Additional Auction Theory
Social Welfare
Commerce is about distributing resources in such a way where everyone is better off after each transaction.
The goal is to maximise social welfare. This is controversial as no-one wants to have less money (rich or poor).
- Maximising Social Welfare
- An auction protocol maximises social welfare if whenever all bidders are rational, the item is guaranteed to end up with the person who values it the most.
- Rational Bidder
- A person who plays an optimal strategy if it exists, otherwise a rationalisable strategy.
It may be the case that the item is not sold as the seller values it more than any buyer.
Limitations of Social Welfare
It is unfortunate that if someone pays more for an item, this maximises social welfare. This leads to poor people unable to get what they need if a rich person can pay more.
We can respond in several ways:
- Evil - Bidder 2 is willing to pay more, so bidder 1 should starve.
- Reasonable - Bidder 1’s inability to pay for food is a societal problem and should be solved by government.
- Pragmatic - Social welfare is not a perfect measure, but it is good enough to be useful.
Truthfulness
To find the value of an item, we ask the bidders their valuation:
- We call this their bid.
The bidder may lie to optimise their profits.
A truthful auction is one where a bidder is forced to bid their valuation of the item in an optimal strategy.
In this case it is easy to optimise social welfare.
A bid is truthful:
- If the amount you bid is equal to your value for the item.
An auction is truthful:
- If bidding truthfully is always (one of) the optimal strategy/ies.
Auction Properties
| Auction Type | Max Social Welfare | Truthful |
|---|---|---|
| English (with minimum) | 0 | 0 |
| English (without minimum) | ~ | ~ |
| Japanese | 1 | 1 |
| Dutch | 0 | 0 |
| First-price Sealed | 0 | 0 |
| Second-price Sealed | 1 | 1 |
| Deterministic All-pay | 0 | 0 |
| Non-deterministic All-pay | 0 | 0 |
It should be common knowledge that all participants are rational for this to be true.
English without minimum increase is generally not truthful or maximising social welfare. However, you can derive the participants valuation from their strategy.
- If an auction if truthful then it maximises social welfare.