Thursday, September 22, 2011

How does your Reservation Value relate to your BATNA?

Your reservation value is the lowest value you will accept in a deal.   It goes by many names -- your bottom line, your walkaway point, but whatever you call it it is the worst possible deal you would be willing to accept.  We always hope to do better than our reservation values, but it's important to know what yours is, both to avoid accepting a deal you shouldn't have and as a reference point for how much a current deal is worth to you.

If you read a typical textbook on negotiation, you might think that the question of how reservation value  relates to BATNA is trivial.  Most books define Reservation Value in terms of the value of one's BATNA and assume that they are equal.  This makes sense -- as long as the deal is better than your BATNA you'd rather take it than walk away; if it's of equal value then you're indifferent and if it's worse than you'd rather follow your BATNA than take the deal.

For example, imagine you're selling a used car and your BATNA is to sell to someone who has offered you $6,000 in cash.  Your BATNA is therefore worth $6,000 and any deal worth less than that will be refused. If you had a deal for $6,100 and were sure you couldn't increase it, you'd take the deal.  Right?

I'm not so sure.  I think there are good reasons to set your reservation price at a premium to your BATNA, coming from such diverse fields as psychology and poker.

Pot Odds

Experienced poker players will make bets they expect to lose because of "pot odds".  If the cost of losing is small relative to the gain of winning, the expected return can be positive even if the most likely outcome is a loss.

Suppose we're playing no-limit poker and I'm down to my last $1,000.  There's $10,000 in the pot and it's raised $1,000 to me.  Based on my read of my opponent I think I'm an underdog, with only a 25% chance to win.  Even though I expect to lose, I should call assuming my decision is based purely on maximizing my expected return on this hand.  The math works as follows:

Fold: 100% chance of having $1,000.

Call: 25% chance of having $12,000 ($10,000 plus $1,000 bet plus $1,000 call) and 75% chance of having $0 which is a weighted average return of $4,000.

Since the payoff was much larger than the investment the expected return on calling was positive even though I expect to lose three times out of four.

One professional negotiator I know defines reservation price as "the lowest price you'd accept if you were positive you couldn't get more" but this assumes knowledge we almost never have -- that the other person really won't do any better than their "final" offer.

In our car example, suppose you refuse the $6,100 offer and say you want $7,000.  What might happen?  It's possible that the other party will say, "Sorry, $6,100 really is the best I can do."  They might groan and say, "I can do $6,300 but that's really it."  Or they might actually value the car at $8,500 and accept your price.  Since $6,100 is really only worth $100 to you (relative to your alternative offer), it's quite likely that you have a positive return on holding out for more, even if you think it's likely that $6,100 really is the buyer's top price.

A final consideration is that refusing someone's final offer isn't always irrevocable.  If you say "no" to $6,100 and the buyer walks away you can often (not always) call back and say you've changed your mind.

Underestimation of your BATNA

I find people frequently underestimate the value of their BATNA -- in particular the potential to improve it.  Is your BATNA regarding the used car really $6,000?  That's an offer you have, but it might be negotiable.  You might also find another buyer.  We tend to focus on the most tangible aspects of our BATNA, which can lead us to undervalue it.  Of course, in theory this means we may need to improve the evaluation of our BATNAs rather than that our reservation price should be set higher, but in practice it speaks to holding out for more.


Many negotiations you undertake are semi-public -- people you'll negotiate with in the future (including those you're negotiating with now!) will have some awareness of the results.  Given that, it's worth thinking about the reputation you'd like to craft and then weighing that in to the decisions you make.  An ideal reputation would include integrity and an ability and willingness to create value but I think it should also include being someone who expects significant value out of a deal and will walk away if that proves impossible to achieve.  This may shield you from wasting time on deals that don't offer you much and it encourages your counterparts to adopt a value-creation posture rather than trying to squeeze you.

Cognitive bias

There are at least two types of common cognitive bias that make a no-gain reservation value dangerous: small pie bias and focal point bias.

Small pie bias is pretty straightforward -- people tend to underestimate the size of the pie, which can lead to missed opportunities to grow it and to accepting too small a piece.  Focal point bias refers to research showing that in stressful, complex situations (e.g. negotiations) people tend to gravitate mentally to whatever focal point is the most significant to them.

Combined, these factors can easily lead us to think that our reservation value is the value to think about and that any gain above that is a win -- a prescription for leaving a lot of value on the table.

