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The effect of two incentive schemes upon the conservation of shared resource by five-person groups
ORGANIZATIONAL BEHAVIOR AND HUMAN PERFORMANCE 13, 330-338 (1975)
The Effect of Two Incentive Schemes upon the Conservation of Shared Resource by Five-Person Groups FRANKLIN D.
RUBENSTEIN
New York University GERARD W A T Z K E
Boston University Overseas Program, Brussels, Belgium
ROBERT H.
DOKTOR
State University of New York at Binghamton AND JONATHAN D A N A
Stanford University Several salient problems in society result from many individuals acting in their own self-interest rather than in the interest of the group. A multistage, n-person, nonzero-sum game allows examination of such conflicts of interest. A central resource which determines each player's winnings is continually degraded; players elect to allow, not to allow, or to reverse the degradation by spending from their respective scores. A total of 195 high school students participated. Subjects w h o w o n amounts based on the group's combined score conserved the resource significantly more than subjects who won amounts based on their personal scores. Subjects conserved the resource more w h e n the resource was already half degraded than when it was pure at the start of the game.
Energy crises, air and water pollution, and traffic congestion are much used examples of problems caused by runaway technology and for which technical solutions must be found if modern society is not to regress to a more primitive state of being. While this type of diagnosis and prognosis may be acceptable to those unburdened with the task of finding technical solutions, it is certainly unrealistic in the short-run. For, as Frank (1966) so aptly described it, the ouffalls of "galloping technology" are social diseases, and "the remedies lie mainly in the realm of human behavior." Hardin's (1968) recounting of "the tragedy of the commons" lends support to Frank's assertion, particularly as the genre of problem was being described in 1833 without the trappings of technology. In the scenario, each rational herdsman added additional animals to his herd which shared the common pasture. In the short-run the marginal gain to each herdsman of adding to this herd was perceived as being only partially offset by the cost of resource consumption. Ultimately the tragedy 33O Copyright © 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
EFFECT
OF TWO
INCENTIVE
SCHEMES
331
of resource destruction was suffered by rational and nonrational herdsmen alike. Whether the particulars are cars on the causeway or cows on the commons, the issue is essentially one of the individual acting without consideration of social costs. For as Kelley and Grzelak (1972) observe, "It is largely in their collective consequences that the competitive actions of a large number of persons have marked detrimental implications for the general welfare." Consider a multistage, n-person, nonzero-sum game reported by Rubenstein (1971) and by Watzke et al. (1972). Its feature is a central resource which is repeatedly distributed to the players; this resource undergoes a systematic deterioration at each stage of the game unless the players act to prevent the degradation. Each player's outcome for each stage is a function of the quality of the resource; before each stage each player may elect to allow, not to allow, or to reverse the automatic deterioration of the central resource, but with different costs. Interdependence is thus established because the overall quality of the central resource depends on the combined actions of all of the players; each player elects resource degrading, resource maintaining, or resource upgrading behavior by the amount that he invests in the quality of the central resource for the next round of the game. (For further clarification, please see the Procedure section which follows.) Two reward schemes were varied with two initial conditions. The player either kept winnings generated by his own net score for the game (keep condition), or he received an equal share of his group's combined earnings (pool condition). The game was begun either with the central resource in perfect condition, or already half degraded. When each player receives an equal share of the group's winnings, the goals of the individual and the group are aligned. However, when each player keeps only his own winnings, the goals of the individual player and the group are not aligned (similar to the case of the tragedy of the common alluded to earlier). In this situation, the individual does not bear the entire cost of his actions. The costs brought about by the deterioration of the resource are shared by all members of the group, while only the player taking the resource degrading actions benefits. The player is forced into a choice each round between group-oriented behavior and self-oriented behavior. It was hypothesized that those groups dividing the combined earnings of the players would spend more to prevent degradation of the resource than those groups in which individuals were rewarded based on personal score alone. Also, it was predicted that more would be spent by those groups beginning with the resource already half-degraded in both reward conditions.
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ET AL.
METHOD
Subjects Male and female secondary school students from Santa Clara County, California, volunteered in response to solicitation by their regular classroom teacher. The subjects had been told in advance only that the activity would be participation in a game with the chance to win an unspecified amount of money.
