Understanding Auctions and Auction Theory: Part 2

Actions and game theory are closely related. This is why many studies concerning any of them touch the other. When people talk about winning and losing, they don't always realize the economic impact of these terms, and this is where auctions may fit perfectly. An action is defined as a mechanism in which potential buyers submit to messages, and were items are distributed on the foundation of messages received and how they are received. In the previous section of the unit, we looked at the meaning of action, how it happens, and the different types used in the modern world.

But this introduction part was only to remind you of the basic idea of an auction. There is so much behind this subject, especially concerning its value to an economics student. It is more than just public or private value actions where everyone may have a different value for goods, and different outcomes are expected. It also goes beyond the common understanding of auction goods like paintings, collectibles, and specialty products.

Economist seeks to model these aspects, to understand why people make certain decisions and choices in life. One assumption when doing this is that individual values are drawn independently from distribution. In simple terms, each participant in an auction values the products and services they are bidding differently. They look at them from a more personal perspective depending on the value of the item and its value to the buyer or the seller's luck.

First-price seal-bid is one of the simplest forms of action. In this case, everyone simultaneously and privately submits a bid for an item – this is where 'sealed-bid' comes from. And whoever submits the highest bid wins the item – which is the 'first price.' This type is more like a game of changes where you place your bets, not knowing the outcome. It can also be compared to making decisions under uncertainty, which forces people to go for the most beneficial option. This type of auction is also a more direct link to the game theory and consumer models.

Generally, actions are events where participants bid for the right to buy a specific product. In other words, they will not be allowed to buy it, even though they are willing unless they win the right to buy through an action. Actions are considered a potentially efficient mechanism for selling and purchasing goods and services – involving different goods, particularly expensive goods.  

With this explanation, it is still hard to understand the in-depth of auctions and why they are relevant to the study of economics. But with the use of the action theory, we can tell which direction to take when faced with different decision-making situations, specifically auctions. It helps us learn more about why people make the decision they make under uncertainty and high-risk situations. This section introduces learners to this idea.

The general Idea in Auction Theory

Auction theory can be defined as the applied branch of economics, which deals with how people react in action markets. There are so many possible designs for an auction or set of rules in auction markets and issues that auction theorists have tried to uncover. Some of the main issues include the efficiency of specific auction design, optimal equilibrium bidding methods, and revenue comparison. Also, auction theory is a useful tool in informing the design of real-world actions. When looking at scenarios like privatization of public-sector company or sale of licenses for the use of the electromagnetic spectrum, there are so many issues, and processes involved that may need clearer explanations and understanding. The auction model and thought are laid bare and solutions to some of the hardest questions discovered.

One of the characteristics of actions is the presence of transactions that follow a specific set of rules exploring resource allocation according to the bids place by involved parties. This is why fall under the category of games with incomplete information, and because in the majority of actions, one party will own information related to the transaction that the other participant lacks. For instance, the bidders usually know the item's value, which other bidders and the seller does not know.

Auctions come in many forms, but they share similar features that are universally accepted and used to buy or sell any item. In many cases, the outcome of the auction does not rely on the identity of the bidders. This means auctions are anonymous. Traditionally, auctions were done in a live form. But with the emergence of the internet and technology, online auctions are becoming more and more popular.

In most auctions, the main feature is that participants submit bids, amount of money they are willing to part with for the item. In standard auctions, the winner of the action is the party with the highest bid, whereas nonstandard actions, like the lottery, do not require this. This leads us to the types of auctions common in the modern market.

- First-price sealed bid action is where bidders place their bids using sealed envelopes and hand them over to the auctioneer at the same time. The auctioneer opens the envelope with the highest bidder and announces them the winner.

- Second-price sealed-bid auctions are like the first-price auctions above, but the winner pay price equal to the second-highest bid.

- Open-ascending -the bid auction is also called the English action where participants place bids that are higher than the previous ones. Each of them stops bidding when they are not ready to pay anything higher than the current bid. This will go on until no party is ready to place a higher bid.

- Open descending bids are also called Dutch actions, in which the auctioneer sets the price high enough to deter all bidders, and decreases it slowly until one is ready to buy at the current price.

These four basic auction types define most auctions. But there are others that have also received some academic study.

The Benchmark Model

The benchmark model was defined by McAfee and MacMillan (1987) as a model that offers a generalization of the auction format. This definition is based on four assumptions:

- All the bidders are taking a neutral risk. In other words, they will lose nothing by either winning or losing the bid.

