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I can't suggest any research papers, but I can suggest one way of studying this problem: using an agent-based model. For example, this is a simple model of an auction on NetLogo: https://ccl.northwestern.edu/netlogo/models/BiddingMarket. Maybe you can tweak the code to make the model run a simulation of your problem. If this wasn't what you were looking for, ...


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I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less. Here is a setting that might be of interest: Kelso & Crawford, Econometrica 1982. They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker ...


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This question is hard to answer, because it is not clear what the appropriate multi-unit version of the single-unit second-price auction (SPA) actually is and which economic environment you have in mind. There are several possibilities, and I mention some. There are 4 bidders and two units. All bidders draw a two values $v_{1i},v_{2i}$ representing the ...


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Elimination of (weakly) dominated actions will not get you far. In fact, all bids strictly between 0 and the value are undominated. Hence, a buyer's optimal bid in a first-price auction can't be determined without knowing the bidder's belief (unless the buyer's value is 0). Claim: For any type $x>0$, all bids $c \in (0,x)$ are undominated. $c$ is not ...


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I suggest to have a look at Krishna's "Auction Theory", Chapter 16 "Non-identical items". Regarding your particular multiproduct problem, I would go from Armstrong's "Multiproduct nonlinear pricing", Econometrica 1996, and see what happens. While I don't want to discourage you, let me mention that mechanism design with ...


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Yes, it is essentially the same idea as with just one unit. For example, see the text leading to Proposition 14.1 in the book "Auction Theory" by Vijay Krishna. Let $x$ be the vector of willingness-to-pay. Define $U(x) = \max_z \{ q(z)x - m(z)\}$ as the equilibrium utility of type $x$. The incentive compatibility (I am quoting Krishna now) "...


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Mechanism design with multi-dimensional types (here: the willingness-to-pay for each object) is a notoriously difficult problem. Even when you abstract from bundling as you do by assuming that the seller only wants to buy one of the goods. Your problem is studied by John Thanassoulis in "Haggling over substitutes", JET 2004. Unfortunately, there is ...


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