Microsoft word - sorry no cods june 2007
An Experimental Analysis of Cooperation and Productivity in the Trust Game
Abstract: In the standard trust game the surplus is increased by the risk taking first mover while cooperation by the second mover is a one-to-one transfer. This paper reports results from experiments in which the reverse holds; the first mover’s risky trust is not productive and the second mover’s cooperation is productive. This subtle difference significantly lowers the likelihood of trust but increases the likelihood of cooperation conditional on trust. Evidence is presented that the change in trust is consistent with first movers failing to anticipate the later result. Drawing upon the analogy that the trust game represents a model of exchange, the results suggest that markets should be organized so that the buyer moves first and not the seller as in the original trust game.
Keywords: trust, reciprocity, exchange JEL Classifications: C7, C9, L1 Researchers continue to grapple with the circumstances that give rise to cooperation,
reciprocity, and trust in or fear of reciprocity.2 In an attempt to understand interactions in
the naturally occurring world, laboratory research has focused on stylized games such as
the ultimatum game, the lost wallet game (Dufenberg and Gneezy 2000), the investment
game (Berg, Dickhaut and McCabe 1995), and the labor market game (Falk, Gächter and
Kovács 1999, Rigdon 2002) among others.3 The insights provided by these games are
helpful for predicting behavior, developing institutions and evaluating policies.4 The
1 The author wishes to thank Mary Rigdon, Bart Wilson and two anonymous referees for helpful comments. Support from the Center for Retailing Excellence at the Sam M. Walton College of Business is gratefully acknowledged as is the valuable research assistance provide by Michael Brown. 2 See Cox and Deck (2005) for an explicit definition of positive and negative reciprocity and a discussion of a triadic design that enable a direct test for reciprocity. 3 At the other extreme, Crockett, Smith and Wilson (2006) examine economic interactions with minimal structure to see how markets and trade arise endogenously. 4 This list is due to Smith (1994)
current paper pushes this line of inquiry by examining the payoff structure of the trust
game introduced by McCabe and Smith (2000).
In the trust game, (see the left hand panel of Figure 2) the first mover can end the game in
which both parties receive a payoff of $10 or can “trust” the second mover to determine
the allocation of $40. The second mover can keep the entire $40 leaving the first mover
$0 or can be cooperative and only keep $25 leaving $15 for the first mover.5 A key
feature of the trust game is that the first mover’s decision to trust increases the total
surplus; therefore, the second mover may feel some obligation to behave cooperatively
when given the chance to act. This feature is present in many games including the
centipede game and the lost wallet game.6 However, trust and productivity need not go
together. One can look at trust that is not productive and second mover cooperation that
is productive rather than a direct transfer payment.
While not framed to subjects as a trade, the trust game as described by Coricelli, McCabe
and Smith (2000) represents a partial equilibrium model of personal exchange.7 The first
party gives up something of value anticipating that the second party will cooperate,
resulting in a mutually beneficial outcome and bearing the risk that the second mover will
not cooperate.8 Social gains are realized when an item is transferred from the seller to the
buyer, while the price represents a transfer from the buyer to the seller. Thus in the trust
game, it is the seller who moves first. Casual observation suggests that many markets are
structured so that the opposite is true; buyers move first. e-Bay contracts often state that
the good will be shipped upon receipt of payment. Many sellers use the phrase “Sorry
No CODs” meaning that the buyer cannot move second and wait to provide cash on
5 This is essentially a simplified version of the investment game in which the first mover can invest all or none of their endowment. If money is passed to the second player, it is tripled and then the second mover has only two allocation choices. 6 The trust game is a two stage centipede game. 7 The trust game framework has an exogenously determined price that fixes the division of the gains from trade, perfect substitutability, and the possibility of short sales. 8 Institutions such as the legal system and escrow accounts are designed to guard against such failures. Online auction houses, where one might expect fraud and failed trades among anonymous parties to be prevalent, use reputation mechanisms in an attempt to increase the likelihood that trades are successful. However, in many situations such institutions are not available or are impractical.
delivery. In such cases, surplus is not increased by trust but rather by cooperation on the
The next section describes in detail a series of extensive form games involving trust and
cooperation but varying which party is productive, meaning taking an action that directly
leads to an increase in total surplus. The experimental design and the results are
presented in a subsequent section. As a preview of the results, the jointly beneficial
outcome occurs with approximately the same frequency regardless of which party is
productive. While productive second movers are more likely to cooperate than
nonproductive second movers, nonproductive first movers are less likely to trust than
productive counterparts. This finding is somewhat surprising when compared to previous
results. An additional series of experiments designed to reconcile this discrepancy is
reported in the penultimate section and the final section contains concluding remarks.
