strict improvement for both sides regardless of their power differential and regardless of the end result, so both sides should (bindingly) accept.
(Kindly ignore the zeros below each game node; I’m using the dev version of GTE, which has a few quirks.)
Roughly speaking:
Bob either has something up his sleeve (an exploit of some sort), or does not.
Bob either:
Offers a flat agreement (well, really surrender) to Alice.
Offers a (binding once both sides agree to it) arbitrated (mediated in the above; I am not going to bother redoing the screenshot above) agreement by a third party (Simon) to Alice.
Goes directly to war with Alice.
Assuming Bob didn’t go directly to war, Alice either:
Accepts (and abides by) said agreement.
Goes to war with Bob.
Does an internal audit[1]/preparation[2] and goes to war with Bob.
Wars cost the winner 2 and the loser 10, and also transfers 20 from the loser to the winner. (So normally war is normally +18 / −30 for the winner/loser.).
Alice doing an audit/preparing costs 3, on top of the usual, regardless of if there’s actually an exploit.
Alice wins all the time unless Bob has something up his sleeve and Alice doesn’t prepare. (+18/-30, or +15/-30 if Alice prepared.) Even in that case, Alice wins 50% of the time. (-6 / −6). Bob has something up his sleeve 50% of the time.
Flat offer here means ‘do the transfer as though there was a war, but don’t destroy anything’. A flat offer is then always +20 for Alice and −20 for Bob.
Arbitrated means ‘do a transfer based on the third party’s evaluation of the probability of Bob winning, but don’t actually destroy anything’. So if Bob has something up his sleeve, Charlie comes back with a coin flip and the result is 0, otherwise it’s +20/-20.
There are some 17 different Nash equilibria here, with an EP from +6 to +8 for Alice and −18 to −13 for Bob. As this is a lot, I’m not going to list them all. I’ll summarize:
There are 4 different equilibria with Bob always going to war immediately. Payoff in all of these cases is +6 / −18.
There are 10 different equilibria with Bob always trying an arbitrated agreement if Bob has nothing up his sleeve, and going to war 2/3rds of the time if Bob has something up his sleeve (otherwise trying a mediated agreement in the other 1/3rd), with various mixed strategies in response. All of these cases are +8 / −14.
There are 3 different equilibria with Bob always going to war if Bob has something up his sleeve, and always trying a flat agreement otherwise, with Alice always accepting a flat agreement and doing various strategies otherwise. All of these cases are +7 / −13.
Notably, Alice and Bob always offering/accepting an arbitrated agreement is not an equilibrium of this game[3]. Noneof these equilibria result in Alice and Bob always doing arbitration. (Also notably: all of these equilibria have the two sides going to war at least occasionally.)
There are likely other cases with different payoffs that have an equilibrium of arbitration/accepting arbitration; this example suffices to show that not all such games lead to said result as an equilibrium.
This is because, roughly, a Nash equilibrium requires that both sides choose a strategy that is best for them given the other party’s response, but if Bob chooses MediatedS / MediatedN, then Alice is better off with PrepM over AcceptM. Average payout of 15 instead of 10. Hence, this is not an equilibrium.
As an example, part of your military strength might be your ability to crash enemy systems with zero-day software exploits (or any other kind of secret weapon they don’t yet have counters for). At least naively, you can’t demonstrate you have such a weapon without rendering it useless. Though this does suggest a (unrealistically) high-coordination solution to at least this version of the problem: have both sides declare all their capabilities to a trusted third party who then figures out the likely costs and chances of winning for each side.
Is that enough?
Say Alice thinks her army is overwhelmingly stronger than Bob. (In fact Bob has a one-time exploit that allows Bob to have a decent chance to win.) The third party says that Bob has a 50% chance of winning. Alice can then update P(exploit), and go ‘uhoh’ and go back and scrub for exploits.
(So… the third-party scheme might still work, but only once I think.)
Good point, so continuing with the superhuman levels of coordination and simulation: instead of Alice and Bob saying “we’re thinking of having a war” and Simon saying “if you did, Bob would win with probability p”; Alice and Bob say “we’ve committed to simulating this war and have pre-signed treaties based on various outcomes”, and then Simon says “Bob wins with probability p by deploying secret weapon X, so Alice you have to pay up according to that if-you-lose treaty”. So Alice does learn about the weapon but also has to pay the price for losing, exactly like she would in an actual war (except without the associated real-world damage).
Interesting!
How does said binding treaty come about? I don’t see any reason for Alice to accept such a treaty in the first place.
