Information Gaps and Unintended Outcomes of Social Movements: The 1989 Chinese Student Movement

by Fang Deng
Information Gaps and Unintended Outcomes of Social Movements: The 1989 Chinese Student Movement
Fang Deng
The American Journal of Sociology
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Information Gaps and Unintended Outcomes of Social Movements: The 1989 Chinese Student Movement1

Fang Deng

North Central College

Under what conditions will threats made by a state hinder social movements? And under what conditions will intended or unintended outcomes occur as a result? This article addresses these ques- tions by applying a dynamic model that depicts the 1989 Chinese student movement as a three-iteration game with incomplete infor- mation. In this model, the Chinese government is willing ultimately to suppress the student resistance by force, but since it is playing a two-level game, it conceals its preferences as private information while initially choosing not to use force. In the end, many demon- strators died believing that the People's Liberation Army would never harm the Chinese people. This model suggests how an infor- mation gap can lead to unintended and undesirable outcomes, even when actors behave rationally.

The study of social movements has done little to illuminate movement development and outcome. Coleman observed that "social scientists have been less concerned with predicting the outcomes of a revolution or even describing the course it takes than with understanding its emergence" (1990, p. 469). Lichbach argued that "those who have applied CA [collec- tive action] theories to conflict have focused almost exclusively on the initial problem of whether anyone who is rational will actually participate in protest and rebellion. The result of such a preoccupation is, firstly, that almost no CA theorists have gone on to study the many substantive prob- lems arising in revolts and protests" (1994, p. 9). This article focuses on a social movement's development and outcomes. It is based on a case study of the 1989 Chinese student movement.

Recent publications on rationality and rebellious collective actions (Lichbach 1995; Moore 1995; Goldstone and Opp 1994; Marwell and Oli-

I would like to thank the AJS reviewers for their valuable comments on a previous draft. Address corresondence to Fang Deng, Department of Sociology, North Central College, P.O. Box 3063, Naperville, Illinois 60566.

O 1997 by The University of Chicago. All rights reserved. 0002-9602/97/10204-0004$01.50

AJS Volume 102 Number 4 (January 1997): 1085-1112 1085

ver 1993; Muller, Dietz, and Finkel 1991; Coleman 1990) reflect a growing interest in using rational choice theory to explain protest and rebellion. In considering the development and outcomes of a social movement, rational choice theorists have proposed an explanation that focuses on the relation- ship between a social movement and the state (Koopmans 1993; McAdam 1982; Perrow 1979; Tilly 1978). According to this explanation, "The state generates many of the issues with which social movements wrestle; as well, the state facilitates or hinders movements, lowering or raising the costs of collective action, operating in coalition with the movement or opposing it" (Zald 1992, p. 339). Morris and Herring contended that "movement participants and their actions are rational; social movements pursue interests; movement mobilization occurs through an infrastructure or power base; outcomes of collective action are central, and they are prod- ucts of strategic choices made by participants; either support or repression by elite groups can affect the outcomes of movements" (1987, p. 157). The core postulate of this explanation is that the state plays an important role in determining a movement's development and outcomes and that high levels of suppression and limited access to power can force challengers to withdraw from collective action.

There are some puzzling aspects of the 1989 Chinese student movement that challenge the adequacy of this explanation.' On April 17, 1989, the Chinese student movement began when about 3,000 university students from Beijing demonstrated against the Chinese government for political reform. When the students requested a meeting with high-level leaders of the Communist Party, the government responded with threats. The students, however, resisted the threats and the government backed down. In 1989, the government threatened the demonstrators three times, but none of the threats influenced the students. Why did the threats fail?

The first threat occurred on April 26, 1989, when an official editorial characterized the student movement as "a planned conspiracy," the es- sence of which was "to repudiate the leadership of the Chinese Communist Party and to repudiate the socialist institutions." The editorial stated that the movement should be suppressed immediately and harshly. But the threat failed to discourage the students as the number of participants rose from 60,000 on April 24 to 250,000 on April 27. The second threat occurred on May 19, when martial law was declared in parts of Beijing. Thousands of troops with tanks were deployed around the city. This plan failed to return the students to their campuses and to "restore order." For two days, more than a million people protested the enforcement of martial law. The

My analysis is based on newspaper accounts and interview data. All of those inter- viewed were eyewitnesses of the movement. Quotations in this article without cita- tions appear in the People's Daily (from April 15 to June 4, 1989).

third threat occurred on June 3, when the demonstrators were warned

that if they persisted, they would "bear responsibility for their own fates."

