Search theory
Encyclopedia
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.
Search theory has been influential in many areas of economics. It 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'.
, on which much later work has been based. McCall's paper studied the problem of which job offers an unemployed worker should accept, and which reject, when the distribution
of alternatives is known and constant, and the value of money is constant. Holding fixed job characteristics, he characterized the job search decision in terms of the reservation wage
, that is, the lowest wage the worker is willing to accept. The worker's optimal strategy is simply to reject any wage offer lower than the reservation wage, and accept any wage offer higher than the reservation wage.
The reservation wage may change over time if some of the conditions assumed by McCall are not met. For example, a worker who fails to find a job might lose skills or face stigma, in which case the distribution of potential offers that worker might receive will get worse, the longer he or she is unemployed. In this case, the worker's optimal reservation wage will decline over time. Likewise, if the worker is risk averse
, the reservation wage will decline over time if the worker gradually runs out of money while searching. The reservation wage would also differ for two jobs of different characteristics; that is, there will be a compensating differential
between different types of jobs.
An interesting observation about McCall's model is that greater variance
of offers may make the searcher better off, and prolong optimal search, even if he or she is risk averse
. This is because when there is more variation in wage offers (holding fixed the mean), the searcher may want to wait longer (that is, set a higher reservation wage) in hopes of receiving an exceptionally high wage offer. The possibility of receiving some exceptionally low offers has less impact on the reservation wage, since bad offers can be turned down.
While McCall framed his theory in terms of the wage search decision of an unemployed worker, similar insights are applicable to a consumer's search for a low price. In that context, the highest price a consumer is willing to pay for a particular good is called the reservation price
.
problem. The name comes from the slang term 'one-armed bandit' for a casino slot machine, and refers to the case in which the only way to learn about the distribution of rewards from a given slot machine is by actually playing that machine. Optimal search strategies for an unknown distribution have been analyzed using allocation indices such as the Gittins index
.
led economists to ask why the same good should ever be sold, in equilibrium, at more than one price. After all, this is by definition a violation of the law of one price
. However, when buyers do not have perfect information about where to find the lowest price (that is, whenever search is necessary), not all sellers may wish to offer the same price, because there is a trade-off between the frequency and the profitability of their sales. That is, firms may be indifferent between posting a high price (thus selling infrequently, only to those consumers with the highest reservation prices) and a low price (at which they will sell more often, because it will fall below the reservation price of more consumers).
, Dale Mortensen, and Christopher A. Pissarides
won the 2010 Nobel prize in economics for their work on matching theory.
In models of matching in the labor market, two types of search interact. That is, the rate at which new jobs are formed is assumed to depend both on workers' search decisions, and on firms' decisions to open job vacancies. While some matching models include a distribution of different wages, others are simplified by ignoring wage differences, and just imply that workers pass through an unemployment spell of random length before beginning work.
Microeconomics
Microeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...
, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting.
Search theory has been influential in many areas of economics. It has been applied in labor economics to analyze frictional unemployment
Frictional unemployment
Frictional unemployment is the time period between jobs when a worker is searching for, or transitioning from one job to another. It is sometimes called search unemployment and can be voluntary based on the circumstances of the unemployed individual....
resulting from job hunting
Job hunting
Job hunting, job seeking, or job searching is the act of looking for employment, due to unemployment or discontent with a current position. The immediate goal of job seeking is usually to obtain a job interview with an employer which may lead to getting hired...
by workers. In consumer theory
Consumer theory
Consumer choice is a theory of microeconomics that relates preferences for consumption goods and services to consumption expenditures and ultimately to consumer demand curves. The link between personal preferences, consumption, and the demand curve is one of the most closely studied relations in...
, 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
Strategy (game theory)
In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
when choosing from a series of potential opportunities of random
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
quality, under the assumption that delaying choice is costly. Search models
Model (economics)
In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using...
illustrate how best to balance the cost of delay against the value of the option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
to try again. Mathematically, search models are optimal stopping
Optimal stopping
In mathematics, the theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance...
problems.
Macroeconomists
Macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...
have extended search theory by studying general equilibrium
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...
models in which one or more types of searchers interact. These macroeconomic theories have been called 'matching theory
Matching theory (macroeconomics)
In macroeconomics, matching theory, also known as search and matching theory,is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time. It offers a way of modeling markets in which frictions prevent instantaneous adjustment of the level of...
', or 'search and matching theory'.
Search from a known distribution
George J. Stigler proposed thinking of searching for bargains or jobs as an economically important problem. John J. McCall proposed a dynamic model of job search, based on the mathematical method of optimal stoppingOptimal stopping
In mathematics, the theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance...
, on which much later work has been based. McCall's paper studied the problem of which job offers an unemployed worker should accept, and which reject, when the distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
of alternatives is known and constant, and the value of money is constant. Holding fixed job characteristics, he characterized the job search decision in terms of the reservation wage
Reservation wage
In labor economics, the reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. A job offer involving the same type of work and the same working conditions, but at a lower wage rate, would be rejected by the worker.An individual's reservation...
, that is, the lowest wage the worker is willing to accept. The worker's optimal strategy is simply to reject any wage offer lower than the reservation wage, and accept any wage offer higher than the reservation wage.
The reservation wage may change over time if some of the conditions assumed by McCall are not met. For example, a worker who fails to find a job might lose skills or face stigma, in which case the distribution of potential offers that worker might receive will get worse, the longer he or she is unemployed. In this case, the worker's optimal reservation wage will decline over time. Likewise, if the worker is risk averse
Risk aversion
Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....
