User:Jingyiiii/Search theory

In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. It involves determining the best approach to use when looking for a specific item or person in a sizable, uncharted environment.The goal of the theory is to determine the best search strategy, one that maximises the chance of finding the target while minimising search-related expenses.

''Search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction. Search theory also provides an explanation for why frictional unemployment happens as people look for jobs and corporations look for new employees.''

''Search theory has been used primarily to explain labor market inefficiencies, but also for all forms of "buyers" and "sellers", whether products, homes or even spouses/partners. It can be applied. The clearing price will be met quickly as supply and demand react freely. However, this does not happen in the real world. Search theory tries to explain how.'' Real-world transactions involve discrete quantities of goods and services, imperfect and expensive information, and possible physical or other barriers separating buyers and sellers. parties looking to conduct business, such as a potential employee and an employer, or a buyer and a seller of goods. Their search for one another is strained by this encounter. These restrictions can come in the form of geographical differences, differing expectations regarding price and specifications, and slow response and negotiation times from one of the parties.

Foundation of Search theory
In a traditional economic equilibrium, small changes in supply or demand have only a small effect on the price. However, in a pairwise matching setting, even slight imbalances can have significant effects on the allocation of resources. For example, in a marriage market with slightly more men than women, all matching rents go to women, and vice versa.Furthermore, the unique nature of the items for sale in a matching market makes it challenging to model as a traditional market. This poses a challenge for online matching services that aim to organize such markets efficiently. Therefore the search frictions affect equilibirum outcomses in matching markets and search theory examines the role of option value in decision-making, including where to search and how long to search. It highlights the relationship between risk and option value and can be modeled as sequential or simultaneous search.

Simultaneous Search
The literature or research theory in economics regarding the Simultaneous Seach in economics was first introduced by Stigler G. in 1961( . In Stigler's simultaneous search model, a consumer selects how many searches to conduct while sampling prices from a distribution. For some distributions, the ideal sample size can be calculated using a straightforward one-variable optimisation problem and expressed in closed form.It is assumed that a non-degenerate distribution F(p) on [0, 1] provides the distribution of prices. A consumer chooses a fixed sample size n to minimize the expected total cost C (expected purchase cost plus search cost) of purchasing the product. With n independent draws, the distribution of the lowest price is

$$Fn(p)=1-[1-F(p)]n$$.

Therefore, the plan of pruchase outlay:

$$P(n)=K\int [(1-F(p)]^n dp $$

The expected price from the given distribution decreases as the number of searches increases, but the rate of decrease becomes smaller. This meets the second-order condition, and the optimal sample size (n*) satisfies the first-order condition, which states that the difference between the probability of finding the lowest price in (n*-1) searches and that of finding it in (n*) searches is greater than or equal to the search cost, which is greater than the difference between the probability of finding the lowest price in (n*) searches and that of finding it in (n*+1) searches.

$$P(n^*-1)-P(n^*)\geq c> P(n^*)-P(n*+1) $$.

Sequential Search
In sequential search, a consumer looks for a product or service one at a time until they find it, McCall J.J. introduced this type of search to economics. In economics, the sequential search model is used to examine how consumers choose which goods or services to purchase when they have asymmetrical information (incomplete)of those goods' quality.

Consumers in sequential search models must choose whether to stop looking for a better good or service or to buy what they have found so far. . The model makes the assumption that customers have some idea of what they want and what the standard of the good or service should be. Models of sequential search have been used in many disciplines, including finance and labour economics. Sequential search models are used in labour economics to examine how employees look for work and how employers hire new employees. Sequential search models are used in the field of finance to examine how investors look for information on stocks and other financial assets.

The assumption that consumers know what they are looking for and what the standard of the product or service should be is one of the limitations of sequential search models. This presumption might not always be accurate in practical circumstances. Another drawback is that sequential search models don't account for the possibility that customers could find out more about the calibre of a good or service as they search further.