Procedure The subjects were asked to be seated by the experimenter. The following instructions were read: D u r i n g the period y o u will be here, you will h a v e an opportunity to win s o m e m o n e y by playing a game. T h e r e will be five people playing the g a m e at once, but in no s e n s e will you, as a game player, be competing with the other players in order to win. It is possible for e v e r y o n e to win at this game; j u s t b e c a u s e one p e r s o n wins does not m e a n all the others, or a n y of the others, h a v e to lose. T h i s will b e c o m e m o r e clear as we proceed. T h e g a m e you will be playing is a card game. It is not a card g a m e in the u s u a l s e n s e of the word, b e c a u s e it is only the backs of the cards about which y o u will be concerned, not the faces. Y o u will be dealt s e v e n cards for each round, the rules for "winning" are very simple. If at least five of the s e v e n cards you receive have blue b a c k s , you win. If three or m o r e of the s e v e n cards y o u receive have red backs, you lose. T h u s y o u c a n see that y o u either " w i n " or " l o s e " on each round; there are no " h a l f w a y " hands. H e r e are s o m e e x a m p l e s of possible hands:
7 blue . . . . . . . . . . . . . . . . . . . . . . . . . . 6blue, 1 red . . . . . . . . . . . . . . . . . . . . . 5 blue, 2 red . . . . . . . . . . . . . . . . . . . . . 4 blue, 3 red . . . . . . . . . . . . . . . . . . . . .
wins wins wins loses
3 blue, 4 red . . . . . . . . . . . . . . . . . . . . 2 blue, 5 red . . . . . . . . . . . . . . . . . . . . . 1 blue, 6 red . . . . . . . . . . . . . . . . . . . . . 7 red . . . . . . . . . . . . . . . . . . . . . . . . . .
loses loses loses loses
A r e there a n y questions as to the m e c h a n i c s of what constitutes a winning h a n d or a losing h a n d ? Let me repeat it one more time. Y o u are dealt s e v e n cards; if at least five cards are blue, y o u win; if not, y o u lose. H e r e is w h e r e things get a little m o r e complicated; please p a y extra careful attention. E a c h round is divided into two parts, or stages; Stage I consists of y o u r getting your cards a n d identifying w h e t h e r y o u h a v e w o n or lost on that particular round, as explained above. Stage II, which wilt be explained in m o r e detail presently, is w h e r e you c a n at least partially determine h o w m u c h you h a v e w o n or lost on that particular round. T h e two stages together c o m b i n e to m a k e y o u r total score for that round. T o explain: E a c h time a set of s e v e n cards is dealt to you, t h e following p h e n o m e n o n occurs: O n e o f the cards w h i c h is blue for the p r e s e n t r o u n d b e c o m e s red w h e n returned to the central deck. Y o u as a n individual always receive s e v e n cards f r o m the deck a n d always return s e v e n cards back to the deck. H o w e v e r , the distribution of blue cards and red cards is subject to certain changes. A s stated above, each player will return to the central deck o n e m o r e red card t h a n he took out. T h a t is, if y o u were dealt six blue a n d o n e red, w h e n you give the cards back to the dealer, the distribution will be
E F F E C T OF T W O INCENTIVE SCHEMES
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changed b y t h e dealer to five blue and two red. T h e n the cards will be placed back into the central deck. However, each player, as an individual, has two alternatives open to him in addition to the one mentioned above. One alternative allows any player, for a certain cost, to cancel out the change of the blue card to red, so that his seven cards return to to the central deck in the same distribution in which he received them. This alternative, in effect, maintains the status quo and will be referred to as "option status quo." The second alternative allows each player to have his cards returned to the central deck with one red card changed to blue. Under this alternative, if a player is dealt five blue and two red, the dealer will return six blue and one red to the central deck. This option in essence is a change of two cards, one to return to the status quo, and one to increase the number of blue cards in the deck. As such, this alternative will cost the player twice as much as the cost of returning to the status quo. T h e alternative which adds one blue card to the deck will be referred to as "option blue." Remember you need five blue cards to win. To recapitulate, once you have received your cards for a game trial and determined whether you have won or lost, you have a three-way choice: (a) H a v e the number of red cards increased by one, which will be called "option red," "option red" has no explicit cost; (b) "Option status quo," which at a cost, keeps the relative number of red and blue cards unchanged, and (c) "Option blue," which at double the cost of option status quo, increases the number of blue cards by one. Are there any questions about mechanics? If not, we will now discuss some of the more specific rules, including the number of points won on each round, how much each point is worth, etc. I shall now pass out the score sheets. (pass out score sheets) As you can see, the rules for scoring points are listed on the top of the sheet. Fill out the score sheet as follows: When you receive your seven cards, count the number of blue cards. Enter that number in the column headed "number of blue cards." Next, enter your Stage I score under the column headed "Stage I score." As the score sheet shows on top, if you have received five or more blue cards, enter a " + 4 " in this column. If you received four or fewer blue cards, enter a " - 1 " in this column. Next, enter your score for the column headed "Stage II score." The number of points you enter here depends on your decision to choose "option red, . . . . option status quo," or "option blue." If you choose "option red," which adds a red card to the deck, enter "0" in the column. If you choose "option status quo," which returns your cards without changes, enter " - 2 " in the column. If you choose "option blue," which adds a blue card to the deck, enter " - 4 " in the column. Next, add your scores for Stage I and Stage II for that round. Enter that number in the column headed "Total for round." Finally add your total for that round to your earnings thus far, and enter that number in the column headed "Cumulative total." There are 50 cards at the start of each round. Before each round the deck will be displayed to all players to show the relative distribution of red and blue cards. At the start of each game the deck is all blue (haft blue). Each point is worth 5 . Each player begins the game with 30 points. Therefore your cumulative total after round #1 will be whatever you win on round #1 + 30. A n y questions before we begin?"