Alice would instead propose (or counter-propose) a treaty that always takes the terms that would result from the simulation according to Alice’s estimate.
Alice is always at least indifferent to this, and the only case where Bob is not at least indifferent to this is if Bob is stronger than Alice’s estimate, in which case accepting said treaty would not be in Alice’s best interest. (Alice should instead stall and hunt for exploits, give or take.)
Simon’s services are only offered to those who submit a treaty over a full range of possible outcomes. Alice could try to bully Bob into accepting a bullshit treaty (“if I win you give me X; if I lose you still give me X”), but just like today Bob has the backup plan of refusing arbitration and actually waging war. (Refusing arbitration is allowed; it’s only going to arbitration and then not abiding by the result that is verboten.) And Alice could avoid committing to concessions-on-loss by herself refusing arbitration and waging war, but she wouldn’t actually be in a better position by doing so, since the real-world war also involves her paying a price in the (to her mind) unlikely event that Bob wins and can extract one. Basically the whole point is that, as long as the simulated war and the agreed-upon consequences of war (minus actual deaths and other stuff) match a potential real-world war closely enough, then accepting the simulation should be a strict improvement for both sides regardless of their power differential and regardless of the end result, so both sides should (bindingly) accept.
Here’s an example game tree:
(Kindly ignore the zeros below each game node; I’m using the dev version of GTE, which has a few quirks.)
Roughly speaking:
Bob either has something up his sleeve (an exploit of some sort), or does not.
Bob either:
Offers a flat agreement (well, really surrender) to Alice.
Offers a (binding once both sides agree to it) arbitrated (mediated in the above; I am not going to bother redoing the screenshot above) agreement by a third party (Simon) to Alice.
Goes directly to war with Alice.
Assuming Bob didn’t go directly to war, Alice either:
Accepts (and abides by) said agreement.
Goes to war with Bob.
Does an internal audit[1]/preparation[2] and goes to war with Bob.
Wars cost the winner 2 and the loser 10, and also transfers 20 from the loser to the winner. (So normally war is normally +18 / −30 for the winner/loser.).
Alice doing an audit/preparing costs 3, on top of the usual, regardless of if there’s actually an exploit.
Alice wins all the time unless Bob has something up his sleeve and Alice doesn’t prepare. (+18/-30, or +15/-30 if Alice prepared.) Even in that case, Alice wins 50% of the time. (-6 / −6). Bob has something up his sleeve 50% of the time.
Flat offer here means ‘do the transfer as though there was a war, but don’t destroy anything’. A flat offer is then always +20 for Alice and −20 for Bob.
Arbitrated means ‘do a transfer based on the third party’s evaluation of the probability of Bob winning, but don’t actually destroy anything’. So if Bob has something up his sleeve, Charlie comes back with a coin flip and the result is 0, otherwise it’s +20/-20.
There are some 17 different Nash equilibria here, with an EP from +6 to +8 for Alice and −18 to −13 for Bob. As this is a lot, I’m not going to list them all. I’ll summarize:
There are 4 different equilibria with Bob always going to war immediately. Payoff in all of these cases is +6 / −18.
There are 10 different equilibria with Bob always trying an arbitrated agreement if Bob has nothing up his sleeve, and going to war 2/3rds of the time if Bob has something up his sleeve (otherwise trying a mediated agreement in the other 1/3rd), with various mixed strategies in response. All of these cases are +8 / −14.
There are 3 different equilibria with Bob always going to war if Bob has something up his sleeve, and always trying a flat agreement otherwise, with Alice always accepting a flat agreement and doing various strategies otherwise. All of these cases are +7 / −13.
Notably, Alice and Bob always offering/accepting an arbitrated agreement is not an equilibrium of this game[3]. None of these equilibria result in Alice and Bob always doing arbitration. (Also notably: all of these equilibria have the two sides going to war at least occasionally.)
There are likely other cases with different payoffs that have an equilibrium of arbitration/accepting arbitration; this example suffices to show that not all such games lead to said result as an equilibrium.
I use ‘audit’ in most of this; I used ‘prep’ for the game tree because otherwise two options started with A.
read: go ‘uhoh’ and spend a bunch of effort finding/fixing Bob’s presumed exploit.
This is because, roughly, a Nash equilibrium requires that both sides choose a strategy that is best for them given the other party’s response, but if Bob chooses MediatedS / MediatedN, then Alice is better off with PrepM over AcceptM. Average payout of 15 instead of 10. Hence, this is not an equilibrium.