Hundreds of thousands of demonstrators refused to comply and the army

opened fire.3

Why did these three threats fail to deter the students? If the demonstra-

tors were rational, why did they persist?

Another question is, Why did the military confrontation occur when both sides hoped to avoid it? After the first threat, for example, the govern- ment backed down when the demonstrators resisted. When martial law was declared, several high-level leaders of the Communist Party asserted in public speeches that the troops were expected "to restore order, and to protect civilians" and that the leaders intended "to avoid a conflict be- tween the demonstrators and the troops." On May 22, some tanks were withdrawn because the government expected that the demonstrators would back down. After a major victory, most of the demonstrators with- drew from Tiananmen Square by May 27, 1989. On May 31, most of the student leaders decided, contrary to their earlier position, to pressure the government by occupying the square until June 20, when the standing committee cf the National People's Congress was expected to convene. Those remaining at Tiananmen Square believed that the longer they stayed, the greater the likelihood that the government would accept their requirements. Why was the outcome so different from that expected by either side?

Sometimes high levels of suppression and limited access to power can force demonstrators to withdraw, and a movement's outcome is as the state intended. At other times the state cannot deter the movement, and unintended outcomes occur. Therefore, any adequate theory of a move- ment's development and outcomes should specify the conditions under which a state can or cannot hinder movements and the conditions under which intended or unintended outcomes occur. The explanation given by the rational choice theorists (e.g., Koopmans 1993; McAdam 1982; Perrow 1979; Tilly 1978) is inadequate because it suggests that a power imbalance in favor of the state can always force demonstrators to withdraw, thus resulting in intended outcomes for the movement. As an alternative to this theory, this article applies game theory to the study of a movement's development and outcomes.

Blaug suggests that "the introduction of a game-theoretical approach to economics has brought with it a new 'understanding' of what is meant by rationality and interdependence and equilibrium" (1992, p. 240). The

There are no official statistics on the number of people who died in the military crackdown. There are many unofficial estimates, but there is a great diversity among them.

understanding was new because "game theorists seek to determine whether a given game (i.e., pay-off structure) can explain social phenom- ena" (Moore 1995, p. 423). When a social movement challenges a state, a game describes the connection between the choices of one side and the options and outcomes for the other side. Over the past 20 years, noncoop- erative game theory has "made serious progress in two crucial areas: dy- namics and asymmetric information" (Tirole 1988, p. 205). Dynamics be- come particularly important in the movement's development in which there are many time periods and intertemporal dependency of action sets. Asymmetric information is also an important issue because some studies have shown that demonstrators sometimes fail to obtain essential informa- tion when they choose strategies (Zald 1992). By studying the equilibrium in certain payoff structures, game theory can predict the choices made by the state and demonstrators and the corresponding outcomes of the movement.

This article is based on the following assumptions:

  1. "People can be modeled as if they have Von Neumann and Morgen- stern utility functions" (Moore 1995, p. 423).
  2. L'People seek to maximize their expected utility" (Moore 1995, p. 423).
  3. There is a single leader of the state who makes decisions on that side, and all of the demonstrators are wholly unified as a single indi- vidual who decides his strategies on the other side (Coleman 1990).4

The single player assumption is very important here because game theorists are inter- ested in explaining social phenomena by payoff structures. When we discuss the pay- off, the player in each side in the game has to be a unitary actor, otherwise, no one will understand whose payoff we are discussing. There is no doubt that almost all unitary actors in game theoretical models are internally divided. But the fragmenta- tion of each side is not an issue in the study of the payoff structure. In other words, the single player and the internal division are two separate issues at different levels of analysis. Is the single player assumption plausible? I will answer this by reflecting on some specific development prior to the 1989 movement. Although the Chinese government was internally divided during the 1989 movement, Deng Xiaoping was the only decision maker. The Central Committee of the Chinese Communist Party made a formal decision in 1987 to grant him this power. Zhao Ziyang, the central secretary of the Chinese Communist Party and a leader of the faction disagreeing with Deng Xiaoping in 1989, failed in his efforts to challenge Deng's authority and resigned on May 19, 1989. The 1989 movement started as a student movement in April, and more than one million people spontaneously participated in May and June. The demonstrators were homogeneous, and all of them struggled for political reform. Although among the students there was internal disagreement, their number was less than 10% of the total number of participants. There was no organizational connection between student and nonstudent demonstrators. Most nonstudent demonstrators at that time never even heard any student leaders' names, and they knew nothing about the fragmentation of the students. The internal disagreement among students had no substantive impact on the strategic choices of 90% of the demonstrators.