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Questions by subjects were answered by rereading or paraphrasing relevant portions of the instructions. Instructions were repeated until the experimenter was convinced that all subjects understood the game. Each subject played the game but once; there was no opportunity to plan joint strategies or communicate in any way before or during the game. Players were arranged in a circle facing out before instructions were read in order to prevent any nonverbal communications. All hands were returned to the dealer; the substitutions for all players were made out of the sight of the other players. The deck was shuffled and fanned to allow the players to judge the relative proportions of red and blue cards in the deck. Players had no information on which players were adding or subtracting red cards from the central deck. Each game was stopped without warning after 25 rounds, although the score sheet had space to record 40 rounds. This was done to eliminate end play, that is, everyone choosing an expenditure of "0" during the second stage of what is expected to be the last few rounds. There are four treatment conditions: (1) All blue-keep: The deck is initially all blue (50 blue cards) and each player keeps his own winnings. (2) All blue-pool: The deck is initially all blue (50 blue), and at the end of the game the total of all points won by all players are pooled, and winnings are split among the players equally. (3) Half blue-keep: The deck is initially half blue (25 red cards, 25 blue cards) and each player keeps his own winnings. (4) Half blue-pool: The deck is initially half blue (25 red cards, 25 blue cards) and at the end of the game the total of all points won by all players are pooled, and winnings are split equally among the players. After the instructions were read, the group was informed that each individual would keep his winnings, or that the winnings would be pooled and shared by all members of the group. After any additional questions were answered, play of the game was begun.
RESU LTS The frequency of choice among the three decision alternatives is given in Table 1 for each of the four treatment conditions. The focus of analysis is the amount of points spent in maintaining the quality of the central resource, i.e., keeping blue cards in sufficient numbers to ensure a favorable probability of winning. (Note that 10 red cards allow an 88% chance of winning, 15 red cards a 67% chance, 20 a 42% chance, etc.) Using the five-person group as the unit of analysis, the Mann-Whitney test was applied to all tests of significance.
335
E F F E C T OF T W O INCENTIVE SCHEMES TABLE 1 FREQUENCY OF STAGE TWO OPTIONS CHOSEN AND POINTS SPENT IN 25 ROUNDS BY GROUPS Frequency of option chosen
Condition
Group #
Mean
-4
-2
0
(blue)
(status quo)
(red)
Total points spent
points spent pergroup
43 48 41 34 69 75 85
220 218 214 200 150 138 88
175
31 43 59 59
264 238 236 224
241
237
All blue
keep
pool
1 2 3 4 5 6 7
28 32 23 9 19 19 4
8 9
38 37 52 46
10 11
54 45 61 82 37 31 36 56 45 14 20 Half blue
keep
pool
12 13 14 15
31 28 31 29
63 61 55 56
31 36 39 40
250 234 234 228
16
38
67
20
286
17 18 19
32 29 40
75 77 52
18 19 33
278 270 264
275
In terms of number of points spent, all groups starting with a half-blue deck in the keep condition spent more than the groups starting with an all-blue deck in the keep condition (p < .025). The same was true for groups in the pool condition (p < .025). Each of the groups starting with a half-blue deck in the pool condition spent as much as or more than the groups in the keep condition with the same initial resource composition (p < .025). For those groups beginning the game with an all-blue deck, each of the groups in the pool condition spent more than any of those in the keep condition (p < .025). Thus both hypotheses were supported.
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ET AL.
