Search Theory

From wiki

search theory: studies buyers or sellers who cannot instantly find a trading partner, and must therefore search
In labor economics → analyze frictional unemployment from job hunting by workers
In consumer theory → analyze purchasing decisions
→ a given job or product is acceptable → depends on the searcher’s beliefs about the alternatives available in the market
=> an individual’s optimal strategy → choosing from a series of potential opportunities of random quality ← under the assumption that delaying choice is costly
=>> search models: how best to balance the cost of delay against the value of the option to try again (optimal stopping problems in math)

Search from a known distribution

George J. Stigler proposed thinking of searching for bargains or jobs as an economically important problem
– Stigler, George J. (1961). “The economics of information”. Journal of Political Economy69 (3): 213–225
– Stigler, George J. (1962). “Information in the labor market”. Journal of Political Economy70 (5): 94–105.

John J. McCall proposed a dynamic model of job search, based on the mathematical method of optimal stopping (base of later work)
– McCall, John J. (1970). “Economics of information and job search”. Quarterly Journal of Economics. 84 (1): 113–126. 
→ which job offers an unemployed worker should accept, and which reject ← when the distribution of alternatives is known and constantvalue of money is constant
=> optimal strategy → reservation wage  (reservation price in consumers searching for low price)
<= reservation wage may change over time if some of the conditions assumed are not met
a) 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 → optimal reservation wage will decline over time
b) if the worker is risk averse, the reservation wage will decline over time if the worker gradually runs out of money while searching.
Danforth, John P. (1979). “On the role of consumption and decreasing absolute risk aversion in the theory of job search”. In Lippman, S. A.; McCall, J. J. Studies in the Economics of Search. New York: North-Holland.
c) reservation wage would also differ for two jobs of different characteristics (compensating differential)
=>>  greater variance of offers → may make the searcher better off + prolong optimal search, even if risk averse → wait longer(set a higher reservation wage) in hopes of receiving an exceptionally high wage offer

Search from an unknown distribution
→ an additional motive for search: by searching longer, more is learned about the range of offers available (multi-armed bandit problem)
optimal search strategies for an unknown distribution have been analyzed using allocation indices such as the Gittins index.

A violation of the law of one price
when buyers do not have perfect information about where to find the lowest price (whenever search is necessary) → sellers may wish to offer different price
=> a trade-off between the frequency and the profitability of their sales (target on consumers with the highest/low reservation prices)
– Butters, G. R. (1977). “Equilibrium distributions of sales and advertising prices”. Review of Economic Studies. 44: 465–491. doi:10.2307/2296902.
– Jump up ^ Burdett, Kenneth; Judd, Kenneth (1983). “Equilibrium price dispersion”. Econometrica. 51 (4): 955–969.

## it is reasonable to argue that the seller is able to change or affect reservation prices if buyer needs to learn the distribution of price from past searching. However, knowledge or other reserved information may also work in the process of searching and learning of distribution.

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. Diamond, Dale Mortensen, and Christopher A. Pissarides won the 2010 Nobel prize in economics for their work on matching theory.
=> 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


Markets with Search Frictions The Nobel Prize in Economic Sciences 2010 – Advanced Information


Classic papers

Information and consumer behavior P Nelson – Journal of political economy, 1970

Economics of information and job search JJ McCall – The Quarterly Journal of Economics, 1970


Job search papers

Directed Search: A Guided Tour R Wright, B Julien, P Kircher, V Guerrieri – 2017

Search theory → understanding many phenomena troublesome for classical theory
(e.g.  coexistence of unemployment and vacancies + price or wage dispersion and stickiness + bid-ask spreads + the difficulties of bilateral trade that generate a role for money and related institutions + partnership formation + long and variable durations in the time to execute trades in labor, housing and other markets)

→ a relatively recent branch of the field called directed, or competitive, search

older literature on random search:
On goods markets, see Burdett and Judd (1983), Rubinstein and Wolinsky (1987), Shi (1995) or Trejos and Wright (1995).
On labor, see Mortensen and Pissarides (1994), Burdett and Mortensen (1998) or Pissarides (2000).
On marriage, see Mortensen (1988), Burdett and Coles (1997) or Shimer and Smith (2000). 

