An Experimental Health Insurance Market with Regulatory Minimums
By Carl A. Johnston
Abstract
We use experiments to explore the effect of imposing minimum standards on a subsidized health insurance
market with four insurers. We discuss evidence showing that the minimum standard may enhance the efficiency
and stability of insurance coverage for insurance recipients with highest costs. However, when the minimum
standard is eliminated, insurers seldom reduce benefits to the Cournot equilibrium but instead find market
levels substantially above the minimum requirement. Unregulated insurers took median profit amounting to
half of the potential Cournot profit, similar to their regulated counterparts. Regulated insurers write fewer but
more generous policies. Puzzlingly, regulated insurers offered more generous benefits even though regulations
permitted oligopolistic behavior. We examine possible explanations for this behavior, including the effect of
reduced information flow in a regulated market that may impede oligopolistic coordination.
Introduction
Governments are exploring the need for minimum standards for health insurance.
Currently, at least a dozen states are considering health care reforms that involve mandated
minimum insurance coverage. The state of Massachusetts required residents to buy a certain
level of health insurance. California has considered a similar move. Medicare Part D, the
government sponsored pharmaceutical drug insurance market for retired persons features
flexible standards based on the notion of “actuarial equivalence” to a standard policy. It is an
open question whether or not these mandates help consumers.
An important reason for setting standards in health insurance is regulators’ assumption
that markets will fail to provide sufficient coverage without regulatory guidance. In this paper,
we devised laboratory experiments to find out if a) regulators’ assumptions are correct in a
controlled environment, and b) we can explore the mechanisms by which the regulation affects
the problem.
In the rest of the paper, we will discuss 1) the literature about minimum standards, 2)
discuss a theoretical model of a subsidized health insurance market including Consumers,
Insurers and Government Regulators; 2) establish proof of an (Insurance Market) Cournot
Equilibrium in the scenario to be used in the experiments; 3) provide a description of the
Experiments, and 4) explain the results of human experimental insurance markets in regulated
and unregulated scenarios.
Minimum Standards in Economic Literature
Why do regulators wish to set standards for insurance value? One objective is to give
exogenous guidance to a market that may not achieve equilibrium without government
intervention. Individuals in insurance markets must somehow divide up a large common cost
such as the cost of disaster or bad health. Because no Pareto solution to the division of a
common cost exists, the outcome of the exercise is frequently inefficient. Another reason for
failure is the informational asymmetry inherent in health care markets. Concern about
1
insurance market failure is relatively recent. (Arrow) argued that if externalities arose that
caused an insurance market to fail, non-market institutions would spontaneously emerge to
bridge the gap and restore markets to equilibrium. Subsequent literature attempted to prove the
existence of equilibrium. (Mossin) set the mathematical basis for research into insurance
optimality by applying the expected utility approach to the calculation of equilibria. (Smith)
further refined the expected utility approach by proving that individuals in certain
circumstances could optimize their utility by self-insuring (not purchasing insurance).
Later some argued that competitive insurance markets rarely reach equilibrium because
of adverse selection bias—the fact that insurance tends to be bought by those who know they
have high costs and shunned by those with low costs. For example, in their seminal article,
{Michael Rothschild and Joseph Stiglitz} (1976) claimed that information externalities in the
competitive insurance market make equilibrium a rare event. They maintained that people with
a propensity for incurring high costs who knowingly purchase insurance priced for lower risk
persons create an externality that the market cannot overcome. They argued high-risk persons
should volunteer information about themselves so that insurers can properly price their risk.
Because high-risk persons seldom volunteer such information, market equilibria are rarely
observed.
“In the insurance market… if individuals were willing or able to reveal their information,
everybody could be made better off. By their very being, high-risk individuals cause an externality: the
low-risk individuals are worse off than they would be in the absence of the high-risk individuals.
However, the high-risk individuals are no better off than they would be in the absence of the low-risk
individuals.”
Several authors have studied the problem of adverse selection in competitive insurance
markets and whether or not selection bias does indeed make it difficult for markets to
equilibrate. Equilibriums may be achieved under circumstances when offerors are able to react
to competitors’ offers (Riley), when unprofitable firms withdraw their offers (Wilson), when
insurance buyers dissemble (Grossman), or when incomplete coverage is allowed (Jeleva and
Villeneuve). A more recent line of inquiry has focused on the existence of characteristic
heterogeneity among insurance buyers and to explore the possibilities this might have on
different kinds of equilibriums. Chiu and Karni (Chiu and Karni) and Miyazaki (Miyazaki)
discuss the broad issue of private information in the unemployment insurance market.