DISCUSSION Clearly, subjects in groups pooling winnings and dividing them equally engaged in more cooperative behavior as seen by level of spending relative to those keeping whatever they managed to win for themselves, demonstrating that group-oriented behavior is more likely when the goals of the group and the individual are aligned than when they are not. For example, for those starting with the deck all-blue, 71% of the decisions of the pool groups maintained or improved the quality of the resources as compared to only 55% for the keep groups. An even larger differential in cooperative behavior is seen in the decisions of those starting with the resources half-degraded: 82% of the pool groups' and 62% of the keep groups' choices favored the status quo or improving the central resource. A second approach to the results is to examine the effectiveness of groups in the various conditions in managing the common resource. Since the probability of winning is greater at lower levels of red cards in the deck, groups that kept the level of red cards to a minimum, managed the resource more effectively. For groups starting with an all-blue deck, the results confirm that no group in the pool condition ever allowed more than 18 red cards in the deck, while all of the groups in the keep condition allowed more than 18 red cards in the deck. A level of 18 red cards was chosen for comparison because at that level the probability of winning is approximately 50%. In fact, the mean level of red cards in the deck was 6.5 for the groups in the pool condition, and 16.9 for the groups in the keep condition (p < .025). For the groups beginning with a haft-blue deck, all groups in the pool condition had reduced the number of red cards to 18 by the 15th round, while only one of the groups in the keep condition had. The mean level of red cards in the deck was 16.6 for the groups in the pool condition, and 31.7 for the groups in the keep condition (p < .025). Thus, the groups in the pool condition were much more effective in maintaining the resource at a high quality level than were the groups under the keep condition. The cumulative data, while useful in describing and necessary to establish fundamental premises, tend to understate the dynamics of stageby-stage behavior. In the case of beginning the game with an all-blue deck, adding red cards at the outset has little effect on the outcome for the round, and the groups tend to add cards with little compunction. However, as the number of red cards increases, each has an incrementally greater effect on the probability of a player's winning, and this seems to serve as a countervailing force against adding red cards. If the rate of degradation is not reduced to zero (or below), the number of red
EFFECT OF TWO INCENTIVE SCHEMES
337
cards rises and, while the cumulative probability of winning decreases, the rate of decrease becomes smaller, so that each additional red card makes less and less of an incremental impact on winning. Subjects, while unsophisticated in a mathematical sense, realized the situation intuitively as seen in round-by-round choices and postexperiment discussions of their behavior. The incremental probability of losing with each additional red card peaks at 18 red cards of the 50 card deck; the marginal difference of adding red cards grows smaller beyond 18. In fact, for groups beginning with an all-blue deck, no group that allowed the number of red cards to rise past 20 was able to reverse the trend. The attitude of the individual subject became one of minimizing personal loss by making no contribution to even holding the level of red cards constant. In the absence of mechanisms for coordination, the groups can readily reach this "point of no return" simply because of individual differences in perceiving the instrumentality of adding the additional red cards. Although it is tempting to draw analogies with community problems, it suffices to say that an experimental device as described here offers a way of investigating the kinds of variables believed to influence everyday behavior. Beyond the obvious dimensions of payoff structure and the number of subjects in a group, the game lends itself to systematically examining questions of the effects of power, influence, information, and planning, to name but a few. For example, what are the effects of peer group pressure? What is the impact of modeling? To what extent does pregame cohesion of the subjects determine behavior? Are there differences if anonymity of actions taken is manipulated? What happens if the power to influence outcomes of the group is differential across players? Such a listing of questions suggests additional questions in turn, each demanding great care in isolating variables and systematically varying experimental conditions. It is hoped that this particular experimentation serves as a stimulus for further exploration, so that community-level problems such as the tragedy of the commons may be better understood and ultimately relieved.
REFERENCES Frank, J. D., Galloping technology, a new social disease. Journal of Social Issues, 1966, 22, 1-14. Hardin, G. The tragedy of the commons. Science, 1968, 162, 1243-1248. Kelley, H. H., & Grzelak, J. The conflict of individual and common interest in a N-person game. Journal of Personality and Social Psychology, 1972, 21, 190-197. Rubenstein, F. D. A behavioral study of pollution: the role of perceived instrumentality in
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an externality situation. Unpublished doctoral dissertation, Stanford University Graduate School of Business, 1971. Shapley, L. S., & Shubik, M. On the core of an economic system with externalities. The American Economic Review, 1969, 59, 678-684. Watzke, G. E., Doktor, R. H., Dana, J, M., & Rubenstein, F. D.: An experimental study of individual vs. group interest. Acta Sociologica, 1972, 15, 366-370.
