In a game of Magic earlier today my opponent played Coercive Portal, which led to a situation in which he could either:
- force me to choose A; or
- allow me to choose A or B.
I was surprised when my opponent let me choose A or B. This struck me as a mistake as it guaranteed me my preferred outcome (assuming correct play):
| choice | my preferred outcome | actual outcome | optimal for me |
| ------ | -------------------- | -------------- | -------------- |
| A | A | A | yes |
| A | B | A | no |
| A or B | A | A | yes |
| A or B | B | B | yes |
How does one express this situation in game theory? Is my reasoning sound? If so, what is the formal proof?
In the situation described, forcing a choice of A dominates allowing either a choice of A or B. That is, the outcome for the opponent is always at least as good if he or she makes the dominating choice.
However, there are some conditions:
1. If there are more than 2 players, there may be good reason to not beat up on someone. #2 might want #3 to stay alive so that together they go after #1.
2. The best play in life might not always be the best play in a game. Perhaps the opponent was trying to be nice.
3. There are no other differences between the two moves for the opponent. This is hard to evaluate not knowing any other details apart from coercive portal.