(Wambach) discusses how wealth of generic insurance buyers can affect the existence of
equilibria, although he concedes that the implications of this are ambiguous. Smart (Smart) and
deMeza and Webb (Meza and Webb) look at the possibility of double-crossing equilibria when
taking risk-aversion into account and give proofs of the existence of these equilibria. An
important study with respect to the experiments described here was {Dionne and Lasserre}
showing that inefficiency due to adverse selection could be eliminated when insurers use multiperiod contracts that induce the insured to announce their true risk, allowing insurers to adjust.
Subsequent to Rothschild, Stiglitz, a body of literature showed that the predicted
informational asymmetry were not evident in statistical analysis of actual insurance markets.
{Cawley and Philipson} (1999) documented the lack of selection in the life insurance market.
Two years later, Cardon and Hendel (Cardon and Hendel) made similar findings. {Finkelstein
and McGarry (2006)} found more evidence in the long-term health care insurance market,
2
although Finkelstein and Poterba {Finkelstein and Poterba 2004} found only partial evidence of
adverse selection in the U.K. Annuity Market. Browne (Browne) made another partial finding in
the U.S. individual health insurance market. A clear finding of absence of adverse selection
came in the market for automobile insurance in France (Chiappori and Salanie), however,
insurers in this case had the ability to quote premiums individually and a substantial amount of
information about prospective clients.
Minimum value standards in health insurance1 can be understood as a type of minimum
quality standard (MQS), which has been widely studied. Much of the discussion has centered
on the trade-off between improvements in quality versus potential costs that tend to reduce
Pareto improvements such as higher prices, or reduced availability of the regulated product.
Ronnen (Ronnen) found that regulation of quality reduced the extent to which companies could
compete on the basis of quality, thereby intensifying price competition. This yielded better
qualities, and lower hedonic prices making all consumers better off. Ronnen’s work has since
been complemented by others who have qualified the finding by stating that regulations should
be sensitively applied so as not to interfere with pre-regulatory profit-making incentives
(Crampes and Hollander) or with firms’ need to innovate (Maxwell). Others have considered
the possibility that social welfare could be damaged if quality standards create an incentive for
regulated firms to collude, resulting in decreasing profit levels, maximum quality and average
quality consumed. (Valletti) (Scarpa) {Valletti, Hoernig et al. 2002} A few authors have
investigated MQS regulation of the health care insurance market and found many of the same
trade-offs between quality improvements (generosity of the health care benefit) and prices
(premiums) and access to insurance. (Neudeck and Podczeck) (Encinosa)
Actual application of a minimum standard to an existing health care insurance regime is
a rare occurrence, so field studies examining such cases are correspondingly few. One such
incident did occur in 1992 when federal legislation required new Medigap policies to conform
to pre-set standardized sets of benefits. Finkelstein (Finkelstein) found that minimum standards
were associated with an 8-percentage point (25%) decrease in the proportion of the population
with coverage in the affected market with no evidence of substitution. Moreover, the minimum
standards were also associated with reduced coverage of non-mandated benefits among the
insured. “The empirical results are most consistent with a model of the effect of minimum
standards on insurance markets with adverse selection, and suggest that adverse selection
exacerbates the potential for unintended negative consequences of minimum standards.” At
least one other study contradicts these findings, but did so within the context of a more broadly
qualitative analysis. {Rice, Graham et al. 1997)}
See also Summers.
Given the amount of theoretical and statistical evidence in favor of insurance market
equilibration in the presence of informational asymmetry and adverse selection, it is reasonable
to ask if a regulated, competitive subsidized insurance market needs exogenous guidance in the
form of minimum value standards to function.
1
Such as the actuarial value standard in Medicare’s Part D pharmaceutical benefit and the minimum
standards set by a board in the State of Massachusetts.
3
Theoretical Model
In theory, a market driven insurance market should align interests of consumers and
insurers and have the correct incentives to minimize costs and premiums. We develop a multiperiod model of a health insurance market in which consumers choose their own insurance
policy, but the government subsidizes the cost of coverage and sets a minimum level of
coverage for participants. Insurers can adjust parameters over time. Our model predicts that
insurers will offer insurance on terms that maximize their income and minimizes their costs
given their beliefs about who will buy their insurance and government regulations. Consumers
will buy only insurance whose price and terms satisfy their needs given their knowledge about
their health status and needs.
