Bidding Collusion Question: Probability of Identical Bids I was asked this question. My initial conclusion is that there isn't enough information to calculate the probability. I would appreciate it if anyone could provide provide their insight.
Scenario:
Department of Defense is looking to purchase a good. Department of Defense has determined that a fair price is 1.0000 and told vendors of this value. Eight vendors submitted independent bids to provide the desired good. 
What are the odds/probability that three vendors would submit the exact same bid (see below)?
0.7700
0.7999
1.1120
0.7000
1.4262
0.6840
0.7000
0.7000

 A: You're right: as stated, there isn't enough information in the question to calculate a probability.
However if you wanted to make assumptions, you could take one of two main routes:


*

*As user Andy Blankterz mentioned in the comments, you could assume payoff functions for each of the bidders. This reduces the problem to a first-price auction. It might be worth mentioning here that first-price auctions are suboptimal for the seller, from what I remember of auction theory.

*You could assume probability distributions over bidders' behavior. This reduces the problem to something like the birthday problem. Keep in mind that the probability of exact equality is zero in the continuous case.


You could also combine these two by assuming stochastic payoffs (e.g. bidders don't know the payoffs for certain) or otherwise incorporating randomness into the first model. This could turn out to be a nontrivial problem to solve. If you're stone-cold confident in your analysis and probability skills, the definitive book on the subject is Putting Auction Theory to Work by Paul Milgrom.