Trust, Productivity, and Trade
While the trust game is only a partial representation of trade, it is useful to draw upon this
analogy. Consider the situation in which one player, called the seller, is endowed a good
intrinsically valued at v
s. The other player, called the buyer, values the seller’s good at
b, with v
b > v
s. The buyer is endowed with money, m
.9 If there is no trade, the total
surplus is m
s. If the parties trade at price p
, the buyer’s payoff will be m
the seller’s payoff will be p
s. The surplus with trade is m
b and both parties are
better off if v
b > p
s. Figure 1 graphically presents the two possible sequential games
that arise depending on who moves first. Notice that in both cases the first mover runs
the risk that the second mover will keep everything and thus reaching the mutually
beneficial outcome requires trust in either case, but only in the game on the left is trust
productive. In this game, the total surplus is m
b if the mover trusts (i.e. the seller
sends the good) even if the second mover is not cooperative (i.e. the buyer does not pay).
9 McCabe, Rigdon and Smith (2003) use a different game in which both players are productive. Their game could be though of as trading two goods with a double coincidence of wants. Fehr, Fishbacher, von Rosenbladt, Schupp, and Wagner (2003) allow both players to be productive in a variation of the investment game that they describe as a model of trade with incomplete contracts.
By contrast, in the game on the right, even if the first mover trusts (i.e. the buyer sends
payment) the total surplus would remain m
s if the second mover does not cooperate
(i.e. the seller does not send the good).
+ v B
Seller First (left) and Buyer First (right)
The decision faced by a second mover also differs between the two games. In the game
on the left, the second mover gives up p
to increase the other player’s payoff by p
is, it costs the buyer $1 to give the seller $1. In contrast, the game on the right is such
that cooperation by the second mover is productive; it costs the second mover v
the other person v
b. That is, it costs the seller $1 to give the buyer $v
b > $1. Recent
dictator game experiments by Andreoni and Vesterlund (2001) and Andreoni and Miller
(2002) highlight the significance of this difference.
In the standard dictator game, the dictator is endowed with some amount of money. The
dictator can then determine how much of the money to keep and how much to give to the
recipient. In dictator games as well as the regular trust game, it is not uncommon to
observe people willing to forego their own payoff to increase someone else’s payoff.
Andreoni and Vesterlund (2001) and Andreoni and Miller (2002) conducted a series of
dictator game experiments in which the dictator and the recipient had differential
exchange rates. At one extreme, when the dictator reduced her payoff by $1, the
recipient received $0.33. At the other extreme, when the dictator reduced her payoff by
$1 the recipient received $3. What they found was that dictators gave more the greater
the return. An alternative way to state this result is that as the cost of giving the recipient
$1 decreased, the dictator gave more. 10
The results of Andreoni and Vesterlund (2001) and Andreoni and Miller (2002) suggest
that second movers should be more likely to cooperate in the game on the right hand
panel of Figure 1 than in the game on the left hand panel. In the trade story, sellers
would be more likely to complete trades than buyers. This could explain why we observe
many naturally occurring markets organized in such a way that buyers move first.11 This
also suggests that the behavior observed in the original trust game is particular to the
location of the productive action. Comparing the game in the left hand panel of Figure 1
with the original trust game of McCabe and Smith (2000) shown in the left hand panel of
Figure 2, it is clear that the games have the identical structure (m
= 10, p
= 15, v
s = 10, v
= 30). Using these parameters but changing the sequence so that the first mover is not
productive (ie. is the buyer) results in the game in the right hand panel of Figure 2.
Figure 2: Original Trust Game (left) and Reversed Trust Game (right)
A natural place to begin comparing productive and nonproductive trust is this reversed
trust game. But quick inspection of Figure 2 reveals that there is the possibility that the
first mover loses money.12 If the experimenter cannot extract a loss from a subject, then
the experimenter loses control over the incentives. A $5 loss is no better or worse than a
payoff of $0 or a loss of $1 million. The typical method of handling the possibility of
10 Fisman, Kariv, and Markovits (2005) find a similar tendency in three person dictator games. 11 If sellers tend to be large and interact with many relatively small buyers so that sellers have to worry more about reputation and repeated game effects, this would suggest that sellers should move second. 12 Following the trade analogy, the problem is that the person has m
= 10 and is paying a price of p
losses is to endow subjects with a positive balance from which losses are deducted.