Consumers
We model consumers as individuals with a wide range of costs. Individual consumers
can offset some of their expected costs by participating in the subsidized government insurance
program. For a consumer in the market to buy insurance, utility, u, of contract θ from insurer n
given the expected damages, d, of consumer individual, i.
(2.1)
In this model, subscribers are perfectly rational, risk-neutral software consumers. They
choose to buy insurance policies that provide the greatest utility defined as net benefit given
their expected pharmaceutical needs. Each consumer determines for itself the value, u, of the
contract by examining the terms of the contracts offered by each of the four insurers and
selecting the best offer: the subscriber then buys the insurance policy that provides the biggest
net benefit.
(2.2)
After making the determination that insurer n offers the best net benefit, the consumer
takes action a with respect to insurer n (noted as a) to buy the insurance policy and revises its
expected cost accordingly. In the event that two insurers offer the same policy or two
configurations result in a tie, the tie may be broken randomly or on the basis of non-calculable
factors, such as the reputation of the insurer.
Insurers
Insurers attempt to minimize their exposure to consumer costs while at the same time
making their policies attractive to draw purchasers—along with accompanying premiums and
government subsidies. Insurers offer policies by publicly posting prices (monthly premiums)
and terms for reimbursing the costs of subscriber consumers. Insurers may not deny service to
any consumer willing to pay the premium. On the other hand, we do not require consumers to
make any purchases. Therefore, consumers may choose to remain “rationally uninsured”
without any insurance coverage if they find no coverage that improves their welfare. The
4
consumers’ costs are unknown to the insurer and no provision is made for consumers to post
bids for insurance coverage. The only way for insurers to influence consumers’ decisions is
through their selection of insurance policy characteristics, θ, which they choose to maximize
profit taking best response of consumers and insurance competitors into account.
(2.3)
How Does Insurer Select θ?
The selection of θ takes into account several factors, including the best response of the
consumers as well as the competitive strategies of other insurers as well as the history of
competitors past offers.
Step I: Maximize subscribers given history and beliefs about competition
(2.4)
Step II: Maximize revenues from subsidies (s) and premiums (p)
(2.5)
Step III: Insurers’ best response (cost reduction) to consumers’ desire to maximize net
benefits
(2.6)
Government Regulation
The government played an active role in this experimental market. It did so through two
instruments: subsidies, and restrictions on the value of insurance that could be offered into the
market. The universe of policy settings was restricted to the set of feasible settings Θ as well as
the set of settings that are permitted by government regulation, Γ, therefore:
(2.7)
5
Figure 1: Schematic of Cournot Strategy in Insurance Game. In the experimental environment, consumers have costs
OC, and insurers get subsidies OB with which to pay off claims. The Maximum amount of benefits insurers can pay out
(because of restrictions on minimum copays and deductibles) is OD, implying that insurers automatically avoid costs of DCE. Therefore, the competitive equilibrium is CE. In the experiment, the government regulates insurers by setting a
minimum value of insurance that effectively requires them to pay out at least the amount shown at the Regulated
Minimum Value. The Cournot/Nash Equilbrium is attained when all four insurers coordinate on a single policy that
maximizes profit in such a way that no change in insurance policies can improve profit of one insurer without making the
other insurers worse off.
In this subsidized, competitive insurance market, insurers must pay costs (represented
by the dashed horizontal line OC at the bottom of Figure 1 using subsidies (solid black
horizontal line OB). Insurers could use the subsidies to pay costs. Alternatively, insurers might
use legitimate techniques (such as deductibles and co pays) to avoid costs (vertical gray stripes).
In theory, insurers might write policies in such a way as to avoid all costs and retain all
subsidies, thereby choosing a point at A in Figure 1. This would be an inefficient use of
subsidies, however. Moreover, in a competitive environment, consumers would not buy a
policy that did not cover any costs if a competitor offered to pay at least some cost. The market
would ultimately force insurers to points closer to B or C. The most efficient use of the
subsidies, from the government’s point of view, would be for insurers to pay all costs when the
costs are equal to subsidies (the point represented by the lower right vertex, B, of the triangle in
Figure 1. This would mean that insurers would not avoid any costs, and would consequently
have no profit (or negative profit in the event that subsidies do not cover costs). Any
combination of avoided costs and benefit pay outs results in a point along the frontier AB.
