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 can be applied primarily to explain labor market inefficiencies, but also for all forms of "buyers" and "sellers", whether products, homes or even spouses/partners. 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. Search theory has been applied in labor economics to analyze frictional unemployment resulting from job hunting by workers. In consumer theory, it has been applied to analyze purchasing decisions. From a worker's perspective, an acceptable job would be one that pays a high wage, one that offers desirable benefits, and/or one that offers pleasant and safe working conditions. From a consumer's perspective, a product worth purchasing would have sufficiently high quality and be offered at a sufficiently low price. In both cases, whether a given job or product is acceptable depends on the searcher's beliefs about the alternatives available in the market. More precisely, search theory studies an individual's optimal strategy when choosing from a series of potential opportunities of random quality, under the assumption that delaying choice is costly. Search models illustrate how best to balance the cost of delay against the value of the option to try again. Mathematically, search models are optimal stopping problems. Macroeconomists have extended search theory by studying general equilibrium models in which one or more types of searchers interact. These macroeconomic theories have been called 'matching theory', or search-and-matching theory.
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 equilibrium outcomes 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 Search 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 optimization 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
F n ( p ) = 1 − [ 1 − F ( p ) ] n {\displaystyle Fn(p)=1-[1-F(p)]n} .
Therefore, the plan of purchase outlay:
P ( n ) = K ∫ [ ( 1 − F ( p ) ] n d p {\displaystyle 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 ∗ ) ≥ c > P ( n ∗ ) − P ( n ∗ + 1 ) {\displaystyle P(n^{*}-1)-P(n^{*})\geq c>P(n^{*})-P(n^{*}+1)} .
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