4. The payoff structure induces or constrains people's choices in a situ- ation in which "two or more individuals make decisions that will influence one another's welfare" (Myerson 1991, p. 5).

This article presents a dynamic model describing the 1989 movement as a game that is based on incomplete information and repeated three times. The first two sections focus on the first round of the repeated game, the next section on the second round, and the last section on the last round.


A basic model describing the 1989 movement can be constructed to reflect

the sequence of choices made by each side and the options available to

each as the confrontation developed. Although the model is much simpler

than the actual course of events, it captures key aspects of the movement's

development (see fig. 1).

In the first stage, the student movement began when the demonstrators pressured the government for political reform. In the second stage, after the emergence of the student movement, the Chinese government had various options, but for now it will be convenient to reduce them to three:

it could accept the demonstrators' demands and the game would end;
it could suppress the movement through might and force the demon- strators to withdraw; (3) it could threaten the demonstrators, if they did not back down, to take some action that would have worse consequences than backing down. The government chose to threaten the demonstrators. In the third stage, the demonstrators responded to the government's threat. They could "resist" or "back down," and they did not back down. In the fourth stage, after the demonstrators resisted the threat, the govern- ment had to choose whether or not to act on its initial threat as stated in option 2-that is, to use force. If the government had chosen to use force, the demonstrators would have been forced to withdraw and the game would have end. But the government decided not to use force, and there- fore, the game began again, when the demonstrators took new actions.

The model in figure 1is a game composed of a four-step sequence. When does it end? Many possibilities have been mentioned above, which means that the game could end at any step or continue endlessly. In 1989, the game was repeated three times because the government used force after the demonstrators resisted for the third time. In game theory, this four- step sequence might be called a "stage game," and a game in which the stage game is repeated many times is called a "repeated game." This sec- tion and the next will assess the first round of the repeated game. In the first round, there are two questions: (1) Why did the demonstrators choose




Back Down



Demonstrators Use Force


<1> Resist


trators <4>

NOT Use Force

. . .

Not to Act


FIG.1.-A basic model of the 1989 movement

to resist after the government threatened them? (2) Why did the govern- ment choose a list of strategies, that is, to threaten and not to use force? This section will focus on the demonstrators' choice, and the next will discuss the government's strategies.

After the government threatened the movement by publishing the offi- cial editorial on April 26, the students were angry. They expected to orga- nize a full-scale resistance, but they were also concerned about the possi- bility of military intervention. Their uncertainty was based on private information held by the government. According to Fearon, "A person who knows something that others do not know about his preferences, inten- tions, or any other variables is said to have private information" (1992,

p. 113). On April 26, 1989, only the government knew its preferences for the use of force. The students did not know. An overwhelming majority of students believed that there was a 50-50 chance that the government would suppress by force. Their beliefs were based on two conflicting facts: (1)the serious warning in the editorial that indicated that the government would use force and (2) the students' knowledge that the Chinese govern- ment had always tried to avoid military intervention during any demon- strations and had maintained this policy in all student movements since Liberation in 1949.



Show Force q 1
Tough I
P Not Show   I Government Use Forces <3> L(Y4,XI) (3.1)
  -(Yl,Xl) (1,3) I  
  (Y1,Xl) (1,3)  
    (Y4,X4) (2,l) Government Use Force
  Show Force 1-q I Resist Not Use Force (Y3,X3) (3,4)

(Y2,XZ) (4,2)

FIG.2.-A main model of the movement's development

On April 27, the government sent mixed signals before the full-scale demonstration began. It signaled first by showing force. Seven blockade lines were erected between a western suburb of Beijing, where most of the universities are located, and the center of the city at Tiananmen Square. Each blockade line was occupied by hundreds of military police. It seemed that the government would act on its initial threat. But there was another signal. None of the police carried a gun or, strictly speaking, none of them was seen carrying a gun. The mixed signals confirmed the students' beliefs that there was a 50% probability that the government would suppress the movement through the use of force.