6
In the Experimental environment, government regulators effectively required a certain
amount of costs avoidance by suggesting certain levels of deductibles and co pays and capping
the amount of subsidies that would be paid for a basic benefit. This statutory cost avoidance is
represented in the graph by the length of subsidies and cost avoidance labeled “D-CE”. If some
subscribers choose not to buy insurance, then total subsidies will not equal total costs. The
length B-C represents this difference. CE is the competitive equilibrium in this situation. In the
situation where costs are equal to subsidies (all consumers buy insurance), the competitive
equilibrium was assumed to be the same as the Cournot equilibrium because marginal costs are
assumed to be zero. However, when subsidies do not entirely cover costs, there are excess costs
in the system represented by the length “B-C”. Unless the insurers take steps to avoid these
excess costs, the insurers must absorb the excess costs by accepting a lower profit. At the
Cournot equilibrium, the competitive insurers have cooperated to avoid all of the extra costs
and achieve extra profit (by avoiding costs equal to “F-Cournot/Nash Equilibrium”). Note that
insurers increase the inefficiency of the subsidy each time they avoid costs. Therefore, the
competitive equilibrium, CE, is more efficient (from the perspective of the Government) than
the Cournot equilibrium.
We will now turn to an investigation of exactly where the Cournot/Nash Equilibrium
and Competitive Equilibrium points occur in our experimental environment.
Experiment
The experiments described here take place in a miniature insurance market using
human subjects as insurers and 1500 computer software objects as customers. The experiment
was designed to mimic major design aspects of a government insurance benefit. We created a
flexible minimum value standard for insurance sold into the market and created a subsidy
structure that would guarantee insurer profit. We then tested whether relaxing the
government’s exogenous minimum value (actuarial value) standard would harm consumers by
reducing net benefits below the standard that the regulations were designed to enforce.
In the case of this experiment the “government” has established a model insurance
policy using the characteristics in θ described below. The implementing regulations require that
any policy offered through the Experimental program must have at least the same actuarial
value as the model policy. This means that certain combinations of the factors that make up θ
are forbidden. The effect of this policy is to ensure that policyholders receive a certain minimum
net benefit for the damages they incur within the range of the mandated benefit and that
insurers have a lower upper bound on the amount of insured costs that they can avoid (convert
into profit).
The minimum value rule was implemented by calculating the benefits of candidate
policy  for a subscriber with close to median cost of 2700. Insurance plans that paid less than
1700 to the theoretical consumer with 2700 in costs were forbidden. Any combination of plan
characteristics that paid out more than 1700 was accepted. This implementation regulated the
benefit of low cost consumers and encouraged insurers to penalize higher cost insured persons
7
by imposing harsher terms on items such as OOP and catastrophic copays that had little effect
on actuarial equivalence value. These harsh terms would allow them to achieve Cournot/Nash
as described below. We will discuss more particulars of the assumptions that we make for
purposes of the experiment later in the paper.
Insurers
In the experiment, human subjects played the role of insurers. They were allowed to
choose six different features, deductible, co pay, initial coverage amount, out-of-pocket limit,
catastrophic co pay and premium, of the insurance policy they offered. Insurers offered a
(single) multi-part insurance contract stipulating a monthly premium and different levels of
reimbursement depending on the level of damage. The insurer/subject used a web-based policy
worksheet to ensure that selected features complied with government regulations. Subjects also
had access to information about consumer costs and how profitable a given policy would be to
them when sold to prospective buyers given their costs. They also had information about
competitors; policies and terms offered as well as profit information.
Figure 2: Screen Shot of Subjects' Computer Screen. In column 1, subjects could choose six features of an insurance
policy that was offered to the market along with those of the three other subjects. In column 2, they received information
about whether or not the policy met government regulations. (A policy that did not have a value of at least 1700
prompted a red-lettered warning to appear on the screen, and the policy could not be entered into the system.) In column
3, subjects could see what the amount of profit the policy would earn among consumers at different policy levels. Subjects
could enter their policies by pressing a submit button. The results of the offer (number of consumers attracted, profits,
8
benefits paid out, etc.) would display in the bottom screen along with the policy terms and results of the other subjects.
Coordination of policies by imitation was easy to do.
There were four human subject insurers per treatment/per session and each insurer was
allowed to sell only one insurance contract during a single trading period. Insurers earned
money by creating insurance policies to cover the expenses of the potential consumers and
selling them to the robot clients who wanted them. The four insurers competed against each
other for clients by submitting their respective bids to a central processor. The 1500 buyer
consumers then simultaneously reviewed all bids and selected the bids that offered the highest
net benefit given their costs. Once the consumers selected their insurers, the central processor
informed the insurers of the number of clients they signed up and the benefits that must be paid
on their behalf. The processor also calculated the amount of subsidies received for all the
beneficiaries for each insurer and subtracted the costs of benefits from the premium and
subsidy totals to obtain a total profit for each insurer.
