Consider a variant of the peace war game in which nation A can "harm" nation B much more than B can harm A if they both go to war, but each nation can also give the other nation tribute.
To formalize this, suppose each nation takes turns with A starting first and there being a total of 100 turns. When it is the nation's turn, the nation has 2 potential actions. One of them is to go to attack the other nation. When A attacks B, A has a payoff of -1 and B has a payoff of -10. When B attacks A, both have a payoff of -1. The other potential action is "parameterized" such as the nation can choose any real number > 0 (this is the "tribute"). In this case, for the nation giving tribute, the payoff = 2 - the number selected, and for the other nation the payoff = 2 + the number selected.
What's the optimal strategy?
This is a game of chicken A can tell B he will only accept tribute of $4$ for peace and B is better off accepting than fighting. B can tell A he will offer $1.001$ for peace and A is better off accepting than fighting. You did not detail how the game is played, so the strategies are not defined.