Given this uncertainty, why did the students decide to resist? Was their decision rational or impulsive? Were there other factors in their decision? The model in figure 2 addresses these questions.

Unlike the model in figure 1, the new model is a game with incomplete information (i.e., a game in which at least one player is uncertain about another player's payoff). In the new model, the demonstrators are con- fronted with the element of uncertainty. Another difference between the models in figures 1 and 2 is that the former is a game with a four-step sequence and the latter is a subgame within that sequence. The subgame begins at one of the government's decision nodes at the second step of the four-step sequence. First, the subgame must be analyzed. By defini- tion, the government in figure 2 is tough if it prefers to use force and weak if it does not.

In the first step of the main model (i.e., fig. 2), suppose the government

is tough or that the demonstrators initially believe it is tough with the probability p and weak with the probability 1 -p. The game is initiated by a choice the government makes between two alternatives: either to show or not to show force after it threatens the demonstrators, that is, to be tough or to be weak. The government recognizes the uncertainty of the demonstrators and, therefore, either the tough or the weak govern- ment can take advantage of the situation to further threaten the move- ment by showing force. In the second step, a dotted line denotes an infor- mation set. The demonstrators have the information set with two nodes, which reflects their inability to verify the node where they are located when they must make a decision. In other words, although the demonstra- tors have observed that the government showed force after the threat (seven blockade lines were erected), they do not know if the government intends to use force. Suppose the demonstrators are located on the tough side with probability q and on the weak side with probability 1 -q. The demonstrators on either side have a choice between resisting or backing down. If they back down, the game ends. In the third step, the government must decide whether to use force after the demonstrators choose to resist.

In figure 2, XI, X2, X3, and X4 are the demonstrators' payoffs, and Y1, Y2, Y3, and Y4 are the government's payoffs. The first number in parentheses denotes the government's preferences. The second denotes the demonstrators' preferences. The greater the number, the stronger the preferences of both sides. The payoffs and preferences for each side are summarized in table 1,which reveals the demonstrators' payoffs and pref- erences as follows:

xl = 42 H denotes honor to the demonstrators. Usually, resisting the threat brings honor to the demonstrators, and here the demonstrators get smaller dH because they are strong and the government is afraid to show force after the threat.

X2 = -F -F denotes a general cost for the demonstrators (F > 0). The demonstrators will lose face whenever they back down, and this cost can be called a general cost.

X3 = H + G The demonstrators resist the threat that will bring honor, H, to them; G denotes an expected gain for the demonstrators, that is, their demands will be accepted when the government backs down (G >

HI. X4 = -L + H When the government suppresses the student movement, there is an expected loss, -L (L > 0).

Because the demonstrators resist the threat first that brings H to them, -L + H < -F.

In table 1, the government's payoffs and preferences are as follows:

Y1 = -B -B denotes the greatest loss for the government
      because it backs down immediately after it threatens
      (B > 0).
Y2 = B B denotes the greatest gain for the government when
      the demonstrators withdraw after the government
      showed force.
Y3 = E -C E denotes a good record on human rights (E > 0);
      -C denotes a loss of credibility (C > 0). The
      government loses credibility when it fails to act on
      its initial threat, but its record on human rights will
      be good.
Y4 = C -E C denotes a gain of credibility; -E denotes a bad
      record on human rights. The government will get a
      bad record on human rights whenever it acts on its
      initial threat.

There is a difference in the preferences between the tough government and the weak one. For the tough government, C > E > 0, therefore,

For the weak government, E > C > 0, therefore,


:. U(Y2) > U(Y3) > U(Y4) > U(Y1).

As mentioned before, the main model in figure 2 is a dynamic game with incomplete information. A very important methodological innovation in game theory is to invent a new equilibrium concept-perfect Bayesian equilibrium-for this kind of game. Gibbons introduces the new solution concept: "The crucial new feature of this equilibrium concept [perfect Bayesian equilibrium] is due to Kreps and Wilson (1982): beliefs are ele- vated to the level of importance of strategies in the definition of equilib- rium. Formally, an equilibrium no longer consists of just a strategy for each player but now also includes a belief for each player at each informa- tion set at which the player has the move" (Gibbons 1992, p. 179). An appendix shows how to find perfect Bayesian equilibria in the game shown in figure 2.5 From the perfect Bayesian equilibria,

1, ifp<p*,

0, if p > p*, (1)

1 12, otherwise.

where A denotes the probability that the demonstrators resist the threat, p represents the demonstrators' beliefs about the government's prefer- ences, p* is a critical condition, and X2, X3, and X4 are the demonstrators' payoffs.