- Each bidder has a private valuation of the item being sold, which is independently drawn from some probability distribution. The is imperfect information where the bidder knows something about the item that other bidders or the seller does not know about.

- The participants are in possession of symmetric information.

- The payment comes as a function of only the bids.

This model has been applied widely in tandem with the Revelation Principle, which states that each of these basic auction approaches has been designed in a way that each bidder is potentially incentivized to report their valuation with honesty. The two are most used by selling parties to determine the type of action, which maximizes the expected price. This is an optimal auction format that is presented in such a manner that the product will be offered the participant with the highest valuation with price equal to their valuation, but the seller will refuse to release the item on sell if they expect all other valuations from the other parties to be less than their own.

Looking at the four assumptions of this model above, we can create auction formats with different characteristics. One, the risk-averse bidders incur some form of cost from participating in risky behavior, which affects how they value the item. For instance, in sealed-bid first-price auctions, these bidders are more willing to bid ore because they are looking for the best chance to win; hence, it increases their expected utility. This is why these type of bids produces more revenues than English and sealed-bid.

In formats that have co-related value, in which how bidders' value the item is not independent, one of the bidders may perceive their value of the item high. This increases the chances that the other bidders will perceive their own values to be high. A good example of this is the 'Winner's curse,' where the auction results tell the winner that their valuation of the item was higher than what the other bidders felt. Also, the linkage principle allows for comparing revenue among a fairly general class of auctions with interdependence between the valuing of different bidders.

In the asymmetric model, bidders are assumed to be separated into two main categories that find valuations from various distributions. For instance, dealers and collectors in an antique action are separated by how they value the items.

Other formats feature royalties or incentive payments, in which the seller incorporates additional factors, especially which can affect the item's value – including supply, production costs, and many others, into the price function.

Models linked to the Game-theory

We can also talk about a game-theoretic auction model, which is a mathematical game represented by a set of players, a set of actions or strategies from each player, and a payoff vector linked to each combination of approaches. In general, the players in this game are the buyers and sellers. Each play has a set action, which is a set of functions, or reservations prices. Each bid function stands for the player's value, or cost, to a bid price. The expected utility comes as the payoff of each player under a combination of strategies.

There are two general categories of the game-theoretic models:

- Private values model, in which a player assumes that competitors obtain private value from the probability distribution.

- The common value model states that the participants have an equal valuation of the item, but the lack of accurately perfect information from these values.  

In order to know the exact value of the item in question, each participant may assume that any other participant receives a random signal, om, which can be applied in finding the true value using the probability distribution that is common to all bidders. In most cases, there is an assumption in the private values model in that values are independent across bidders, and in the common value model, it is assumed that the values are only independent as far as the common factors of the probability distribution are concerned.

The affiliated values models are perhaps a more general category for strategic bidding. In this case, the player's total utility is dependent on private signal and some uncommon value. We can view both private vale and common value models as extensions of this model.

Sometimes it becomes necessary to make explicit assumptions about bidders' value distributions, where most published research assumes symmetric bidders. In other words, a probability distribution that gives bidders clues of their value is the same across players. Where the private values model is applied, independence is assumed, implying that the player's valuations are independently and identically distributed.

Revenue equivalence theorem and the Winner curse

The auction theory is highly applauded for finding the revenue equivalence theorem. In the earlier application of equivalence, much focus was placed on the comparison of revenue in the most common auctions.  Vickrey (1961) came out with the first such proof with a focus on two buyers and uniformly distributed values. Riley & Samuelson (1981) came up with proof of a more general result. 

With the revenue equivalence theory, any allocation strategy or action that is in line with the four main assumptions in the benchmark model will result in the same expected revenue for the selling party.

The winner's curse is another result that comes in common value settings (when the true values to the various bidders are not common but correlated). The bidders make a decision based on estimated values, in which case, the winner tends to be the one who placed the highest estimate, yet the final results will show the estimates from the other bidders on the value of the item are less, which give the winner a 'too-much-bid' impression. The winner's curse does not happen in the equilibrium of such a game since the players account for the bias in the strategies.

The auction theory tries to present some facts about what happens in decision-makers' minds, helping participants and other interested parties make a more informed decision. In economics, this is very crucial to economic growth and decision-making processes.

Author: James Hamilton