How did Nanjie Village Overcome the Free-Rider Problem?

How Did Nanjie Village Overcome the Free-Rider Problem?

Zhiyuan CUI

(Editor's Note: This article was published in Chinese in the book "From Planned Economy to Market Economy," Economics, Finance and Trade Publishing Agency of China, 1998. It was translated into English by Xinyi WANG.)

1. The Background

Nanjie, a village in Ying County of Henan Province, has prospered on the village enterprises that primarily engage in food processing. It is currently the largest base for the production of instant noodles and rice chips in China. Its production value reached RMB 824 million in 1994, and was predicted to rise above RMB 1.2 billion in 1995.

Interestingly, the agricultural and industrial enterprises in Nanjie Village are not only collectively owned but also collectively managed. None of the twenty six village enterprises is under the "manager responsibility system." The agricultural land is also managed collectively by the village. The entire process from fertilizing and plowing, to seeding and spreading pesticide, and then to harvesting and transporting crops has all been mechanized.

The success of Nanjie's collective economy is a puzzle to many people. There is a folk saying in Henan: "for a public job, you cannot be too slow." The corresponding idea in modern economics is that a collective economy cannot overcome the "free-rider problem." The free-rider problem, put simply, refers to the selfish shirking behavior of some group members in collective actions. A free rider is usually guided by the following reasoning: "if others work hard, I can share in the good result even if I do not put in any effort; if others do not work hard, I have no reason to work hard either because other people will share the result of my hard work while I myself can only receive a small portion of what I produce." Obviously, if every member of the group behaves according to this reasoning, a collective economy cannot survive. In fact, many collective enterprises in China declined or even collapsed for this very reason.

But is the free-rider problem insurmountable? The experience of Nanjie Village demonstrates that it is not. Some recent developments in economic theory also suggest that the free-rider problem can be overcome. In this essay, I will use game theory and the team incentive scheme to explain how Nanjie succeeds in overcoming the free-rider problem.

For clarity of presentation, I will outline the major arguments before I go into the details.

PROPOSITION 1: In repeated games (i.e., not one-shot transactions), cooperative behavior (i.e., no free riding) can emerge.

A corollary of Proposition 1 is that in order to overcome the free-rider problem, a group needs to enhance the "repeatability" of the games and cultivate the long-term orientation of its members, so that members will not think and act as in a one-shot transaction.

Nanjie's method of increasing the "repeatability" of the games was to enhance the existing "communality" of the village community and raise the "exit costs" to its members. For instance, from 1986 to 1994, social welfare in Nanjie developed rapidly. Originally, Nanjie provided free water and electricity to its residents. Now it provides fourteen public welfare benefits. In addition to free water and electricity, coal, natural gas, cooking oil, flour, education, medical care, family planning fees and agricultural taxes have all been made free or paid by the village collectively. Since 1993, Nanjie people have been living in communal family apartments. Each of these three-bedroom apartments, ninety-two square meters in area, has central air conditioning, a TV, a refrigerator and a washing machine, all free of charge. These non-monetary welfare benefits considerably increased the "exit costs" to village residents because non-monetary benefits cannot be carried away or transfered. As a consequence, the "repeatability" of the games played by Nanjie people was greatly increased. Cooperative behavior (i.e., no free riding) of the villagers became possible.

PROPOSITION 2: In repeated games, "cooperation" is a possibility, not a necessity. Whether "cooperation" will emerge in equilibrium depends on whether the players have cooperation-inducing expectations. The challenge for a leader is to create and sustain such expectations in a group.

The experience of Nanjie has fully demonstrated that cooperation-inducing expectations are not something natural, but are created by people. Nanjie's take-off started from "playing with clay eggs", i.e., building a brick factory. In 1981, village leaders wanted to raise RMB 300,000 from the villagers to build a brick factory, but were afraid that previous conflicts between cadres and villagers would lead to "free-rider" expectations and make it impossible to raise the needed funds. Wang Hongbing, the village party secretary, then designed a strategy called "pointing to the mountain while selling the millstone." The village announced the sale of "future bricks" at the price of 2.5 cents per brick and that the village cadres had the privilege to buy the bricks first. The villagers, anxious about the possibility that the cadres were getting special favors, demanded the right to buy these "future bricks" too. Within half a month, the needed RMB 300,000 were collected. The story vividly demonstrates that people in Nanjie had the free-rider inclination too, otherwise there would have been no need for the "pointing-to-the-mountain-while-selling-the-millstone" strategy. But the story also shows that the free-rider problem can be overcome. Another example is when the village built its flour factory, in which case the village cadres contributed capital first, and then the villagers began to contribute too. We can see that the "leading-by-example" actions of the cadres changed the villagers' expectations and induced their cooperative behavior. Instead of thinking and behaving like free riders, community members came to realize the interdependence between the individual and the community, and they acted accordingly.