In (I), if the demonstrators' belief, p, that the government is tough is smaller than the critical condition, p*, they will resist. If their beliefs about p are greater thanp*, they will back down. As mentioned before, students in the 1989 movement believed that there was a 50-50 chance that the government would suppress their movement by force, which means that, in figure 2, the demonstrators' p = 50%. Is p greater or smaller than p*, when p = 50%?

<p*, if (X3 -X2) > (X2 -X4),

>p*, if (X3 -X2) < (X2 -X4),

(3) = p*, otherwise.

In (3), p(50%) < p*, if (X3 -X2) > (X2 -X4); and p(50%) > p*, if (X3 -X2) < (X2 -X4). It is obvious that the demonstrators' beliefs, that the probability for the government to suppress by force is less than 50%, is smaller than p* when p(50%) <p*.

In (3), X3 is the demonstrators' payoff when they resist and the govern- ment does not use force (X3 = H + G); X2 is their payoff when they back down (X2 = -F); X4 is their payoff when they resist, and the government uses force (X4 = -L + H). Then

> (X2 -X4), if IGI -I-LI > -2(F + H),

< (X2 -X4), if IGI -1-4 < -2(F + HI,

(4) = (X2 -X4), otherwise.

According to (4), if IG( -I -LI > -2(F + H),(X3 -X2) > (X2 -X4), then p(50%) <p*; if IGI -I-LI < -2(F + H), (X3 -X2) < (X2 -X4),

An appendix, including all proofs of the equations used in this article, is available on request.

then p(50%) >p*. As mentioned before, for the demonstrators G denotes

an expected gain, -L is an expected loss, -F denotes a general cost, and

H is honor. Suppose the demonstrators think that the general cost and

honor are not very important when compared with the expected gain

and loss, which means that F + H is close to zero. But F + H is always

greater than zero and -2(F + H) is always smaller than zero. Therefore,

the condition for (X3 -X2) > (X2 -X4) can be relaxed to IG( -I-L(

r0. In other words, the condition for p(p = 50%) <p* in the main model

is (GI 2 1-LI, that is, the expected gain is not smaller than the expected

loss for the demonstrators. Here, the expected gain (or loss) is equal to

multiplying a substantive gain (or loss) and the probability associated with

the success (or failure) of the demonstrators' resistance.

According to the perfect Bayesian equilibrium in the main model, when the government threatens after the emergence of a movement, the demon- strators will resist if they believe that the chance is 50-50 or less that the government will use force and if their expected gain is equal to or greater than their expected loss. In 1989, after the government's first threat, the students realized that their substantive gain (the government would ac- cept their demands for political reform) was not smaller than their sub- stantive loss (the police would attack them). They perceived no difference between the substantive gain (or loss) and the expected gain (or loss) be- cause they believed that the probability associated with their success or failure was 50-50. Therefore, they decided to resist, even though they were uncertain of the government's preferences.


In the last section, the main theoretical claim is that interaction between the government and the demonstrators in the first round resulted in a payoff structure, in a game with incomplete information. Owing to the effect of the payoff structure, the demonstrators resisted the government's threat regardless of its military strength. A key element in the game with incomplete information is that the government concealed its preference for the use of force as private information. Why did this occur? In 1989, China's leading strategist, Deng Xiaoping, decided that the Communist Party would never relinquish any of its power. This meant that the gov- ernment would eventually suppress the movement by force. Why did the government fail to send a clear signal to the demonstrators after it threat- ened them? On April 27, 1989, when the students demonstrated, the mili- tary police withdrew and the seven blockade lines broke one by one. After showing force, why did the government choose not to use it?

It is probable that the government was engaged in a two-level game. This concept was first used by Putnam (1988) as a metaphor for domestic-

international interactions. Putnam observed: "The politics of many inter-

national negotiations can usefully be conceived as a two-level game. At

the national level, domestic groups pursue their interests by pressuring

the government to adopt favorable policies, and politicians seek power

by constructing coalitions among those groups. At the international level,

national governments seek to maximize their own ability to satisfy domes-

tic pressures, while minimizing the adverse consequences of foreign devel-

opments. Neither of the two games can be ignored by central decision-

makers, so long as their countries remain interdependent, yet sovereign"

(Putnam 1988, p. 434).

