Objective:

In this paper we study, from the seller’s perspective, how to auction a finite set of identical items when the buyer who obtains the whole set of goods (if any) gets a bonus, such that the seller maximizes his expected revenue and taking into account the strategic behavior of the bidders.

Methodology:

We use Bayesian Games for modelling the situation considering a strategy space equal to ${\mathbb{R}}_{+}^m$ for each bidder.

Results:

We show a Symmetric Bayesian Equilibrium for the model as well as the seller’s indifference between several natural ways for offering the bonus to a bidder getting the whole set of items, because he obtains the same expected revenue.

Limitations:

The model regards only identical items.

Originality:

We show an equilibrium bid for a n-personal model of m Simultaneous Auctions under first-price close mechanism considering that there is a kind of extra profit.

Conclusions:

The seller is indifferent between several ways to offer the bonus. It could be interesting to contrast the theoretical results under an experimental framework.

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