What are pay-per-bid auctions

Games, simulation and dynamic systems

Auctions and their simulation


If many trading partners are interested in buying or selling a common good (wheat, oil, emission rights), an auction will often be held in reality. In the following we will always talk about emission rights because of the reference to chapter EmiHandel.html, but the explanations apply generally to commercial goods.

Establishing the "right" rules for auctions is not easy, and this chapter introduces some of the most important auction terms.

Aim: Understanding the basic mechanisms of auctions and introducing basic terms. Analysis of how pricing comes about in the auction.

Method: In a computer simulation, we develop a simplified auction and price model that enables the modeling of market events.


An auction mechanism - the so-called Ascending / Descending Auction - can look like this:

1.      The sellers submit their sales bids to the auctioneer, the sum of all emission rights to be sold is X.

2.      The auctioneer names an (initial) price p.

3.      The buyers submit their purchase bids at this price p, the sum of all emission rights to be bought is Y.

4.      If X = Y, the auction is closed and trading is carried out at price p

5.      If X> Y, the auctioneer lowers the price from p to p - dp. Go to 3.

6.      If X

In step 3, the buyers have the option, depending on the price, of leaving / entering the auction or changing the quantity of their purchase bids. In this way we get a price that is in line with the market.

A disadvantage for the simulation (and also for the auction in reality!) Is that you have to go through many iterations with each trading period until the price is fixed. A simplified variant in which you can use one Step can carry out the trade is the so-called Sealed bid auction. In this auction, each buyer gives the auctioneer his bid in a sealed envelope; he does not just name a purchase amount yibut also one Purchase price pi. (It is also permitted for a buyer to submit several bids with different prices.) Each seller informs the auctioneer - also in a sealed envelope - of his / her offer xi. The auctioneer arranges the purchase bids according to the purchase price (see picture).

The price at which the quantity X = Sxi of all sales offers is achieved Clearing price. All buyers who have bid this price or a higher price get their purchase amount at the clearing price.[1] All other buyers get nothing. If the purchase amount is less than X, all rights go out at the price of the lowest purchase bid. Usually the auctioneer sets a minimum price in consultation with the sellers. But be careful: If the reserve price is too high, the buyer will not be able to bid, the seller will not convert anything![2]

"Pay-Your-Bid" variant: Each buyer with a bid greater than or equal to the clearing price does not pay the clearing price but the price he has offered. The sellers receive the average price resulting from the total purchase price for each emission right sold,

which is above the clearing price. The advantage is a "smoother" price function: If only 1 out of 1000 rights was sold at a very low clearing price, this does not immediately destroy the price for all the other 999 rights.


Emission rights (or other commercial goods) do not expire. If a company has "produced" more rights - through allocation or purchase - than it has "used" - through actual issue or sale - then it can "put them on the bank" and use them in the next period. This process is called banking in the literature. If less is implemented in an auction than the sellers have offered, then they can also transfer their excess rights to banking.

We will see that banking is important in order to establish an economically better functioning market (see exercise 2). In reality, of course, no company will lay too many rights on the bank. It could be that in a year another government comes to power, abolishes emissions trading and all rights become worthless!


To carry out the simulation of a sealed bid auction using the example of emissions trading, reference is made to EmiHandel.html.

A simple sealed bid auction (initially without banking) is created in exercise 3.

A multi-person auction game is available in SealedBid.xls and spieler1.xls, ..., spieler8.xls. It can be played on the network. Which group dynamic effects occur when the simulation is played over several rounds under similar conditions?

Analysis: pricing by auction

After we have gained initial experience with the mechanisms of the auction in the simulation, we want to try to understand what the underlying mechanisms are, according to which each individual participant acts individually and rationally and whether and when this action also to achieve the global optimum (for the national economy) leads. This is important against the background that the rules of trade have to be correctly defined in order to actually achieve the ecological reduction target (at an acceptable cost).

So how does emissions trading (a) set a fair market price and how are (b) the right measures to reduce emissions taken by the right (i.e. economically most cost-effective reduction companies)?

Let us make the following simplifying assumptions:

O The framework conditions (cost structures, emission targets) remain constant and trading takes place over many periods in which companies can adjust to the situation

O Every company acts individually and rationally (maximizes its profit).

O There is no price fixing, no price wars or battles for market power.