Received: April 22, 1974
The Effect of Two Incentive Schemes upon the Conservation of Shared Resource by Five-Person Groups FRANKLIN D.
RUBENSTEIN
New York University GERARD W A T Z K E
Boston University Overseas Program, Brussels, Belgium
ROBERT H.
DOKTOR
State University of New York at Binghamton AND JONATHAN D A N A
Stanford University Several salient problems in society result from many individuals acting in their own self-interest rather than in the interest of the group. A multistage, n-person, nonzero-sum game allows examination of such conflicts of interest. A central resource which determines each player's winnings is continually degraded; players elect to allow, not to allow, or to reverse the degradation by spending from their respective scores. A total of 195 high school students participated. Subjects w h o w o n amounts based on the group's combined score conserved the resource significantly more than subjects who won amounts based on their personal scores. Subjects conserved the resource more w h e n the resource was already half degraded than when it was pure at the start of the game.
Energy crises, air and water pollution, and traffic congestion are much used examples of problems caused by runaway technology and for which technical solutions must be found if modern society is not to regress to a more primitive state of being. While this type of diagnosis and prognosis may be acceptable to those unburdened with the task of finding technical solutions, it is certainly unrealistic in the short-run. For, as Frank (1966) so aptly described it, the ouffalls of "galloping technology" are social diseases, and "the remedies lie mainly in the realm of human behavior." Hardin's (1968) recounting of "the tragedy of the commons" lends support to Frank's assertion, particularly as the genre of problem was being described in 1833 without the trappings of technology. In the scenario, each rational herdsman added additional animals to his herd which shared the common pasture. In the short-run the marginal gain to each herdsman of adding to this herd was perceived as being only partially offset by the cost of resource consumption. Ultimately the tragedy 33O Copyright © 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
EFFECT
OF TWO
INCENTIVE
SCHEMES
331
of resource destruction was suffered by rational and nonrational herdsmen alike. Whether the particulars are cars on the causeway or cows on the commons, the issue is essentially one of the individual acting without consideration of social costs. For as Kelley and Grzelak (1972) observe, "It is largely in their collective consequences that the competitive actions of a large number of persons have marked detrimental implications for the general welfare." Consider a multistage, n-person, nonzero-sum game reported by Rubenstein (1971) and by Watzke et al. (1972). Its feature is a central resource which is repeatedly distributed to the players; this resource undergoes a systematic deterioration at each stage of the game unless the players act to prevent the degradation. Each player's outcome for each stage is a function of the quality of the resource; before each stage each player may elect to allow, not to allow, or to reverse the automatic deterioration of the central resource, but with different costs. Interdependence is thus established because the overall quality of the central resource depends on the combined actions of all of the players; each player elects resource degrading, resource maintaining, or resource upgrading behavior by the amount that he invests in the quality of the central resource for the next round of the game. (For further clarification, please see the Procedure section which follows.) Two reward schemes were varied with two initial conditions. The player either kept winnings generated by his own net score for the game (keep condition), or he received an equal share of his group's combined earnings (pool condition). The game was begun either with the central resource in perfect condition, or already half degraded. When each player receives an equal share of the group's winnings, the goals of the individual and the group are aligned. However, when each player keeps only his own winnings, the goals of the individual player and the group are not aligned (similar to the case of the tragedy of the common alluded to earlier). In this situation, the individual does not bear the entire cost of his actions. The costs brought about by the deterioration of the resource are shared by all members of the group, while only the player taking the resource degrading actions benefits. The player is forced into a choice each round between group-oriented behavior and self-oriented behavior. It was hypothesized that those groups dividing the combined earnings of the players would spend more to prevent degradation of the resource than those groups in which individuals were rewarded based on personal score alone. Also, it was predicted that more would be spent by those groups beginning with the resource already half-degraded in both reward conditions.
332
RUBENSTEIN
ET AL.
METHOD
Subjects Male and female secondary school students from Santa Clara County, California, volunteered in response to solicitation by their regular classroom teacher. The subjects had been told in advance only that the activity would be participation in a game with the chance to win an unspecified amount of money.