Using the jargon of game theory, we can say that "free riding" and "one for all and all for one" are both equilibrium strategies for group members. The actual outcome crucially depends on the leaders' behavior. The key factor shaping expectations of the members is whether the leaders lead by example or attempt to take advantage of their positions.

PROPOSITION 3: Even in a non-repeated game, the free-rider problem can be overcome. The "team incentive scheme" is one way to overcome the free-rider problem in a non-repeated game.

Nanjie has about three thousand residents ("inside workers") for whom the repeated game theory seems to apply. But Nanjie also has more than ten thousand temporary workers coming from other regions ("outside workers"). The mobility of the latter group is so high that the repeated game argument does not fit them very well. But the "team incentive scheme" could solve the free-rider problem among outside workers. In fact, the team incentive scheme is widely adopted by all twenty six village enterprises in Nanjie. For instance, in a rice chip production line, the production quota for each team is 280 bags per day. If certain team cannot achieve the quota, then every team member will be punished. As such, team members have a strong incentive to monitor each other, which effectively reduces the possibility of free riding.

With the above introduction, I will now elaborate my propositions in the following sections.

2. The Possibility of Cooperation in Repeated Games

Let us consider the following "work hard vs. free ride" game. The two players both have two strategies to choose from, "work hard" or "free ride" (shirk). The game has four possible outcomes, i.e., four possible payoff profiles for the players. (See Table 1)

Table 1

Player B's Choice

Player A's choice Work hard Free ride

Work hard 2,2 0,3

Free ride 3,0 1,1

If the game is to be played only once, then the "dominant strategy" for both sides is to "free ride." A player's dominant strategy is a strategy that can give the player the best payoff regardless of the strategy used by the other player. In other words, a player's dominant strategy is always the best response to the other player's strategy. For example, from Player A's point of view, if Player B chooses to "work hard," then A's best strategy is to "free ride" because she will then get a payoff of 3, which is greater than 2 (A's payoff should she choose to "work hard"). If B chooses to "free ride," then A's best response is still to "free ride" because she will then get 1 instead of 0, the latter of which would be A's payoff should she choose to "work hard." Therefore, to "free ride" is the dominant strategy for A. By the same reasoning, free riding is also B's dominant strategy.

But as we can see from Table 1, if both players choose their dominant strategies ("free ride"), each will get a payoff of 1, which is less than the 2 that each of them can get if both choose to "work hard." The best strategy profile from each individual's point of view actually produces a result that is bad for both of them. This example clearly demonstrates a divergence between individual rationality and group rationality in the context of a simple game.

In game theory, the above game is usually referred to as the "Prisoners' Dilemma." If we change "work hard" to "cooperate" and "free ride" to "defect" in Table 1, we can see that "defect" is the dominant strategy for each of the prisoners (we can interpret "defect" as "confess"). And as before, if both sides adopt the "defect" strategy, which is the best choice from each individual's point of view, both sides will be worse off (as compared to both players choosing "cooperate").

In the Prisoners' Dilemma (PD) game, the dilemma is that if each individual chooses the strategy that is optimal from her individual point of view, the result is actually not optimal for both of them. In a one-shot PD game, the dilemma cannot be solved because both sides choosing "free ride" is the only equilibrium strategy profile (that is, the best strategy for each player is "free ride" when the opponent chooses "free ride," and this is the only strategy profile with such a property). Another significant property of the dilemma is that using the strategy that is optimal from each individual point of view in fact brings the worst total payoff of the game: 1+1< 3+0 < 2+2.

In a repeated PD game, however, to "free ride" or "defect" is no longer the dominant strategy. In other words, the possibility of cooperation emerges. Now, let us consider a new strategy in a repeated game, "tit-for tat." For each player, the strategy works in the following way. In the first round, the player plays "cooperate." In each of the rounds after the first one, she plays the strategy used by the opponent in the previous round, i.e., she cooperates if the opponent cooperated in the previous round and defects if the opponents did so in the previous round. As we can see, "tit-for-tat" is in its nature similar to Mao's famous strategy: "if others do not infringe upon us, we will not infringe upon them; but if others do infringe upon us, we will definitely infringe upon them." Now the interesting question is, in a repeated game, is "always defect" still a dominant strategy? To answer this question, let us redraw Table 1 as Table 2.