Once profits were reported, the insurers were able to see their costs, profit, and actuarial
value as well as the corresponding information about each of their competitors. Insurers were
not informed that any losses would be forgiven at the end of the experiment. Insurers then had
another opportunity to revise and submit bids, repeating the process described above. The
experiment lasted 25 periods
Table 1: Choices in first and second treatments. In treatment 2, the regulated treatment, the system would not
accept a policy that paid less than 1700 for a claim of 2700, an amount just short of the median subscriber.
Insurers could only choose between three different settings for each of the six policy
characteristics. The settings are given in Table 1. The policy characteristics are described below.
We restricted the number of choices available to the insurers to three for several reasons. First,
the settings covered the appropriate range. The available choices made it possible for insurers to
offer policies with actuarial value of less than 1700 up to a maximum of more than 3000.
Therefore, the same settings could be reused in the second treatment, minimizing differences in
the environment experienced by subjects over treatments. Second, even though there were only
three choices per setting, the strategy space was still large. The number of choices allowed each
insurer 729 ( 36 ) different combinations of settings for each subject. Moreover, each of the four
insurers with 729 combinations created a strategy space of about 2.3 x 10
9
9
(billion). Third,
although the strategy universe was large we could still sample the space to calculate the profits
and net benefits for each strategy, making it easier to interpret the data.
Insurers (human subjects) could manipulate each of six characteristics of the contract:
deductibles, co pays, insurance amount, out-of-pocket limit, catastrophic co pay and premium,
each of which is described below.
1) Premiums (r) Premiums are the monthly payments made by the client to the insurer
in order to maintain coverage. Increases in premiums lower the value of insurance for the
subscriber.
2) Deductibles (e) The Deductible represents the amount of Medical expenses that will
not be reimbursed by the Insurer. The larger the deductible, the smaller the benefit paid by the
insurer and the lower the value for the subscriber.
3) Co-Pays (o) Co-Pay is the percentage of insured expense that the client (not the
insurer) must pay. An increase in the amount of Co-Pay lowers the amount that the insurer
must pay. Higher co pays lower the value of the benefit to the subscriber.
4) Insurance Amount (m) Insurance Amount is the level of expenses that the insurer is
obligated to cover, less the deductible and co pays. For example, if a client with $1000 in
expenses obtains a policy with Insurance Amount of $2000, then all expenses are covered—
except for deductible and co pays. If the client has $3000 in expenses, then only $2000, less
deductible and co pays, would be covered.
5) Out-of-pocket limit (l) Out-of-pocket limit is the maximum client expense before
catastrophic coverage begins to apply.
6) Catastrophic co-pay (k) catastrophic co-pay is the percentage of catastrophic expense
that the client, not the insurer, must pay out of his or her own pocket.
The effect of altering any one of the six factors on the value of the policy for a
prospective customer is described in Government Regulation
The Experimental Consumers
Consumers were modeled as software agents, each with degrees of expected damage d.
The consumers knew what their own costs would be. The consumers’ costs were drawn from a
piecewise uniform distribution described here:
for di : i  1000
di ~ 
for di :1001  i  15000


di ~ U[1000..50000]
di ~ U[1..1000]
10
DamageLevel
50000
40000
30000
20000
10000
200
400
600
800
1000
1200
1400
SubjectCount
Figure 3: Distribution of consumers' pharmaceutical costs (expressed as Damage Level)
The average amount of damage to a Buyer was 10529. The bulk of heavy expenses was
centered in about 500 potential Consumers who had average expenses of 24,406.
Subsidies
The size of the subsidy paid to the insurer after a consumer signs up for the program
was set at the average cost per consumer, 10,529, for all 1,500 consumers. This meant that if all
consumers participated in the program, the government could cover all their costs. If, on the
other hand, some buyer consumers failed to sign up for the insurance program, then there
might be insufficient funds to pay all costs, depending on which consumers failed to purchase
insurance. The amount of the subsidy was fixed.