Let us first consider the Buyers: If I as a company z. B. 1,000 t CO2 emit more than I am allowed according to the emissions target, I will want to buy rights, at least as long as their price is below my reduction costs Ki(1000, T.0) lies. As an entrepreneur who acts individually and rationally, I will make a purchase bid for 1,000 t at a price of K.i(1000, T.0) / 1000 per ton. (Because if I offer less and therefore fly out of the auction, I have to reduce more expensive myself.)

That's all? - no! After all, what if the sellers offer more emission rights than the buyers need directly? I can place another bid with a significantly lower price. If this bid wins, I have (a) pressed the price (clearing price variant) and (b) purchased emission rights, which I will save for the next period (banking) and which will reduce my costs there.

One could argue that buyers do too all could offer targeted lower prices and then get the rights cheaper. However, this requires binding agreements between all buyers (because if only one fails, he can secure more / all rights, to the detriment of the other buyers). We want to refrain from such agreements here because they are "fragile".

Now to the situation of Seller: They have to consider how many rights they are putting on the market. They know about the possibility of buyers to submit banking bids and will therefore endeavor to put as many rights on the market as the buyers need directly (this year) - at least as long as the buyer's price is higher than the sellers' generation costs. If a seller deviates from this and "produces" more rights, he will - if a banking bid from a buyer is successful - harm all sellers, including himself, by an auction price that is too low.

In order to protect myself against banking bids that are too low from buyers, I as a seller can also come up with the following idea: In addition to my offer to sell, I put a buy bid with a price (well) below my reduction costs in the auction. If the bid amount was too high, then I make sure that an extremely low banking bid from a buyer cannot win. Instead I buy back myself, keep the clearing price at an acceptable level and save the rights for the next period (banking).

The various banking bids only serve the purpose of dampening short-term inflationers or "price bubbles" by ensuring that every company has a supply from which it can shoot in the event of unfavorable price situations. Long term can constant Banking cannot be a solution for the equilibrium state, as this would bind more and more "dead" capital.

If banking were forbidden and unused sales offers would expire without the reduction quantities being reducible (reduction was possible in the simulation), then every seller would try very hard not to offer too many emission rights. With the result that there would be an undersupply on the market with a probability bordering on certainty.


If all players behave individually and rationally and the framework conditions remain constant, a fair balance should be established for buyer and seller after a few periods:

·         The buyers receive as many rights as they would otherwise have to reduce more expensively;

·         they pay a price for it just below their reduction costs.

·         The sellers produce as many emission rights as the buyers need.

·         Banking does not or hardly takes place.

Exercises, discussion points

1 At what price will company i get out of an ascending auction with a given cost structure if it behaves individually and rationally?

2 Discuss whether it is ecologically or economically beneficial to allow banking. Based on special cases, consider which prices can arise in an ascending auction when banking is permitted or when banking is prohibited. It is clear that banking can bring advantages if the framework conditions (emission targets) change (in which direction?) You can also argue why banking is also economically important in stationary framework conditions.

3 Create the simulation of a sealed bid auction in Excel folder AuktionSB.xls. Notes on implementation:

  • You can handle buy bids and sell bids compactly in one line if you introduce the following convention:
    • negative: sale, price is the minimum selling price
    • positive: purchase, price is purchase price














Player A buys at € 50. Player B sells 800 rights, but only at a minimum price of € 40. That means, at a price of 40 €, he effectively joins the ranks of buyers and "buys back" up to 800 rights. In the example, 600 rights move from B to A, B buys back 200 rights from himself and C comes away empty-handed.

  • After the bids (player number, quantity buy / sell, price) have been noted for each player 1, .., n, it is advisable to do the following via macro recording: Copy data into the work area, sort there by price, use ( previously created) formulas calculate result, copy results as values ​​(edit - paste content - values), back to player no. sort by.
    Or implement it via VBA.
  • Other realizations are of course also conceivable.

4 When does a clearing price auction lead to an unfair result? Who pays on it? Why can this be prevented with the Pay-Your-Bid variant?

Back to the outline

© Wolfgang Konen, July 1st, 2004, November 6th, 2005, August 11th, 2006

[2]One difficulty with the sealed bid auction in practice is whether it is really possible to ensure that it is “sealed”. There may be agreements between buyers (cartels) with which they can consciously “push” the price. This is not so easy with the Ascending Auction because the price and bids are open at all times.