"Painless bargaining" procedure proposal, in the eyes of game-theory

Question

I thought about a procedure to set an accepted price of a bargain, that aimed to maximize the sides' satisfaction and minimized the face-to-face tiresome bargain process.

Let's call the sides a buyer and a seller. The idea is:

1) each side figure a range that he willing to pay/sell, and write it on a paper, for instance
2) the two sides reveal the ranges
3) if there is an intersection:
    3.1) the price is set to be the average of its range
   otherwise:
    3.2) if the lower bound price that the buyer is willing to pay is higher than the higher bound price of the seller:
        3.2.1) the price is set to be the average of these bounds
         otherwise:
        3.2.2) there is no deal

in addition, this procedure must be done only once; in case that there is no deal (3.2.2) the bargain is terminated.

Examples:

3.2) buyer - 200-230
     seller - 220-240
     the intersection is 220-230, so the price is 225
3.2.1) buyer - 200-230
       seller - 150-180
       buyer's lower bound is 200, seller's higher bound is 180, so the price is 190

I believe this procedure is very convenient of both sides, and because of the option of breaking the deal (3.2.1) both sides will give the best offers they willing to carry. Is this correct, in the eyes of game-theory?

Answer 1

You are basically asking each party to propose a price, the high end for the buyer and the low end for the seller, then splitting the difference. The problem with this is that each one is tempted to propose a price that is not the limit of what they would accept. If the seller raises his limit price by 10 he gets 5 more after the split. He might miss out on a few sales when he goes by the buyer's limit but those sales are not very profitable anyway. Another problem is when the seller sells the same thing to various buyers. The number he quotes the first buyer may get out, giving future buyers an unfair advantage.