11
InsurerProfits
2.2 10
2 10
1.8 10
1.6 10
1.4 10
1.2 10
6
6
6
6
6
6
1.32 10
7
1.34 10
7
1.36 10
7
1.38 10
7
1.4 10
7
NetBenefits
Figure 4:Map of potential insurer offers as a function of net benefits paid and insurer profits
Simulations
Because all costs and possible combinations of offers of insurance were known to the
experimenter in advance, and we also know the true cost of all of the consumers, each quartet of
possible offers by the four insurers was associated with a profit and net benefit for clients could
be calculated. Prior to the running of the experiment, we calculated a large sample of the
payoffs and net profits that would be generated by each of the 2.3 billion possible quartets of
insurance policy combinations. . The program then reviewed all values of the 1500 potential
subscribers and determined the value of each policy for each subscriber and then matched each
subscriber with the insurer with the ‘best’ product given their needs. Policies and market
results, including total payments and profits were recorded. The sample policy outputs were
then mapped onto a graph, giving Figure 4.
Each combination of net benefit and profit represented a set (a quadruplet) of policy
offers, and best response purchases by consumer consumers, therefore, constituting a frontier of
Nash equilibria along the profit/net benefit axes, creating a triangle shape (in Figure 4) similar
to Figure 1.
Note in Figure 4 that there are multiple parallel lines that form as we plot the various
combinations of net benefits paid and profits retained by insurers in each quadruplet of
insurance offers. The optimal combinations in which the most buyer consumers found it
beneficial to buy Experimental insurance policies form the line that is farthest out from the
origin. Each of the inner lines represents successively more restrictive sets of policies that drew
12
fewer and fewer total buyers and consequently fewer subsidies. As the number of buyers
dwindled, the amounts of subsidies and premium income also declined making larger
combinations of net benefits and profits impossible. Consider what happens when all insurers
offer policies with $250 deductibles. All of the consumers with costs of more than $250 buy
insurance. If some insurers offer $250 deductibles and others offer $400 deductibles, then it is
likely (all else equal) that the same number of buyers will enter the market, but the composition
of the profit might change in various ways that move the point to various locations on the outer
line. If, however, all insurers offer a deductible of $400 and no insurers offer a deductible of
$250, then the number of participants in the market will shrink as the number of insured
persons with costs between $250 and $400 leave the market. The points where all insurance
companies are offering $400 deductibles and more are all on interior frontiers in the figure
above. The simulations helped identify key strategies that experimental subjects might follow as
described in Table 2.
Proof of Cournot
In addition to the sampling program described above, we also wanted to determine the
Cournot/Nash strategy—which under the circumstances was possible only through
enumeration. Strict enumeration of all 2.3 billion combinations is computationally difficult, so
we opted for a simpler strategy. We examined the smaller number (19.2 million permutations)
of three player markets. We then introduced the fourth insurer into each of these markets by
finding the best response to each of these 19.2 million three-insurer markets. Assuming that the
Cournot/Nash must be in this reduced set, we then compared the resulting quartets, and
discarded combinations with suboptimal responses until only the Cournot/Nash remained.
If policy “a” is best response to the combination “bcd” ( a  bcd ), then it follows that if
b  dca , c  dab , and d  bca , then strategies a,b,c,d are the Cournot/Nash equilibrium.
The Cournot/Nash turned out to be a single symmetric strategy (all four insurers playing the
same policy) outlined in Table 2. The finding also makes intuitive sense because it offers the
lowest Co Pay and Deductible, and the highest initial insurance Amount—characteristics that
appeal to the lowest cost (and highest profit) consumers. However, it also gives the harshest
possible terms for high cost consumers in terms of Out of Pocket Limit and Catastrophe Copay,
thereby discouraging high cost consumers. Finally, the policy exceeds the government actuarial
minimum value standard and can be offered under regulated and unregulated scenarios.
As previously stated, total consumer costs in the system were 15.8 million. The available
settings, however, restrict the amount of money that insurers can pay out to consumers to
compensate damages. The maximum amount that can be paid out by insurers is 14.1 million.
For example, if all insurers offered the most permissive policy possible, i.e. a policy with lowest
possible 250 deductible, 3000 insurance amount, 3000 out of pocket limit, minimal co pays and
smallest premium, they would spend 14.1 million. By contrast, if insurers coordinated on the
least generous plan, they would spend 11.4 million. If all four insurers coordinated on the most
profitable plan, they would pay 12.59 million. If they all sold the minimum legal plan (when
standards were enforced in Treatment 1), they would pay out 12.11 million. Minimum
standards were not enforced at all in Treatment 2. We note that the Cournot strategy was legal
in both treatments.
