Number 1 limits the model very harshly. If you absolutely need to secure a contract, you need to keep bidding your minimum price. Else, we can view this as a s

Number 1 limits the model very harshly. If you absolutely need to secure a contract, you need to keep bidding your minimum price. Else, we can view this as a simple utility maximization problem where each high offer costs you one period of no work. If you knew distribution of MDR exactly, this would be a simple problem. So you can throw away your first two offers (by bidding infinity) to obtain estimators for the mean and standard error of the distribution. Although you should have an idea on the shape of the distribution as you realistically can not gather enough data to derive it. From there on, you have an estimated probability on whether your offer will be accepted or rejected. If it's accepted, you end up with the money. If not, you end up in the same place, but your utility will be discounted for one time period. To simplify the solution, you can disregard the effects of learning for now and solve the problem to include that later. Once you factor out the recursion from your utility function (which includes a discounted version of itself, in case of rejection), you should end up with a nice but complex calculus problem. Nonetheless, your optimal offer will depend on the estimators of mean and standard deviation. So each period, you should offer your "optimal number", update the mean/standard deviation with respect to the response and calculate the offer for the next period accordingly. ED: You can ping me if you need a contract microeconomist :p