> What about strategies that involve blowing up the bridge
The article rules those out by presenting scenarios in which there is always some advantage to trade. In any such scenario, neither party has any incentive to blow up the bridge, since there is always some way for each party to improve their situation by using the bridge to trade, compared to what their situation would be if the bridge did not exist.
In the real world, there are cases where there is no advantage to trade, usually because one or more of the "complexities" described in section III of the article applies. The obvious one, of course, is "there might be more than two people"--in the real world, there are always more than two parties with whom potential trades can be made (this is true even if we consider the "parties" to be nations instead of individuals), and as the article notes, in that case there can be scenarios where at least one party will gain nothing from trade.
But can't you leverage cutting off trade in the same way that he talks about threatening to blow up your island, and it wouldn't result in total loss of everything (which any rational player would see through as a bluff, as opposed to losing trade which would be a negative but still survivable).
IE think about the modal logic intersected with the game theory, no one will believe that you will blow up your own island, but they may believe that you will blow up the bridge.
> can't you leverage cutting off trade in the same way that he talks about threatening to blow up your island
If you are the only possible party the other party can trade with, then blowing up the bridge and blowing up your own island are, as far as the other party is concerned, equivalent, yes. So if there is any benefit to the other party in trading with you, they have an incentive to have that trade available to them, and hence to do whatever it takes to have you not blow up either your own island or the bridge.
However, if there are any other parties besides you that can be traded with, that is no longer the case, because you not being there just means they go trade with someone else.
Another thing to note is that the article's assumption of non-violence, which basically means neither party will do anything to harm anything that isn't their own property, also rules out blowing up the bridge, since the bridge, by hypothesis, is not the property of either party. A better analogy to withholding trade in the article's scenario would be something like building an impenetrable wall at your end of the bridge.
I'm not sure you are following my point though, whether its blowing up a bridge or building a wall, if you look at the payout to the party that is blocking it is higher than blowing up the island. If you then use modal logic to analyze the opposite parties perspective of whether or not that party would actually go through with it then their threat seems much more believable.
> if you look at the payout to the party that is blocking it is higher than blowing up the island
Ah, yes, you're right. I was only looking at the payoff for the other party. You're correct that for the party that is making the threat, they're much better off after blowing up the bridge or building a wall than they are after blowing up their own island, so the former is a much more credible threat. I think the "modal logic" thing confused me because I don't really see how modal logic in particular is involved here; but game theory certainly is, yes.
Once I realize there is a possible trade I can make a boat, or swim. The bridge is the easiest way, and allows us to ignore the (very real) cost of transport in this example. In the real world most trade involves third party delivery companies with trucks, trains, or boats.