Table 2: Showing Possible Minimum, Competitive and Cournot Strategies In Experiment. The Total Benefits
payment was calculated assuming that all four insurers offered the same policy during the same period.
13
Description of Experimental Treatments
We devised two treatments for the experiment. In the first treatment, insurers were
required to meet an insurance minimum value before offering their policies to subscribers. In
the second treatment, the insurance value minimum was eliminated. We ran four experiments
in each of the two treatments with four human subjects in each experiment. Experiments were
run at George Mason University’s economics experiments laboratory facilities.
First Treatment
In the first treatment of the experiment, the subjects selected policy characteristics from a
series of drawdown menus each of which allowed three possibilities for each policy attribute.
The computer also calculated the value of the policy for an average buyer and blocked insurers
attempting to enter any insurance policy with a value of less than 1700. The potential settings
for the treatments are in Table 1.
Second Treatment
In the second treatment, we allowed insurers to offer policies that were below the 1700
per subscriber level. Eliminating the value requirement permitted insurers to offer higher
premiums, deductibles, co pays, and out of pocket limits. Insurers could thereby avoid more
costs than they could in Treatment 1 and boost their own profits while reducing benefits.
14
Results
2500000
Profit
2000000
1500000
Cournot
1000000
Regulated Min.
500000
12000000
12500000
13000000
13500000
Total Net Benefits
14000000
Figure 5: Combined Profits and Net-Benefit Payouts of Four Insurers. This displays the total net benefit payouts and
profits of the four insurers in each period for all eight experiments. Results from the treatment with minimum standard
are represented by the darker diamonds. The treatment without standards are marked with the lighter diamonds. The
horizontal line shows the amount paid out when all insurers play the Cournot combination.
Actuarial values were the same in both treatments as shown in regulated markets as
shown in the box plots in Figure 7. At the median, net benefit payments were lower in the
unregulated markets compared to regulated markets as shown in Figure 8. However, there
were more suboptimal outcomes in the regulated market as shown by the number of darker
dots inside the outer frontier of the triangle in Figure 5 as regulated insurers tended to pick
combinations of insurance terms that attracted fewer consumers—largely because of higher
deductibles offered in the regulated market.
Closer inspection reveals substantially different strategies used by insurers in the two
treatments: Competitive Equilibrium strategies were more common in the regulated market
than in the unregulated scenario where Cournot Strategies were used more frequently.
Table 3: Number of Times Insurers Played Cournot Strategy by Treatment. This table shows how often individual
insurers played the Cournot strategy by minimizing payments to subscribers with higher costs and providing
generous benefits to low-cost customers. Cournot play was observed nearly twice as often in the “No Minimum
Standard” treatment as in the “Minimum Standard” treatment. Cournot play was not illegal in either treatment.
15
Table 3 shows that the presence of value regulations did not prevent insurers in this
experimental market from engaging in Cournot/Nash oligopolistic collusion. However, Cournot
play was rarely achieved in the regulated market. Table 3 showed that insurers played Cournot
strategies three times as often as they did in the regulated market. Moreover, insurers in the
unregulated market played Cournot mainly in the final periods of the game, as though they
were learning how to coordinate with each other but still not quite able to coordinate
completely. More study needs to be done to find out if extended periods of play would allow all
four insurers to play Cournot strategy after a long enough period had passed.
16
Table 4: Number of Times Insurers Played Competitive Strategy by Treatment. This table shows the
number of times during the experiment in which subjects played a “Competitive Strategy” by offering the
most generous terms to subscribers in both the regulated and unregulated treatments. Competitive play
was observed nearly 20 times as often in the “Minimum Standard” treatment as in the “No Minimum
Standard” treatment. There was no incentive to play the competitive strategy in either treatment.
Table 4 shows that insurers in the regulated market coordinate on the competitive
equilibrium strategy (i.e. the most generous insurance policies) more often than in the
unregulated market. Indeed, coordination on the competitive strategy (in which the insurers set
the most liberal terms for insurance) was nearly 17 times as frequent in the regulated market as
in the non-regulated market.
17
Figure 6: Breakdown of Benefits Paid by Period, Experiment, Treatment. The markers represent the combined
benefits paid during one period of the experiment. In the top row are experiments in which a minimum insurance
standard was enforced, and the bottom row shows experiments where there was no minimum standard. In most
experiments, some coordination of benefits among insurers is evident in the data where insurers go through several
periods without changing benefit payouts. Coordination occurs at higher benefit levels in the regulated environment than
in the unregulated environment. In experiments 7 and 8, in the bottom row, insurers frequently coordinate on a standard
that is only one feature different from the Cournot equilibrium. The Cournot strategy was legal in both treatments.