A two-level game is not just a combination of any two games played by

a government simultaneously. One important aspect of a two-level game is

that a particular player plays two games with two different opponents at

the same time, and the player's options in one game are limited by his

strategies in another. In Putnam's two-level game, for example, a national

government plays two games against distinct opponents: domestic constit-

uents and foreign trading partners, who have opposing interests.

When the Chinese government confronted the student movement in 1989, it was engaged in several other games. Some of these were not a part of a two-level game because the government's options in these games were not limited by its strategies in the game with the demonstrators. One of these games was to control regional leaders who were ordering units in their province to lend too much money and to start too many projects. The most important economic task in 1989, then, was to restrict the money supply, which created a major constraint on regional leaders and pro- pelled China into a recession. To suppress the students would signal a strong central government, one that could effectively constrain the money supply and inflation.

But in other games not directly related to the student movement, the government had interests in pursuing strategies that would have been damaged by the overt suppression of the students. For example, one of these games was to please the international community in order to attract foreign investors. If we take this game as an example, it is obvious that the Chinese government was playing a two-level game in 1989.6 At the

There are significant differences between Putnam's two-level game (1988) and the game played by the Chinese government in 1989. For Putnam, there is an interest conflict between domestic constituents and foreign trading partners, and the govern- ment is neutral in this conflict. In 1989, the Chinese government pursued opposing strategies in the two games, but there was no interest conflict between the demonstra- tors and the international community. Putnam explains the consistency between the two games by a concept, "win-sets," and by recognizing a difference between involun- tary and voluntary defection. I explain the consistency by recognizing a difference between suboptimal and optimal strategies.



Game with Game with
STRATEGY Demonstrators International Community
Threaten and suppress .................... Government wins Government loses
Do not threaten or suppress ........... Government loses Government wins
Threaten but do not suppress ........ Government wins if Government does not lose
  demonstrators back  
  down; loses if dem-  
  onstrators resist  

national level, it tried to force the student movement to back down in order to keep the core of the Communist government system intact. At the international level, it tried to avoid a poor record on human rights by avoiding military intervention.

According to Putnam (1988), the unusual complexity of a two-level game is that a player's rational moves in one game may be irrational in another game. Due to the unusual complexity of a two-level game, the Chinese government faced a dilemma in 1989 that is outlined in table 2.

If the government is only concerned about losing political power, its best strategy should be "threaten and suppress." But it did not choose this strategy because it perceived that a military crackdown would result in economic sanctions by other nations. It decided to avoid these sanctions because it was engaged in economic reform, and in 1989 it urgently needed foreign investment. If it was only concerned about economic development, its best strategy would be "do not threaten or suppress." But any tolerance of the movement would result in a loss of power for the Communist Party. This was also an adverse consequence that the government tried to avoid. Because of this dilemma it decided not to disclose its preference to use force, even though it had strong intentions to suppress the movement. This resulted in a game with incomplete information during the first round (see rows 1 and 2 of table 2).

Putnam stated that, while there is the unusual complexity of a two- level game, "there are powerful incentives for consistency between the two games7' (1988, p. 434). Where do these incentives originate? How can consistency be achieved? As mentioned before, in the two-level game a given action for one player is simultaneously a move in two different games, and the player does not want to lose either game. Therefore, he must balance his interests by maximizing the sum of his payoffs in the two games.


Game with International
Government's Strategy Set Game with Demonstrators Community
Optimal .........................Threaten and suppress Do not threaten or suppress
Suboptimal ................... Threaten but do not suppress Threaten but do not suppress

In 1989, the Chinese government had one set of strategies for the dem- onstrators, and another for other nations. Each set is composed of optimal strategies and suboptimal strategies, which are illustrated in table 3.