Creating such a balance essentially adds some constant term to all of the subject’s
payoffs. But doing this to the reversed trust game would necessitate doing the same to
the trust game as well, which would make the game different from what is presented in
the left hand panel of Figure 1. Hence, one cannot simply reverse the order of players
and compare the results to previous work.
Experimental Design and Results
Groups of between eight and fourteen subjects were recruited for a one hour experiment
from undergraduate business and economics courses. In each session, the subjects were
seated at individual computer terminals which were separated by privacy dividers. After
reading computerized directions each subjects completed a brief comprehension handout.
While the subjects were reading the directions, the experimenter handed each participant
the $5 show-up fee that was promised during the recruiting process. After all subjects
completed the handout, an additional set of paper directions was distributed explaining
the double-blind payoff procedure that would be used for maintaining the anonymity of
the decision-makers. While these additional directions were being read aloud, the
subjects were able to select one of several identical sealed envelopes containing mailbox
keys with which the subjects would later be able to retrieve their payoff with privacy.13
After the experimenter left the room, subjects opened their envelopes, entered their secret
identification codes, and were shown the “decision-tree.”14 Subjects played one one-shot
game in only one role. Second movers only made decisions if the first mover attempted
to trade. That is, the game was sequential and did not use the strategy method. After all
of the payoffs had been determined, cash was placed in plain white envelopes which were
then inserted into the mailboxes that were in a separate room just down the hallway from
the laboratory. The entire experiment lasted approximately 30 minutes.
13 The computerized directions, comprehension handout, and double blind procedures are identical to those used by Cox and Deck (2005, 2006a, 2006b). Copies are available upon request. 14 Neutral terms were used throughout the experiment. Extensive form games were referred to as decision-trees. No mention was made of buyers, sellers, trade, productivity, trust, cooperation, etc.
The use of double blind payoff procedures provides a difficult environment for fostering
cooperation. Hoffman, McCabe, Shachat and Smith (1994) examine dictator games with
double blind payoff procedures and find greater material self-interest than when single
blind procedures are implemented. The numbers beside each branch in the left hand
panel of Figure 2 represent the number of subjects making that choice in double blind
original trust game experiments of Cox and Deck (2005). The approximately 25%
cooperation rate they report is significantly lower than the 75% cooperation rate reported
by McCabe and Smith (2005) and replicated by Cox and Deck (2005) for single blind
payoff procedures. It should be noted that the dictator games of Andreoni and Vesterlund
(2001) and Andreoni and Miller (2002) use single blind payoff procedures. It is not clear
if their results are applicable in a double blind environment. For example, it could be that
subjects do not want to appear to the experimenter as being so selfish that they would not
There are two interesting features of the trust game. One is that the two endowments are
identical; if the first mover does not trust both parties receive $10. Another interesting
feature is that trusting exposes the first mover to the possibility of receiving a $0 payoff.
Unfortunately, it is not possible to maintain both of these features with the same
parameters for the two game structures shown in Figure 1 and have both parties prefer the
“cooperative” outcome. The unproductive first mover risks earning m
. If this equals
0, then m
. If the initial endowments are equal then m
s. Together, these imply that
s which means that the cooperative outcome is no better than the initial allocation for
The following parameters were chosen for the experiments: v
S = 5, v
B = 15, m
= 10, and
p = 10. The productive and nonproductive trust games with these values are shown in
Figure 3. The parameters are based in part on the half payoff treatments of Cox and Deck
(2005, 2006b). The values vs and vb are exactly half of those in the original trust game.
Setting p=10 divides the gains from cooperation evenly between the two parties whereas
the price of $15 in the original trust game allocated 75% of the gains to the second
mover. To maintain the first mover’s exposure to a $0 payoff between treatments, m
In each laboratory session, some subjects were making decisions in each of the two
Figure 3. Productive Trust (left) and Nonproductive Trust (right) Games
The results are based upon 102 subject pairs playing one of the games of interest,
collected from 24 distinct experimental sessions. The number of subjects making each
decision is reported beside that branch in Figure 3.
In the productive trust game, 55% percent of first movers trusted. In response, 30% of
the second movers were cooperative. These numbers are statistically similar to the 52%
trust rate and 29% cooperation rate reported by Cox and Deck (2005) for double blind
payoffs (p-values of 0.7704 and 0.9283 based upon the 2-sample proportion test for equal
proportions against the two sided alternative).
