• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Explain the proposition that it does not matter to a seller which type of auction is used.

Extracts from this document...

Introduction

Name: Upesh Patel

Course: ES3600

Tutor: Martin Currie

Microeconomics Essay

Explain the proposition that it does not matter to a seller which type of auction is used.

        Some of the most exciting advances in recent microeconomic theory have been in the modelling of strategic behaviour under asymmetric information. One of the fundamental aspects of this area is the theory of bidding systems in auctions. An auction is a formal institutional arrangement for allocating scarce commodities among competing bidders. According to McAfee and McMillan (1989), “some theoretical study of auctions is warranted,” seeing as they are increasingly used in the exchange of goods in modern times.

        Many advances have been made in creating theories to explain auctions. When discussing theories on auctions, we focus on the case of N bidders competing to buy a single unit of a commodity. Economic theorists have identified four primary auction mechanisms, the first of which is the English auction. This is the type most people are familiar with. An English auction is an open one, which involves ascending bids, and the auction ends when no higher bids are forthcoming. The good goes to the bidder who makes the final bid at a price equal to that bid. The Dutch auction is also an open auction, but involves descending bids, where the price is reduced until some bidder indicates their willingness to pay the going price. First Price Sealed Bidding auctions differ from the auctions mentioned above because they are “closed” auctions.

...read more.

Middle

th order statistic is: N+1-g/N+1.  Finally, at the time of bidding, any particular bidder is the only one who knows his own valuation. The fact that there are N risk neutral bidders, and that each bidders valuation is drawn from the uniform distribution mentioned earlier, are common knowledge.

        I will now go on to analyse the outcomes of each of the four different auctions. I will begin with the English auction. Assuming infinitesimally small increments are possible, bidder i has a dominant strategy: raise the standing bid if and only if i’s valuation is more than the bid made by bidder k. To understand why this is the case, we need to realise that as the auction progresses, bidders drop out when the standing bid reaches their valuations. Thus, when the bidder with the highest valuation submits a bid equal to the second highest valuation, the bidding process stops. Therefore, the highest bidder receives the good and pays a price equal to the second-highest valuation, which we denote Pe = v2. (where Pe denotes the equilibrium price for the English auction, and v2 is the second highest valuation.)  The expected price to the seller is N-1/N+1. (Obtained from the equation for the gth order statistic.)

        The English auction bears a strong resemblance to the case of Second Price Sealed Bidding.

...read more.

Conclusion

        To determine the outcome of the auctions, theorists have focused on Nash equilibria. Each bidder is employing their optimal bidding strategy given their beliefs about the bidding strategy of others, where their beliefs are confirmed in equilibrium. With N bidders, a symmetric Nash equilibrium for our uniform distribution involves: bi(vi)=N-1/N(vi), for i=1…N. since each bidders bid is increasing in their own valuation, the item goes  to bidder 1 at a price N-1/N(vi). The expected price in these auctions is: N-1 / N x E(vi) = (N-1/N) x (N/N+1) = N-1/N+1. As we can see, all four auctions result in the same expected price to the seller. In general, the actual prices will not be the same for all auctions, since the equilibrium price for the Dutch and FPSB auctions does not equal the equilibrium price for the Dutch an SPSB auctions. However, the fact that the expected prices are the same is nonetheless an important result. We have thus confirmed the revenue equivalence theorem. Under the stipulated assumptions, the four primary types of auction are “equivalent” in that they would all yield the same expected price to the seller, with the item going to bidder who values it most highly. This theorem explains why it would not matter to a seller which type of auction is used.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Investigating the Relationship Between the Amount of Money a Football Club Receives and its ...

    34 76 25000 �2,500,000 19 1 Bradford City 2 46 15 4 4 48 20 11 5 7 34 27 87 18018 �2,004,000 35 1 Bristol City 24 46 7 8 8 35 36 2 7 14 22 44 42 21479 �1,185,000 -23 1 Bury 22 46 9 7 7

  2. "The lengths of lines are easier to guess than angles. Also, that year 11's ...

    the equation for standard deviation, which is shown on page 17, was -0.066620879, this means that5 there would be VERY slight negative correlation, but hardly any at all, meaning that if a year 9 isn't very good at estimating the length of a line, then they are not necessarily bad at estimating the angle size.

  1. Data Analysis of American House Price

    By looking at the table it is clear that the majority of the houses with a pool have also a garage, with 58,18% (32 out of 55 houses with a pool); while 41,82% (23 out of 55) houses with a pool do not have a garage.

  2. Used Cars - What main factor that affects the price of a second hand ...

    I have chosen these factors to investigation as I think they are the most relevant to the price of a car and the most important things to consider when purchasing a second hand car. Obtaining a sample of cars From the database of used cars I will collect a sample of 50 cars.

  1. Case study -Super Savers is wishing to move into the UK Food Retail market.

    Technical personnel can make mistakes in serving other sequences. Unwanted fluctuations in sample temperature or other conditions may enter the picture. On the other hand, most of these problems can be eliminated or minimised in a well-designed test. Rules followed for effective performance and accurate results: * Do not make things too complicated for the assessors * Recruit the

  2. Factors that most affect the prices of second hand cars

    I realised this after I had completed my first graph, in this graph I compared the decrease in price and the age and this is what the results showed: As you can see these results are not accurate at all, it does not demonstrate my point clearly at all and I then decided to do the percentage decrease.

  1. The case is about the Monetta Financial Services Company, an investment house.

    of 16.7%. As compared to IPOs allocated to fund clients where the mean appreciation in the price is 22.7% with a standard deviation of 19.3%. It clearly indicates that IPOs allocated to directors have higher returns with low risk attached to them.

  2. Reaction Times

    To pick the 25 girls and 25 boys from the data bank, I will use systematic sampling whereby I will role a dice, then take the number it lands on and then pick every 'nth' person on the list. I have rolled a 4, so I will pick every 4th

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work