Table 5: Tabulation of Total Insured Population in Regulated versus Unregulated
Markets
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The number of insured persons was a little higher on average in the unregulated scenario
than in the regulated one. The number of times that insurers were able to attract less than
1446 (out of 1500) insured persons was about 35% in the regulated market, versus about
20% in the unregulated market. (See Table 5) On the other hand, terms of insurance,
including premiums, deductibles, and copays, were typically more liberal in the regulated
market than in the unregulated scenario. (See Table 6)
Table 6: Tabulation of Insurance Terms by Treatment. Most of the difference between treatments can be explained by
the difference in Catastrophic Copay, the amount that the highest cost consumers had to absorb without reimbursement.
The highest possible Catastrophic Copay was offered twice as often in the unregulated market as in the unregulated
market. High copays were permitted in both
treatments.
19
Observations
A subsidized insurance market where private insurers compete against each other to
offer insurance but are free to set terms for policies appears to function profitably but with a
substantial amount of inefficiency in both regulated and non-regulated environments. The
sources of inefficiency are: 1) the minimum standard that sets a lower boundary on aggregate
net benefits paid to consumers but also establishes a minimum profit level for insurers; 2)
insurers’ inability to set terms that are attractive to low-risk consumers result in persistent
underinsurance of the population; 3) the system provides incentive for insurers to find
unregulated co pays and deductibles that can be increased without losing market share (i.e. at
the expense of the consumers with highest cost).
Insurance minimum standards did not directly affect insurers’ policies since the
actuarial value of the policies offered was essentially the same in both treatments. The
standards did have a significant effect on the size of benefit payouts that were larger in the
regulated market than in the unregulated treatment. However, competitive pressure prevented
both regulated and unregulated insurers from offering the lowest value policies achievable in
both treatments. Regulated insurers tended to cluster around the most efficient (from the
government’s perspective) Competitive Equilibrium and unregulated insurers tended to cluster
closer to the Cournot Equilibrium. But the distribution of benefit payouts in both treatments
was different by a relatively small amount.
Subjects were much less able to find the Cournot/Nash strategy in the regulated market
and much more inclined to Competitive Equilibrium strategy. However, this does not mean
that the regulated market is “better.” In this particular example, regulation worked in favor of
the government because the rules—even though they did not explicitly illegalize oligopolistic
activity—effectively prevented Cournot play. The more competitive/low profit strategy
enriched benefits for higher-cost consumers and made the government’s spending on this
program more efficient. One can easily imagine circumstances where the result would be less
favorable. For example, if the regulator were depending on signals from the private market to
draw competitors into the market, then the regulated market would be less likely to signal the
need for market entry than an unregulated market.
The exact mechanism that caused the strategies to differ in the two environments is a
topic for further research. Two possibilities warrant examination. (1) Market regulations
prevented participants from offering policies that would have revealed important information
about marketplace demand and supply to the subjects and thereby made it more difficult for
them to coordinate their strategies. (2) Regulation invoked a behavioral response that inhibited
profit seeking. This might have happened when subjects occasionally observed that efforts to
ratchet down benefits sometimes drew a “rebuke” from the computer which flashed a red
warning signal and refused to accept their terms when they tried to become greedy. It was
simpler, and may have felt better, to coordinate on the most generous policies available even
though it meant accepting lower profit.
It might be argued that policy setting in the insurance world is so technical that
modeling it in a laboratory is too difficult. On the other hand, we have seen that incentivized
human subjects are quite good at navigating to technically correct outcomes despite a complex
environment. Moreover, even non-experimental markets are influenced by non-actuarial
20
considerations. Regulations devised by non-actuaries, and political considerations going
beyond actuarial calculations also play a role in business decisions.
This study may shed light on how regulation works in a complex environment. It also
shows that human subjects with incentives in an experimental market are capable of sorting
through a complex environment (in this case an environment with 2.2 billion permutations
available collectively to them) in order to get very close to and occasionally hit the unique
Cournot Nash Equilibrium strategy that required considerable technical skill and nearly 50
hours of time for a 100 processor computer grid to calculate.
Figure 7: Actuarial Value by Treatment
21
Total Net Benefits Paid
Min Standard
No Min. Standard
1.4e+07
1.35e+07
1.3e+07
1.25e+07
Graphs by Treatment
Figure 8: Net Benefits by Treatment
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