There is a deep problem here, this cannot separate the two outcomes, parties are not allied because they expect to be on the opposite sides of coercive bargaining, and that being allied is the source of these utilities, as an estimator, though, that states dont make alliances that lead to them being forced to pick between allies, or with those they expect they might fight, is a good one for quantitative estimation, however. I expect that if you had fine grained versions of when pairs of countries came to a coercive settlement short of war, almost many pairs with +EV from fighting show up here, because the offer power to coerce people in the case where there are costs to war and it is mutually -EV to fight, is rare to have credibly if fighting is not +EV in the absence of a deal.
There is a deep problem here, this cannot separate the two outcomes, parties are not allied because they expect to be on the opposite sides of coercive bargaining, and that being allied is the source of these utilities, as an estimator, though, that states dont make alliances that lead to them being forced to pick between allies, or with those they expect they might fight, is a good one for quantitative estimation, however. I expect that if you had fine grained versions of when pairs of countries came to a coercive settlement short of war, almost many pairs with +EV from fighting show up here, because the offer power to coerce people in the case where there are costs to war and it is mutually -EV to fight, is rare to have credibly if fighting is not +EV in the absence of a deal.