Table 2

Player B's Choice

Player A's Choice Tit-for-tat Always Defect

Tit-for-tat 2/(1-w), 2/(1-w) -1+1/(1-w), 2+1/(1-w)

Always Defect 2+1/(1-w), -1+1(1-w) 1/(1-w), 1/(1-w)

In Table 2, w stands for the probability that after the first round, the game will be repeated for the second round. Then w^{2} (read "w squared") is the probability that the game will continue into the third round. And so on. Therefore, if both sides use the "always defect" strategy, then in the first round each will get a payoff of 1; in the second round each will get another 1 with probability w; in the third round each will get 1 again with probability w^{2}; and so on. As such, the expected value of the payoff for each player is:

1+w+w^{2}+w^{3} ... = 1/(1-w).

If both sides play "tit-for-tat," then in the first round each gets a payoff of 2; in the second round each gets 2 with probability w; in the third round each gets 2 with probability w^{2}; and so on. Therefore the expected value of the payoff for each player is:

2+2w+2w^{2}+... = 2/(1-w).

Now we can see whether "always defect" is still a dominant strategy for each player. Obviously, it depends on whether or not the expected payoff of playing "always defect" is greater than that of playing "tit-for-tat" for each of the other player's strategy. When w is greater than 1/2, 2/(1-w) is greater than 2+1/(1-w); when w is smaller than 1/2, 2/(1-w) is smaller than 2+1/(1-w). In other words, when w is greater than 1/2, "always defect" is no longer a dominant strategy because the best response when the other player is playing "tit-for-tat" is to "tit-for-tat." The possibility of cooperation emerges!

W being greater than 1/2 means that both sides think the game has a large probability to continue into the next round. That is, it is not a one-shot game. The characteristics of the Nanjie community and the stability of the agricultural population make transactions among Nanjie people more like repeated games, which makes it possible to overcome the free-rider problem or the prisoners' dilemma.

What we need to stress here is that "possibility" does not mean "necessity." Although "always defect" is not a dominant strategy, neither is "tit-for-tat." For example, in the first round of the game, if one player believes that the other side is playing "always defect," this player will not use the "tit-for-tat" strategy because 1/(1-w) is greater than -1+1/(1-w). Therefore, in a repeated PD game, neither "always defect" nor "tit-for-tat" is a dominant strategy. In this game, both (always defect, always defect) and (tit-for-tat, tit-for-tat) are equilibrium strategy profiles. That is, in each of the two strategy profiles, each player is playing the best response given the other side's strategy in the profile.

In fact, in game theory there is a more general theorem known as the "folk theorem." The theorem says that in repeated games it is possible for all kinds of strategy profiles, including cooperative ones and non-cooperative ones, to become equilibrium strategy profiles (i.e., no player has any incentive to change her own strategy given others' strategies in the profile). The actual equilibrium outcome depends on the compatible expectations of the players. Take the repeated PD game as an example. In the first round, if both sides play "tit-for-tat," then they must have the following expectations (or "knowledge" in game theory jargon): each side expects her opponent to play "tit-for-tat." In addition, each side knows that her opponent expects her to play "tit-for-tat." Furthermore, each side knows that her opponent knows that she expects the opponent to play "tit-for-tat." And so on. This is called "common knowledge" in game theory. However, this kind of mutually compatible expectations will not necessarily emerge. It must be created. The function and art of a good leader is to create this kind of mutually compatible, cooperation-inducing expectations.

The experience of Nanjie has fully demonstrated that in a community with repeated games, it is possible to overcome the free-rider problem to achieve cooperation. But this possibility would not necessarily become reality. At the time of "playing with clay eggs," Nanjie village still needed to sell "future bricks" in order to raise capital, which shows that "cooperation" was still not the equilibrium strategy. But when the time came to "play with flour bags," the village could rely on the capital contribution of cadres and villagers, which suggests that people's expectation had changed to the cooperation-inducing type. In the process of changing the expectations, Wang Hongbing and his colleagues' "leading by example" and volunteer behavior played a key role. When people began to expect a more developed collective economy to bring benefits to every individual, the cooperative strategy of "one for all and all for one" started to replace the non-cooperative strategy of "free ride."

To summarize, in a collective economy, the free-rider problem is not insurmountable. In a community with suitable conditions for repeated games, if the political and social environment creates and sustains mutually compatible, cooperation-inducing expectations, "one for all and all for one" will become a better strategy for everyone than "free ride." As a consequence, the aggregate welfare of the community will be maximized. When the maximized total payoff is distributed fairly among the community members, the mutually compatible, cooperation-inducing expectations will be reinforced. Through such a feedback loop, a benign circle of good will and good behavior arises.