In the nonproductive trust game, 53% of second movers were cooperative when given the
opportunity. This is in the direction expected based upon the results of Andreoni and
Vesterlund (2001) and Andreoni and Miller (2002) and is marginally statistically
significant (p-value of 0.0783 based upon the 2-sample proportion test for equal
proportions against the one sided alternative that cooperation is greater in the
15 In the initial sessions, approximately half of the participants were playing each game. But difference in the trusting rate made it such that very little data were being collected on second movers in the nonproductive trust game. To enable more observations of second mover in this game, relatively more of these games were run in later sessions. The next section describes a third game that was introduced in later sessions to explore why observed behavior of nonproductive first movers differed so dramatically from previous experiments.
nonproductive trust game).16 This increase in cooperation from switching the order
occurs despite the fact that payoffs are double-blind. What is perplexing regarding the
nonproductive trust game is that first movers are statistically less likely to trust than first
movers in the productive trust game, 26% versus 56% (p-value of 0.0028 based upon the
2-sample proportion test for equal proportions against the two sided alternative).
Given the observed likelihood of cooperation, productive first movers on average receive
$3 from trusting ($10 x 0.3 + $0 x 0.7) as compared to $5 from not trusting. This
suggests that first movers overestimate the likelihood the second mover will cooperate.
A similar pattern was noted by Berg, Dickhaut and McCabe (1995) in the investment
game and in the trust game by Cox and Deck (2005). Nonproductive first movers receive
$7.95 on average from trusting ($15 x 0.53 + $0 x .47) as opposed to $10 from not
trusting. Interestingly, in this treatment second movers are actually more likely to
cooperate but first movers expect second movers to be less willing to cooperate. Cox and
Deck (2006a) observe a similar phenomenon when they introduce a treatment in which
there is a random chance that the first mover’s decision in the trust game will be reversed.
In that treatment, less trust is observed and the authors conclude that this is due to the
first movers falsely anticipating that second movers will give them the benefit of the
Further Exploration of Behavior in the Nonproductive Trust Game
In comparing the nonproductive trust game with the original trust game one notices that
the payoffs to the first mover are identical. The games differ only in the payoffs to
second mover. Despite this fact, first mover behavior is significantly different between
the two games (p-value of 0.0154 based upon the 2-sample proportion test for equal
proportions against the two sided alternative). Clearly the first movers are responding to
16 An alterative explanation for second mover behavior is the cost differential. It costs the second mover $5 to cooperate in the nonproductive trust game and $10 in the productive trust game. Of course, this cost differential is an inherent aspect of the trade story as v
. Cox and Deck (2005) conducted experiments where the payoffs were half of those shown in Figure 1 and found that the payoff level did not change the frequency of cooperation; however, when controlling for gender Cox and Deck (2006b) report that female subjects are less likely to cooperate when the costs is increased.
the payoffs of the second mover. How do the payoffs of the second move differ? First,
the endowments favor the first mover in the nonproductive trust game, but not in the
original trust game. Secondly, the mutually beneficial outcome favors the first mover in
the non-productive trust game but favors the second mover in the trust game. This
suggests at least two possible explanations for the first mover behavior, one is a desire to
beat the other person and the other is a fear that the other player will not be willing to
lose. Alternatively, it could be that subjects value the total surplus and thus are more
likely to engage in trust when this activity is productive. Though not directly
comparable, dictator control treatments reported in Cox and Deck (2005) indicate that
subjects preferred both players receiving $5 to receiving $0 while the other player
For a first mover in the nonproductive trust game to trust, she must believe that the
second mover is sufficiently likely to accept an unequal split that favors the first mover.
Experiments on mini-ultimatum games by Güth, Huck, and Müller (2001) provide some
insight on this issue. The ultimatum game is similar to a dictator game except that the
recipient has the option to reject the proposed allocation in which case both parties
receive $0. In a mini-ultimatum game, the first mover has only two possible divisions
from which to choose. In Güth et al. (2001), first movers always had the lopsided
proposal to keep an 85% share, but the more equitable proposal varied among keeping
55%, 50%, and 45% shares. They observed that even these small deviation from an equal
split changed first mover behavior. When the equal split was possible, 44% of first
movers asked for 85% share but when the more equitable option retained only a 45%
share, 67% of first movers asked for the 85% share. This would suggest that second
movers in the nonproductive trust game would be reluctant to cooperate. Anticipating
this behavior, first movers in the nonproductive trust game would be less likely to trust.