Traditional search theory
→ typically assumes the agents meet bilaterally and at random
← a meeting results in matching (trading or forming a relationship) can be endogenous, especially when there is heterogeneity
→ assume the terms of trade are determined by bargaining, or some related mechanism, after agents meet

Directed/Competitive search
agents have information to target their search towards particular types, or sometimes particular individuals, in the market
→ the terms of trade (prices, or more generally, contracts or mechanisms) are announced or posted in advance to attract/direct agents on the other side of the market

=> posted prices have an allocative role → giving agents incentives to seek out particular counterparties → often leads to efficiency  ## can also be misleading  
=> posting entails commitment → circumvents holdup problems with bargaining  (# a claimant of welcome for bargain or no bargain improve efficiency of searching given the bargaining cost)

More realistic
In contrast to what happens in [random] search models, exchanges in actual market economies are organized by specialist traders, who mitigate search costs by providing facilities that are easy to locate.
(Thus when people wish to buy shoes they go to a shoe store; when hungry they go to a grocer; when desiring to sell their labor services they go to firms known to offer employment. Few people would think of planning their economic lives on the basis of random encounters.”)

Peter Howitt (2005) “Beyond Search: Fiat Money in Organized Exchange,” IER 46, 405-429.

“someone wishing to exchange his house goes to estate agents or advertises — he does not, like some crazed particle, wait to bump into a buyer.”
“I think the bilateral monopoly problem has been solved. There are stores that compete. I know where the drug store and the supermarket are, and I take their posted prices as given. If some supermarket offers the same quality of services and charges lower prices, I shop at that lower price supermarket.”

frictions take center stage, even when the set of agents is large
← Research often makes a concerted effort to analyze strategic aspects of markets with finite numbers of agents → in several settings as these numbers get large, strategic considerations vanish
→ a competitive search model means a limiting large economy → large markets, finite markets and limiting results (limiting results are nice because intuition that markets becoming competitive when the set of agents is large, but formalizing this can be difficult (see Gale 2000 and references therein))
=> some sellers can have few or no customers, while others have more than they can handle → leading to rationing, unsold inventories, the coexistence of vacancies and unemployment, etc.

A simple yet powerful idea:
if you post more favorable terms customers come to you with higher probability, but not necessarily probability 1, due to capacity issues
=> Agents on both sides of the market face thus a trade off between prices and probabilities →  may not be smart to go where everyone else goes
=> pricing not only quantities but also the time required to trade → delivers unique outcomes with remarkable efficiency properties (traditional search theory is typically rife with inefficiencies) → competitive search can also accommodate complications (like private information or liquidity frictions) → may lead to multiplicity or inefficiency


Search-theoretic models of the labor market: A survey R Rogerson, R Shimer… – Journal of …, 2005


Looking into the black box: A survey of the matching function B Petrongolo, CA Pissarides – Journal of Economic literature, 2001


Sorting through search and matching models in economics H Chade, J Eeckhout, L Smith – Journal of Economic Literature, 2017



Consumer search theory papers

Firm Pricing with Consumer Search Simon P Anderson § Régis Renault CEPR Discussion Paper

Search costs are often ignored by economist ← few people actually actively searched much + less visible as a friction in market + treating set of available products as effectively given and known => important for better matching and lower prices from more competition (less oligopoly pricing)
Consumer search: internet → lower search cost + low transaction costs for shipping => consumers enable to access a huge variety of options → used to be silently curtailed by sc now visible → nonetheless, significant search frictions remains

2. Price dispersion

Stigler (1961):  price dispersion may persist ← consumers are not aware of all prices + therefore cannot properly arbitrage price differences
=> costly search by buyers generates price dispersion → from the price mixed strategies used by firms