Procedure The subjects were asked to be seated by the experimenter. The following instructions were read: D u r i n g the period y o u will be here, you will h a v e an opportunity to win s o m e m o n e y by playing a game. T h e r e will be five people playing the g a m e at once, but in no s e n s e will you, as a game player, be competing with the other players in order to win. It is possible for e v e r y o n e to win at this game; j u s t b e c a u s e one p e r s o n wins does not m e a n all the others, or a n y of the others, h a v e to lose. T h i s will b e c o m e m o r e clear as we proceed. T h e g a m e you will be playing is a card game. It is not a card g a m e in the u s u a l s e n s e of the word, b e c a u s e it is only the backs of the cards about which y o u will be concerned, not the faces. Y o u will be dealt s e v e n cards for each round, the rules for "winning" are very simple. If at least five of the s e v e n cards you receive have blue b a c k s , you win. If three or m o r e of the s e v e n cards y o u receive have red backs, you lose. T h u s y o u c a n see that y o u either " w i n " or " l o s e " on each round; there are no " h a l f w a y " hands. H e r e are s o m e e x a m p l e s of possible hands:
7 blue . . . . . . . . . . . . . . . . . . . . . . . . . . 6blue, 1 red . . . . . . . . . . . . . . . . . . . . . 5 blue, 2 red . . . . . . . . . . . . . . . . . . . . . 4 blue, 3 red . . . . . . . . . . . . . . . . . . . . .
wins wins wins loses
3 blue, 4 red . . . . . . . . . . . . . . . . . . . . 2 blue, 5 red . . . . . . . . . . . . . . . . . . . . . 1 blue, 6 red . . . . . . . . . . . . . . . . . . . . . 7 red . . . . . . . . . . . . . . . . . . . . . . . . . .
loses loses loses loses
A r e there a n y questions as to the m e c h a n i c s of what constitutes a winning h a n d or a losing h a n d ? Let me repeat it one more time. Y o u are dealt s e v e n cards; if at least five cards are blue, y o u win; if not, y o u lose. H e r e is w h e r e things get a little m o r e complicated; please p a y extra careful attention. E a c h round is divided into two parts, or stages; Stage I consists of y o u r getting your cards a n d identifying w h e t h e r y o u h a v e w o n or lost on that particular round, as explained above. Stage II, which wilt be explained in m o r e detail presently, is w h e r e you c a n at least partially determine h o w m u c h you h a v e w o n or lost on that particular round. T h e two stages together c o m b i n e to m a k e y o u r total score for that round. T o explain: E a c h time a set of s e v e n cards is dealt to you, t h e following p h e n o m e n o n occurs: O n e o f the cards w h i c h is blue for the p r e s e n t r o u n d b e c o m e s red w h e n returned to the central deck. Y o u as a n individual always receive s e v e n cards f r o m the deck a n d always return s e v e n cards back to the deck. H o w e v e r , the distribution of blue cards and red cards is subject to certain changes. A s stated above, each player will return to the central deck o n e m o r e red card t h a n he took out. T h a t is, if y o u were dealt six blue a n d o n e red, w h e n you give the cards back to the dealer, the distribution will be
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333
changed b y t h e dealer to five blue and two red. T h e n the cards will be placed back into the central deck. However, each player, as an individual, has two alternatives open to him in addition to the one mentioned above. One alternative allows any player, for a certain cost, to cancel out the change of the blue card to red, so that his seven cards return to to the central deck in the same distribution in which he received them. This alternative, in effect, maintains the status quo and will be referred to as "option status quo." The second alternative allows each player to have his cards returned to the central deck with one red card changed to blue. Under this alternative, if a player is dealt five blue and two red, the dealer will return six blue and one red to the central deck. This option in essence is a change of two cards, one to return to the status quo, and one to increase the number of blue cards in the deck. As such, this alternative will cost the player twice as much as the cost of returning to the status quo. T h e alternative which adds one blue card to the deck will be referred to as "option blue." Remember you need five blue cards to win. To recapitulate, once you have received your cards for a game trial and determined whether you have won or lost, you have a three-way choice: (a) H a v e the number of red cards increased by one, which will be called "option red," "option red" has no explicit cost; (b) "Option status quo," which at a cost, keeps the relative number of red and blue cards unchanged, and (c) "Option blue," which at double the cost of option status quo, increases the number of blue cards by one. Are there any questions about mechanics? If not, we will now discuss some of the more specific rules, including the number of points won on each round, how much each point is worth, etc. I shall now pass out the score sheets. (pass out score sheets) As you can see, the rules for scoring points are listed on the top of the sheet. Fill out the score sheet as follows: When you receive your seven cards, count the number of blue cards. Enter that number in the column headed "number of blue cards." Next, enter your Stage I score under the column headed "Stage I score." As the score sheet shows on top, if you have received five or more blue cards, enter a " + 4 " in this column. If you received four or fewer blue cards, enter a " - 1 " in this column. Next, enter your score for the column headed "Stage II score." The number of points you enter here depends on your decision to choose "option red, . . . . option status quo," or "option blue." If you choose "option red," which adds a red card to the deck, enter "0" in the column. If you choose "option status quo," which returns your cards without changes, enter " - 2 " in the column. If you choose "option blue," which adds a blue card to the deck, enter " - 4 " in the column. Next, add your scores for Stage I and Stage II for that round. Enter that number in the column headed "Total for round." Finally add your total for that round to your earnings thus far, and enter that number in the column headed "Cumulative total." There are 50 cards at the start of each round. Before each round the deck will be displayed to all players to show the relative distribution of red and blue cards. At the start of each game the deck is all blue (haft blue). Each point is worth 5 . Each player begins the game with 30 points. Therefore your cumulative total after round #1 will be whatever you win on round #1 + 30. A n y questions before we begin?"