3. The Team Incentive Scheme

We just saw that the free-rider problem can be solved in a repeated game setting. But can it be solved in situations where games are non-repetitive or repeated for only a very small number of times? This question is very relevant for Nanjie village because there are more and more outside workers working in various village enterprises. Compared to Nanjie residents, these migrant workers have much higher mobility and greater freedom of exit. The repeated game argument cannot explain the incentive structure that Nanjie village has created for these outside workers.

For most of the outside workers, the team incentive scheme is a more direct way for overcoming the free-rider problem. Even for the inside workers (Nanjie residents), the team incentive scheme can also re-enforce the inclination towards cooperation generated by the repeated game setting.

The goal of the team incentive scheme is to create a situation where each team member's losses result in losses of all and each team member's gains bring gains for all, so that the group members do not have any incentive to "free ride." The reason for the rise of free-rider behavior lies in the discrepancy between individual rationality and collective rationality. Individual rationality requires that every individual's marginal costs of additional effort equal her marginal benefits for the additional effort. If every team member behaves individually rationally, each member's work effort will reach a "Nash equilibrium" level where no single individual wants to change her own effort level alone, given the effort levels of other members. The collective rationality, however, requires that the group's production reach a "Pareto optimal" level where the marginal costs of a single member's additional effort are equal to its marginal benefits for the group as a whole. Under the condition of "budget balance" for the group (i.e. the sum of each individuals' benefits equals the total production level of the group), the Nash equilibrium required by individual rationality is in conflict with the Pareto optimality required by collective rationality.

We can use an example to illustrate the above point. Assume a team member's effort has a marginal contribution of 10 to the group's income. >From the angle of collective rationality, as long as the marginal cost of this member's effort is less than 10, the member in question should make the effort until the marginal cost of effort reaches 10. But from the angle of individual rationality, this member should not make any effort at the marginal cost of 10 unless her individual marginal benefit is greater or equal to 10. If this member's individual marginal benefit is only 5, then she should stop when the marginal cost of her effort reaches 5, although stopping at the marginal cost of 10 is "Pareto optimal" for the group. This is what "free ride" means in the context of a team.

We are now ready to formalize the "Holmstrom impossibility theorem," which states that Nash equilibrium (individual rationality) is incompatible with Pareto optimality (collective rationality) in a team under a budget balance constraint. Suppose a team has n members. When member i uses strategy (effort level) "ai," the group produces "x." Si(x) is how much member i gets from the group production x. Under the condition of budget balance, we have:

sum(Si(x)) = x. (1)

Let Vi(ai) be the individual effort cost for member I who exerts effort ai. Then member i's individual income is

Si(x(a)) - Vi(ai), (2)

where a=(a1, a2, ... an). Now we will prove Holmstrom's theorem by contradiction. If we assume that there exists a Nash equilibrium that also satisfies Pareto optimality, then we can deduce a result that is contradictory to equation (1). In equation (2), if we take the derivative with respect to ai, we have a first order condition for the Nash equilibrium:

Si'xi - Vi' = 0, (3)

where xi is the partial derivative of x with respect to ai. For ai to satisfy Pareto optimality, we have:

xi - Vi' = 0. (4)

Comparing (3) against (4), we have Si'=1 (i = 1, 2, ..., n) and sum(Si')=n, but this contradicts (1) because (1) implies that sum(Si')=1.

The Holmstrom impossibility theorem shows that, if we want to satisfy individual rationality and collective rationality at the same time, we have to break the budget balance. That is to say, the sum of group members' individual incomes needs to be less than the total output of the team.

Holmstrom designed a group incentive scheme that breaks the budget balance. The scheme is similar to the peer supervision system adopted by village enterprises in Nanjie. Holmstrom's scheme sets a production target for the team, which equals the Pareto optimal production level x(a*). If the total production of the team is less than x(a*), then every team member will be punished: income becomes 0 for each individual member. This mechanism breaks the budget balance for all x less than x(a*), making it possible for individual rationality to coincide with collective rationality. In addition, under the Holmstrom scheme the Pareto optimal level of production becomes the focus of every team member. If any team member attempts to "free ride," she will reduce not only others' income but also her own. The members themselves now have an incentive to watch out and guard against free-rider behavior within the team. This peer monitoring system is more effective than any outside supervision from above.

Holmstrom's team incentive scheme is widely used in Nanjie. Nanjie's famous "six fix and one compensation" system usually sets quotas at the workshop or production team level rather than the individual level, which provides room and incentives for peer monitoring among the members. Nanjie's frequent "quality team" competition since 1992 is another example of the team incentive scheme. The "ten-family collective responsibility" system introduced under Nanjie's family planning campaign is still a third example of such incentive schemes. In Nanjie, the team incentive scheme has become a powerful tool combating the free-rider problem.