One strategy for fighting this is to set an aspirational target and try to focus on that, keeping the reservation value in your back pocket to be looked at only if the negotiation goes more poorly than expected.  This approach has some validity but I think it's risky for all but the most experienced negotiators.  Moreover, if you come to believe you've misunderstood the ZOPA and are faced with a deal that is better than your BATNA but worse than the reservation value you've set there's nothing stopping you from taking a step back, re-examining the new information you've received, and adjusting your numbers accordingly.

Putting it all together

Let's look at an example.  You've been tasked with buying the patent rights for a piece of technology that's worth $10 million more to your company than your best alternative.  Based on a classic BATNA analysis, you'd set your reservation price at $10 million.  Your company, however, is the only natural buyer for the technology and you're fairly confident from your analysis that the patent isn't worth anything to its owners and that the best rival offer they're likely to get (from a company in a different business) is in the $3-4 million range and probably less.

There are a lot of away-from-the-table steps you'd take if this was a real situation, but to keep it simple let's assume that they have an unknown but firm offer and are negotiating with you to see whether your company gets the patent.

Suppose they say, "We have a very good offer from (the firm you expected would pay at most $3-4 million), but we know this technology is very valuable to your firm.  We'll sell it to you for $15 million."

You take this in stride as an anchoring tactic, state clearly that they have substantially overestimated how much the patent is worth, and make a counter-offer of $2 million.  There is some back-and-forth but abruptly they say, "Our absolute final offer is $9.7 million.  If you won't pay that, we'll have to go with the other company."

You tell them you'll consider their offer, cautioning them that it's high, and go back to your desk.  You revisit your analysis with your team and bring in an outside expert for a fresh view.  You still can't believe that it's worth more than $4 million to the other company.  But what if it is?  You don't want to throw away money, even if it's "only" $300K.

In this situation, there are some compelling reasons not to accept their "final" offer.

First, let's be pessimistic and assume there's only a 20% chance that they're bluffing -- but that if they're bluffing you'll be in the driver's seat and can reasonably expect to pay $5 million.  That's an expected return of $1 million relative to your BATNA, which is greater than the $300K on offer.

Second, if your analysis is correct and the ZOPA is $6 million or $7 million in size, neither your firm nor your own career benefits from capturing so small a piece of it.

Next, is your BATNA really to do without the technology?  If the firm that buys it is in a different business you may be able to license the technology from them.

This is, of course, simplified.  You have a range of tactics available to gain information...but at some point in a negotiation you can be presented with a "final" offer that doesn't make sense given everything you can learn but that is slightly better than your BATNA.  Theory says you should take it -- I hope I've provided some reasons to question theory on this point.


  1. A good thing to think about is, what would your reservation price be if you knew it would be known to your opponent? Obviously you don't want to choose a reservation price equal to your BATNA in that case, you guarantee they will hold out for that and your surplus from the negotiation will be zero. There is a considerable amount to be said for setting your reservation price at the surplus-maximizing value, i.e., maximize (probability of acceptance)*(gain over BATNA). A big advantage then is that you no longer need, and indeed may not even want, to keep your reservation price secret. It's a lot easier to negotiate effectively when you aren't trying to mislead your adversary but just seeking a win-win agreement.

  2. By the way, one place this comes up in real life is in online Vickrey auctions (e.g., Adwords), where you have to specify your reservation price in advance. But it's a little bit different because your competitors do, also, and there's no real "negotiation". In that case, there's a theorem that suggests you should bid your BATNA. But even then, it's not necessarily true.

  3. Hi David,

    Great comments. I really like thinking about where your reservation value would be if your counterpart was going to find it out. Maximizing expected surplus is similar to the consideration of "pot odds", although in practice I think we're uncertain enough about the ZOPA that it's risky to commit to too aggressive a reservation price up front.

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  6. would you please post a concrete difference between BATNA and WATNA

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  8. HI, I have a question. Let's say Im selling my used car and I have only one offer from the car dealer where I want to purchase a new car. The offer is 1700 euros but I need 2300 Euros to put in an offer for the new car. My interest is to sell this car and get the new one. Does this mean my Reservation price is 1700 as this is a firm option or is it 2300 because thats what I need to purchase my new car? Through blue print I have valued my car to 2900 euros.
    Thanks for your input