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Questions by subjects were answered by rereading or paraphrasing relevant portions of the instructions. Instructions were repeated until the experimenter was convinced that all subjects understood the game. Each subject played the game but once; there was no opportunity to plan joint strategies or communicate in any way before or during the game. Players were arranged in a circle facing out before instructions were read in order to prevent any nonverbal communications. All hands were returned to the dealer; the substitutions for all players were made out of the sight of the other players. The deck was shuffled and fanned to allow the players to judge the relative proportions of red and blue cards in the deck. Players had no information on which players were adding or subtracting red cards from the central deck. Each game was stopped without warning after 25 rounds, although the score sheet had space to record 40 rounds. This was done to eliminate end play, that is, everyone choosing an expenditure of "0" during the second stage of what is expected to be the last few rounds. There are four treatment conditions: (1) All blue-keep: The deck is initially all blue (50 blue cards) and each player keeps his own winnings. (2) All blue-pool: The deck is initially all blue (50 blue), and at the end of the game the total of all points won by all players are pooled, and winnings are split among the players equally. (3) Half blue-keep: The deck is initially half blue (25 red cards, 25 blue cards) and each player keeps his own winnings. (4) Half blue-pool: The deck is initially half blue (25 red cards, 25 blue cards) and at the end of the game the total of all points won by all players are pooled, and winnings are split equally among the players. After the instructions were read, the group was informed that each individual would keep his winnings, or that the winnings would be pooled and shared by all members of the group. After any additional questions were answered, play of the game was begun.
RESU LTS The frequency of choice among the three decision alternatives is given in Table 1 for each of the four treatment conditions. The focus of analysis is the amount of points spent in maintaining the quality of the central resource, i.e., keeping blue cards in sufficient numbers to ensure a favorable probability of winning. (Note that 10 red cards allow an 88% chance of winning, 15 red cards a 67% chance, 20 a 42% chance, etc.) Using the five-person group as the unit of analysis, the Mann-Whitney test was applied to all tests of significance.
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E F F E C T OF T W O INCENTIVE SCHEMES TABLE 1 FREQUENCY OF STAGE TWO OPTIONS CHOSEN AND POINTS SPENT IN 25 ROUNDS BY GROUPS Frequency of option chosen
Condition
Group #
Mean
-4
-2
0
(blue)
(status quo)
(red)
Total points spent
points spent pergroup
43 48 41 34 69 75 85
220 218 214 200 150 138 88
175
31 43 59 59
264 238 236 224
241
237
All blue
keep
pool
1 2 3 4 5 6 7
28 32 23 9 19 19 4
8 9
38 37 52 46
10 11
54 45 61 82 37 31 36 56 45 14 20 Half blue
keep
pool
12 13 14 15
31 28 31 29
63 61 55 56
31 36 39 40
250 234 234 228
16
38
67
20
286
17 18 19
32 29 40
75 77 52
18 19 33
278 270 264
275
In terms of number of points spent, all groups starting with a half-blue deck in the keep condition spent more than the groups starting with an all-blue deck in the keep condition (p < .025). The same was true for groups in the pool condition (p < .025). Each of the groups starting with a half-blue deck in the pool condition spent as much as or more than the groups in the keep condition with the same initial resource composition (p < .025). For those groups beginning the game with an all-blue deck, each of the groups in the pool condition spent more than any of those in the keep condition (p < .025). Thus both hypotheses were supported.