However, as reported in the previous section, the second movers are actually more likely
17 Another potential explanation is that subjects have some form of other regarding preferences though evidence reported in Deck (2001) and Engleman and Strobel (2004) contradicts the specific forms
To explore the dramatic decrease in trust observed in the nonproductive trust game,
additional experiments were conducted with a trust game with asymmetric endowments.
In this game, shown in the center panel of Figure 4, the first mover has the same outside
option as in the nonproductive trust game, but trusting gives the second mover the same
choice as in the original trust game. Notice that all three games have the identical
payoffs for the first mover and only differ in the second mover’s payoffs. The only
difference between this new game and the original trust game is that that the second
mover’s payoff is smaller if the first mover does not trust. Therefore, a trusting action in
appears to be at least as nice in this game as in the original trust game. The difference
between this new game and the nonproductive trust game is that the jointly beneficial
outcome has increased by 15 for the second mover while the selfish outcome has
increased by 25. Based upon the previous results, one would expect this to make second
movers more likely to defect in this new game relative to the nonproductive trust game.
Figure 4. Comparison of Original Trust (left),
Trust with Asymmetric Endowments (center), and Nonproductive Trust (right) Games
The numbers beside each branch of Figure 4 indicate the number of subjects making each
choice. The 26 subject pairs in this treatment were part of the groups of 8 to 14 subjects
in the lab starting with session 14. Behavior in the asymmetric endowment trust game is
very similar to the productive trust game and game and the results of Cox and Deck
(2005). There is no statistical difference for first movers or second movers between the
trust game and this new game (p-values of 0.6783 and 0.8378 respectively based upon the
suggested by Fehr and Schmidt (1999) and Bolton and Ockenfels (2000).
2-sample proportion test for equal proportions against the two sided alternative). It is
interesting to note that second movers nominally defect more often with the asymmetric
endowments where the first mover’s decision to trust is at least as nice, a similar pattern
to what is reported in Deck (2001). However, first mover behavior in this new game is
different from what was observed in the nonproductive trust game (p-value of 0.0580
based upon the 2-sample proportion test for equal proportions against the two sided
alternative). Consistent with the previous results, second movers were more likely to
defect in the trust game with asymmetric endowments relative to the nonproductive trust
game (p-values of 0.0662 based upon the 2-sample proportion test for equal proportions
The results of the trust game with asymmetric endowments suggest that it is not the
desire to have the larger share of the total payoff that is influencing first mover buyers,
but rather a fear that second mover sellers will be unwilling to accept a smaller share.18
Acting on trust means that the first mover will risk something of value anticipating that
the second mover will be cooperative. In the standard trust game, the first mover is
productive meaning trusting increases total surplus, while the second mover’s action is a
simple transfer between the two parties. However, this need not be the case. As a partial
equilibrium trade story, the standard trust game is structured so that the seller sends a
good to the buyer, hoping for payment in return but running the risk that the buyer does
not pay. Many naturally occurring markets are such that buyers move first by sending
payment. In this case trust is not productive and the second mover’s cooperation is
18Again, this is consistent with the first mover valuing the total payment. One could separate these two explanations by conducting additional an additional set of experiments in which the payoff of the second mover in the unproductive trust game was raised by more than $5. In the trade analogy, this would mean that the seller is endowed with an intrinsically valued good plus some additional money or a second intrinsically value good.
The experimental results indicate that nonproductive second movers are less likely to
cooperate in response to the trust of a productive first mover than productive second
movers are in response to nonproductive first movers. This is consistent with previous
experimental work that has found people are more likely to give money to others, the
lower the costs to one’s self. This result was not obvious a priori
as one might expect
greater cooperation when the first mover is productive as the second mover may feel an
obligation to cooperate given the first mover’s responsibility for the increase in available
surplus. Following the trade analogy, this implies that sellers are more likely than buyers
Somewhat surprisingly, this is not anticipated by first movers. Nonproductive first
movers are less likely to trust than productive first movers. One possible explanation,
which is consistent with additional treatment in the paper, is a belief on the part of first
movers is that second movers are willing to be cooperative so long as it does not result in
the second mover receiving a less than fifty percent share. The changes in first and
mover behavior are such that the likelihood of a pair reaching the cooperative outcome is
the same regardless of which mover is productive. This also means that having the
nonproductive party move first is less likely to result in the defection outcome.
Returning to the trade analogy, having buyers move first minimizes the likelihood of a
failed exchange. Of course, one must be cautious in drawing conclusions between these
games and exchange. In naturally occurring trades, prices and hence surplus shares are
endogenously determined, which may impact the behavior of either party and the relative
size and reputation effects would become important.
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