, the reservation wage will decline over time if the worker gradually runs out of money while searching. The reservation wage would also differ for two jobs of different characteristics; that is, there will be a compensating differential
Compensating differential
Compensating differential is a term used in labor economics to analyze the relation between the wage rate and the unpleasantness, risk, or other undesirable attributes of a particular job...
between different types of jobs.
An interesting observation about McCall's model is that greater variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
of offers may make the searcher better off, and prolong optimal search, even if he or she is risk averse
Risk aversion
Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....
. This is because when there is more variation in wage offers (holding fixed the mean), the searcher may want to wait longer (that is, set a higher reservation wage) in hopes of receiving an exceptionally high wage offer. The possibility of receiving some exceptionally low offers has less impact on the reservation wage, since bad offers can be turned down.
While McCall framed his theory in terms of the wage search decision of an unemployed worker, similar insights are applicable to a consumer's search for a low price. In that context, the highest price a consumer is willing to pay for a particular good is called the reservation price
Reservation price
In microeconomics, the reservation price is the highest price a buyer is willing to pay for goods or a service; or; the smallest price at which a seller is willing to sell a good or service...
.
Search from an unknown distribution
When the searcher does not even know the distribution of offers, then there is an additional motive for search: by searching longer, more is learned about the range of offers available. Search from one or more unknown distributions is called a multi-armed banditMulti-armed bandit
In statistics, particularly in the design of sequential experiments, a multi-armed bandit takes its name from a traditional slot machine . Multiple levers are considered in the motivating applications in statistics. When pulled, each lever provides a reward drawn from a distribution associated...
problem. The name comes from the slang term 'one-armed bandit' for a casino slot machine, and refers to the case in which the only way to learn about the distribution of rewards from a given slot machine is by actually playing that machine. Optimal search strategies for an unknown distribution have been analyzed using allocation indices such as the Gittins index
Gittins index
The Gittins index is a measure of the reward that can be achieved by a process evolving from its present state onwards with the probability that it will be terminated in future...
.
Endogenizing the price distribution
Studying optimal search from a given distribution of pricesPrice dispersion
In economics, price dispersion is variation in prices across sellers of the same item, holding fixed the item's characteristics. Price dispersion can be viewed as a measure of trading frictions . It is often attributed to consumer search costs or unmeasured attributes of the retailing outlets...
led economists to ask why the same good should ever be sold, in equilibrium, at more than one price. After all, this is by definition a violation of the law of one price
Law of one price
The law of one price is an economic law stated as: "In an efficient market, all identical goods must have only one price."-Intuition:The intuition for this law is that all sellers will flock to the highest prevailing price, and all buyers to the lowest current market price. In an efficient market...
. However, when buyers do not have perfect information about where to find the lowest price (that is, whenever search is necessary), not all sellers may wish to offer the same price, because there is a trade-off between the frequency and the profitability of their sales. That is, firms may be indifferent between posting a high price (thus selling infrequently, only to those consumers with the highest reservation prices) and a low price (at which they will sell more often, because it will fall below the reservation price of more consumers).
Matching theory
More recently, job search, and other types of search, have been incorporated into macroeconomic models, using a framework called 'matching theory'. Peter A. DiamondPeter A. Diamond
Peter Arthur Diamond is an American economist known for his analysis of U.S. Social Security policy and his work as an advisor to the Advisory Council on Social Security in the late 1980s and 1990s. He was awarded the Nobel Memorial Prize in Economic Sciences in 2010, along with Dale T. Mortensen...
, Dale Mortensen, and Christopher A. Pissarides
Christopher A. Pissarides
Christopher Antoniou Pissarides F.B.A. is a Cypriot economist. He currently holds the Norman Sosnow Chair in Economics at the London School of Economics. His research interests focus on several topics of macroeconomics, notably labor, economic growth, and economic policy. In 2010, he was awarded...
won the 2010 Nobel prize in economics for their work on matching theory.
In models of matching in the labor market, two types of search interact. That is, the rate at which new jobs are formed is assumed to depend both on workers' search decisions, and on firms' decisions to open job vacancies. While some matching models include a distribution of different wages, others are simplified by ignoring wage differences, and just imply that workers pass through an unemployment spell of random length before beginning work.
See also
- Optimal stoppingOptimal stoppingIn mathematics, the theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance...
- Job huntingJob huntingJob hunting, job seeking, or job searching is the act of looking for employment, due to unemployment or discontent with a current position. The immediate goal of job seeking is usually to obtain a job interview with an employer which may lead to getting hired...
- Reservation wageReservation wageIn labor economics, the reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. A job offer involving the same type of work and the same working conditions, but at a lower wage rate, would be rejected by the worker.An individual's reservation...
- Frictional unemploymentFrictional unemploymentFrictional unemployment is the time period between jobs when a worker is searching for, or transitioning from one job to another. It is sometimes called search unemployment and can be voluntary based on the circumstances of the unemployed individual....
- Price dispersionPrice dispersionIn economics, price dispersion is variation in prices across sellers of the same item, holding fixed the item's characteristics. Price dispersion can be viewed as a measure of trading frictions . It is often attributed to consumer search costs or unmeasured attributes of the retailing outlets...
- Information economicsInformation economicsInformation economics or the economics of informationis a branch of microeconomic theory that studies how information affects an economy and economic decisions. Information has special characteristics. It is easy to create but hard to trust. It is easy to spread but hard to control. It...
- Labor economics
- Real options analysisReal options analysisReal options valuation, also often termed Real options analysis, applies option valuation techniques to capital budgeting decisions. A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or contract a...
- Search costSearch costSearch costs are one facet of transaction costs or switching costs. Rational consumers will continue to search for a better product or service until the marginal cost of searching exceeds the marginal benefit. Search theory is a branch of microeconomics that studies decisions of this type.The costs...