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DISCUSSION Clearly, subjects in groups pooling winnings and dividing them equally engaged in more cooperative behavior as seen by level of spending relative to those keeping whatever they managed to win for themselves, demonstrating that group-oriented behavior is more likely when the goals of the group and the individual are aligned than when they are not. For example, for those starting with the deck all-blue, 71% of the decisions of the pool groups maintained or improved the quality of the resources as compared to only 55% for the keep groups. An even larger differential in cooperative behavior is seen in the decisions of those starting with the resources half-degraded: 82% of the pool groups' and 62% of the keep groups' choices favored the status quo or improving the central resource. A second approach to the results is to examine the effectiveness of groups in the various conditions in managing the common resource. Since the probability of winning is greater at lower levels of red cards in the deck, groups that kept the level of red cards to a minimum, managed the resource more effectively. For groups starting with an all-blue deck, the results confirm that no group in the pool condition ever allowed more than 18 red cards in the deck, while all of the groups in the keep condition allowed more than 18 red cards in the deck. A level of 18 red cards was chosen for comparison because at that level the probability of winning is approximately 50%. In fact, the mean level of red cards in the deck was 6.5 for the groups in the pool condition, and 16.9 for the groups in the keep condition (p < .025). For the groups beginning with a haft-blue deck, all groups in the pool condition had reduced the number of red cards to 18 by the 15th round, while only one of the groups in the keep condition had. The mean level of red cards in the deck was 16.6 for the groups in the pool condition, and 31.7 for the groups in the keep condition (p < .025). Thus, the groups in the pool condition were much more effective in maintaining the resource at a high quality level than were the groups under the keep condition. The cumulative data, while useful in describing and necessary to establish fundamental premises, tend to understate the dynamics of stageby-stage behavior. In the case of beginning the game with an all-blue deck, adding red cards at the outset has little effect on the outcome for the round, and the groups tend to add cards with little compunction. However, as the number of red cards increases, each has an incrementally greater effect on the probability of a player's winning, and this seems to serve as a countervailing force against adding red cards. If the rate of degradation is not reduced to zero (or below), the number of red
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cards rises and, while the cumulative probability of winning decreases, the rate of decrease becomes smaller, so that each additional red card makes less and less of an incremental impact on winning. Subjects, while unsophisticated in a mathematical sense, realized the situation intuitively as seen in round-by-round choices and postexperiment discussions of their behavior. The incremental probability of losing with each additional red card peaks at 18 red cards of the 50 card deck; the marginal difference of adding red cards grows smaller beyond 18. In fact, for groups beginning with an all-blue deck, no group that allowed the number of red cards to rise past 20 was able to reverse the trend. The attitude of the individual subject became one of minimizing personal loss by making no contribution to even holding the level of red cards constant. In the absence of mechanisms for coordination, the groups can readily reach this "point of no return" simply because of individual differences in perceiving the instrumentality of adding the additional red cards. Although it is tempting to draw analogies with community problems, it suffices to say that an experimental device as described here offers a way of investigating the kinds of variables believed to influence everyday behavior. Beyond the obvious dimensions of payoff structure and the number of subjects in a group, the game lends itself to systematically examining questions of the effects of power, influence, information, and planning, to name but a few. For example, what are the effects of peer group pressure? What is the impact of modeling? To what extent does pregame cohesion of the subjects determine behavior? Are there differences if anonymity of actions taken is manipulated? What happens if the power to influence outcomes of the group is differential across players? Such a listing of questions suggests additional questions in turn, each demanding great care in isolating variables and systematically varying experimental conditions. It is hoped that this particular experimentation serves as a stimulus for further exploration, so that community-level problems such as the tragedy of the commons may be better understood and ultimately relieved.
REFERENCES Frank, J. D., Galloping technology, a new social disease. Journal of Social Issues, 1966, 22, 1-14. Hardin, G. The tragedy of the commons. Science, 1968, 162, 1243-1248. Kelley, H. H., & Grzelak, J. The conflict of individual and common interest in a N-person game. Journal of Personality and Social Psychology, 1972, 21, 190-197. Rubenstein, F. D. A behavioral study of pollution: the role of perceived instrumentality in
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an externality situation. Unpublished doctoral dissertation, Stanford University Graduate School of Business, 1971. Shapley, L. S., & Shubik, M. On the core of an economic system with externalities. The American Economic Review, 1969, 59, 678-684. Watzke, G. E., Doktor, R. H., Dana, J, M., & Rubenstein, F. D.: An experimental study of individual vs. group interest. Acta Sociologica, 1972, 15, 366-370.
Received: April 22, 1974