2.1 Imperfect buyer information yields price dispersion

n firms: pc=0, homogeneous production
m consumers: valuation=r, σ shoppers: sc=0 → always buy at the lowest price in the market,  (m-σ) shoppers: observe only one price for free and high sc for an additional price → buy from free price quote, γ=(m-σ)/n = captive consumer per firm → firm guarantee a profit of γr by charging the monopoly price r and selling exclusively to γ

Bertrand undercutting: no pure strategy equilibrium for a price exceeds mc → a firm at a price above mc could always profitably capture entire σ demand by slightly undercutting price
← but pricing at mc cannot be an equilibrium → no profit → can always guarantee a strictly positive profit by giving up selling to σ and extracting the entire surplus from γ
→ it is optimal for that firm to charge r and get γr

=> minimum equilibrium price:  (γ + σ)p = γr  →  p_ = γ/(γ+σ) * r
(no one does actually search again in equilibrium → prices are rationally expected to be same for all firms → no search that monopoly price sustains)

(even a small search cost radically tips the Bertrand Paradox to the Diamond Paradox which has all firms pricing at monopoly price)

(## 1) there is not reasonable to assume 0 sc if we think of unknown of unknown. 2) why cannot firm also search for the type of consumer, then price r to γ and p to σ ? 3) firm can affect the consequent searching cost by misleading when they touch with consumers. 4) why are price dispersion shown among different brands rather than different districts, while the later seems more related to sc)

Varian(1980) + followers: unique symmetric mixed strategy equilibrium
スクリーンショット 2017-10-01 14.16.11スクリーンショット 2017-10-01 14.10.15

2.2 Simultaneous search and the coordination problem

2.3 Sequential search and the Diamond paradox

2.4 Price advertising 

3. Matching products to consumers

3.1 optimal search behavior

3.2 Equilibrium and comparative statics

3.3 Mergers and cartels

3.4 Ordered search

4. Seller heterogeneity 

5. Buyer heterogeneity

6. Conclusions



Business as usual: A consumer search theory of sticky prices and asymmetric price adjustment L Cabral, A Fishman – International Journal of Industrial Organization, 2012

Empirical evidence suggests that prices are sticky with respect to cost changes. Moreover, prices respond more rapidly to cost increases than to cost decreases. We develop a search theoretic model which is consistent with this evidence and allows for additional testable predictions. Our results are based on the assumption that buyers do not observe the sellers’ costs, but know that cost changes are positively correlated across sellers. In equilibrium, a change in price is likely to induce consumer search, which explains sticky prices. Moreover, the signal conveyed by a price decrease is different from the signal conveyed by a price increase, which explains asymmetry in price adjustment.

When do consumers search? MS Lewis, HP Marvel – The Journal of Industrial Economics, 2011


Oligopolistic markets with sequential search and production cost uncertainty
M Janssen, P Pichler… – The RAND Journal of …, 2011

Search costs in concentrated markets: An experimental analysis C Moellers, T Stühmeier, T Wenzel – 2016



# Questions:

What decide the searching costs which is surly subjective and endogenous?
How does the distribution of results which is also subjective change along with searching activities? (bayesian adjustment)

Moreover, there is searching strategy like inquiring someone who has better knowledge about searching cost and result distribution. (directed search) However in such case, there are also adverse selection problem born from asymmetric information.



Other theories about consumer searching (marketing & behavior economics)

Consumer information search revisited: Theory and empirical analysis S Moorthy, BT Ratchford… – Journal of consumer …, 1997

Toward a positive theory of consumer choice R Thaler – Journal of Economic Behavior & Organization, 1980

A model of consumer information search behavior for new automobiles GN Punj, R Staelin – Journal of consumer research, 1983

Consumer information search behavior and the Internet RA Peterson, MC Merino – Psychology & Marketing, 2003

A proposed model of external consumer information search JB Schmidt, RA Spreng – Journal of the academy of marketing science, 1996


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