In summary, I have argued in this and the last section that the free-rider problem in collective economies is not insurmountable. "One for all and all for one" is not a utopia too idealistic to be realized. Rather, it is just another possible equilibrium, and individually rational, strategy just like the "free ride" strategy. Once the possibility becomes reality, the superiority of the collective economy will be seen.

4. Credible Commitments

I will use this concluding section to give a few remarks on credible commitments. From Table 1, we can see that when a team member plays "free ride," although she may be punished by others (who would also play "free ride") and get a low payoff of 1, she also has a chance to take advantage of others (by "shirking") and gets a payoff of 3 if others are working hard. Note this payoff (3) is larger than the payoff (2) if the team member in question works hard when everyone else is working hard, although everyone working hard will produce the best total payoff of the game (2+2=4). The discrepancy between individual rationality and collective rationality is the root of the opportunistic behavior of the players.

The possibility, however, of being punished in repeated games, and peer monitoring in the team incentive scheme, can thwart the attempt to get higher payoffs through free riding because the benefits of free riding can be outweighed by losses in future games or by the possibility of being caught and expelled from the team. In this dynamic process within the team, a team member's opportunistic behavior may not produce even short-term benefits. As such, collective rationality and individual rationality converge. As Nanjie people like to say, "the factory prospers then I prosper, the factory runs out of fortune then I go out of fortune." In fact, for an overwhelming majority of the team, it is impossible to maximize one's own long-term interest without maximizing the team's aggregate long-term interest. Nanjie's success is the best proof of this claim. Since 1986, Nanjie village has been back on the road of developing a collective economy and "achieving prosperity together."

There is, however, a caveat. For public ownership to be more efficient than private ownership, there is one crucial condition: the leaders must lead by example. The leaders must take the lead in combating the hard times before they can enjoy the good times. They must make credible commitments to behave this way.

There are two Chinese folk sayings. One is "three monks have no water to drink," and the other is "the flame becomes high when many are adding firewood." The two sayings suggest two possible equilibria for the interactions among community or team members. One is the "free ride" equilibrium (1+1<2), and the other is the "cooperate" equilibrium (1+1>2). The analysis above has shown that in repeated games it is possible for all kinds of strategy profiles, both the cooperative ones and the non-cooperative ones, to become equilibrium strategy profiles. The actual outcome depends on the mutually compatible expectations of the players. The function and art of leadership are to create mutually compatible, cooperation-inducing expectations.

Obviously, once "to cooperate" becomes the equilibrium strategy for everyone, i.e., once the logic of "the flame becomes high when many are adding firewood" has overcome the logic of "three monks have no water to drink," the motivational efficiency inside an enterprise, which is very different from the allocative efficiency of the market, will be greatly raised. The experience of Nanjie tells us that the key to forming cooperation-inducing expectations lies in whether or not team leaders lead by example and make credible commitments to team members.

Credible commitments are the opposite of empty promises. If the leaders do not go in the front of the line, do not set examples for the members to follow, but only ask the members to work hard for the sake of the team, they are making empty promises. On the other hand, if the leaders work hard before, or together with, the team members, and enjoy the benefits after the team members, then they can motivate the team members to work hard for the collective enterprise and enhance the motivational efficiency inside the team. One of the lessons we learn from Nanjie is that the key to increasing motivational efficiency is the cooperation-inducing, and credible, commitments made by the leaders.

What Wang Hongbing, Nanjie's Party secretary, says may help us understand how credible commitments work in Nanjie. According to Wang Hongbing, any cadre of Nanjie has the ability to become very rich if she is concerned only with her own fortune. But each cadre receives a monthly salary of only RMB 250. This fact forms a credible commitment and makes the villagers believe that the collective economy has a great future, which in turn gives rise to the expectation of cooperation.

In other regions of China, however, we often hear people saying that if you want to find the cadres of a village, you only need to look for the most luxurious houses. This situation reflects a cadre-mass relationship opposite of what we find in Nanjie. It is not difficult to imagine that in these other villages, "free ride" rather than "cooperate" becomes the equilibrium strategy for everyone. The logic of "three monks do not have water to drink" will overcome the logic of "the flame becomes high when many are adding firewood." The motivational efficiency in these villages will remain low. Obviously, if the leaders act like "hanging the goat head while selling the dog meat" and apply double standards, the result must be that "the monk becomes rich while the temple is being impoverished." If so, there would be no hope for "achieving prosperity together."

(The author is Associate Professor of Political Science in the Massachusetts Institute of Technology.)