you can just consider yourself committed to not even consider subsequent worse-than-fair offers after you’ve rejected the first one
Note that if you do that, I can exploit you by offering 9:1 split, getting it accepted 50% of the time, and getting a 5:5 split another 50% of the time, which leaves me with 7 in expectation (and you with 3 in expectation).
If you interact with the kind of entity that offers you a better deal if you reject their first offer, and they make an offer before you explain what you’ll do, you just always reject their first offer, explain your strategy to them, and say that it’s in their interest to make a fair offer, and if you probabilistically reject that one, they won’t be able to make more offers.
Or, a thing you can do in reality might be, e.g., deterministically rejecting all of their initial offers, making counteroffers that are better-than-fair for you, and bargaining this way until they reach a point where they don’t go lower because this is their best offer, and then probabilistically accepting or rejecting that best offer.
If you interact with the kind of entity that offers you a better deal if you reject their first offer, and they make an offer before you explain what you’ll do, you just always reject their first offer, explain your strategy to them, and say that it’s in their interest to make a fair offer, and if you probabilistically reject that one, they won’t be able to make more offers.
I’m not convinced that this remains optimal when you’re bargaining with an entity that might offer you a better deal if you reject their first offer for legitimate reasons, rather than in an attempt to exploit your bargaining strategy.
Suppose a deal falls through, your counterparty tries their BATNA, it goes worse than they thought, so they come back and make a better offer than they did the first time. Or maybe they, or you, learn something new regarding the value of the goods being negotiated for. Shouldn’t it be possible to take this into account and reopen negotiations? If not, a lot of mutually beneficial trades become impossible.
But I don’t see a specific strategy that allows for this without being exploitable, since you can’t necessarily tell whether a new offer is prompted by new information or whether it’s just a bargaining tactic.
Note that if you do that, I can exploit you by offering 9:1 split, getting it accepted 50% of the time, and getting a 5:5 split another 50% of the time, which leaves me with 7 in expectation (and you with 3 in expectation).
If you interact with the kind of entity that offers you a better deal if you reject their first offer, and they make an offer before you explain what you’ll do, you just always reject their first offer, explain your strategy to them, and say that it’s in their interest to make a fair offer, and if you probabilistically reject that one, they won’t be able to make more offers.
Or, a thing you can do in reality might be, e.g., deterministically rejecting all of their initial offers, making counteroffers that are better-than-fair for you, and bargaining this way until they reach a point where they don’t go lower because this is their best offer, and then probabilistically accepting or rejecting that best offer.
I’m not convinced that this remains optimal when you’re bargaining with an entity that might offer you a better deal if you reject their first offer for legitimate reasons, rather than in an attempt to exploit your bargaining strategy.
Suppose a deal falls through, your counterparty tries their BATNA, it goes worse than they thought, so they come back and make a better offer than they did the first time. Or maybe they, or you, learn something new regarding the value of the goods being negotiated for. Shouldn’t it be possible to take this into account and reopen negotiations? If not, a lot of mutually beneficial trades become impossible.
But I don’t see a specific strategy that allows for this without being exploitable, since you can’t necessarily tell whether a new offer is prompted by new information or whether it’s just a bargaining tactic.