Facing a dilemma after the emergence of the 1989 student movement, the Chinese government's only choice was to abandon the optimal strate- gies in either game and to follow the suboptimal strategies that might mitigate the contradiction between the two games. As illustrated in the third row of table 2, there are two possible outcomes when the government chooses the suboptimal strategies. First, while the government avoids a poor record on human rights, it will win in the game with the demonstra- tors if they back down. The second possible outcome is that, although the government does not lose in the international game, it will lose in the game with the demonstrators if they resist. It is very obvious that the first outcome is much better than not only the second one but the ones shown in the first two rows of table 2. Therefore, the government must choose the suboptimal strategies if it expects to maximize its utility in the two games.

In short, the two-level game presents the government with a dilemma because it may lose either political power or foreign investment. To max- imize the sum of its utility in the two games, it must not disclose its prefer- ences in either game, and its only options are the suboptimal strategies.


As mentioned before, the 1989 movement is a repeated game in which the four-step game is iterated three times. In the second round, the demon- strators adopted a new strategy. Beginning on May 13, more than 300 students staged a hunger strike at Tiananmen Square, and by May 16, almost 3,000 students were involved. They demanded a meeting with top party leaders and a fair reappraisal of the student movement. On May 20, the government responded by declaring martial law and deploying thousands of troops with tanks around Beijing. While the demonstrators still did not know the government's preferences for the use of force, the hunger strike stopped. Still, the demonstrators did not back down, and about one million people protested against martial law on May 20 and

21. Local residents in Beijing tried to stop the tanks with barricades and with their own bodies. The Chinese government chose not to use force for the second time.

It is not difficult to explain the government's strategies in the second round by a framework of a two-level game. It still chose the suboptimal strategies: to show force, to conceal its preferences as private information, and to refrain from using force. But it is difficult to explain the demonstra- tors' actions in the second round. If they were anxious about their confron- tation with the police on April 27, how could they lie fearlessly in front of tanks on May 201 Why did thousands of tanks fail to deter the unarmed demonstrators? The first section of this article specified two conditions under which the demonstrators would resist the threat: first, they must believe that the chance is 50-50 or less that the government will use force; second, their expected gain is equal to or greater than their expected loss. Are there any changes in their beliefs, their expected gain and loss, in the second round? What are the dynamics in the repeated game?

The intertemporal dependency of strategy sets is an important concept in answering these questions as well as being a key factor in the repeated game. This term means that "the choices made by the actors in period t affect their set of feasible choices in a future time period t + t', where t' > 07' (Tirole 1988, p. 206). This section will show how the government's suboptimal strategies in the first round affect the demonstrators' choice in the second round, and the next section will assess how the government's options in the third round become a function of the demonstrators' actions in the second round. Here, the study of the dynamics in the repeated game will focus on the changes in the demonstrators7 beliefs and their expected gains and losses in the second round.

A Decrease in the Demonstrators' Beliefs

When the government concealed its preferences as private information, the demonstrators developed beliefs about them. These beliefs developed from a learning process in which they drew inferences and formed beliefs based on the government's statements and actions. In the repeated game, the demonstrators also modified their beliefs in each round.

There are three variables in this learning process: prior beliefs, new information, and posterior beliefs. First, the demonstrators have prior be- liefs in the beginning of each round. In 1989, their prior belief in the first round was that there was a 50% chance that the government would use force to suppress their movement. The second variable is new informa- tion. The government's statements and actions in each round provide new information that the demonstrators use to assess the government's prefer- ences. The third variable is posterior beliefs. After receiving new informa- tion, the demonstrators always revise their prior beliefs and develop poste- rior beliefs. Posterior beliefs in the first round become prior beliefs in the second round, and so on.

Bayes's rule, a consequence of the axioms of probability theory, de- scribes how posterior beliefs are based on prior beliefs and new informa- tion. According to Bayes's rule,

p(H) = probability (the hypothesis H is true)
P(-H) = probability (the hypothesis H is false)
P(D1H) = probability (the data would be observed if the

hypothesis H were true) P(DJ-H) = probability (the data would be observed if the hypothesis H were false) P(H1D) = probability (the hypothesis H is true conditional on having observed new data D)

More specifically, in the main model (fig. 2) the hypothesis H is that the government is tough, and the data D is that the government shows force but does not use it. Therefore,

p(H) = probability (the government is tough) P(-H) = probability (the government is weak) P(D1H) = probability (the government shows force but does not

use it I the government is tough) P(D1-H) = probability (the government shows force but does not use it I the government is weak) P(H1D) = probability (the government is tough I the government shows force but does not use it).

From (5),

In (6), the effect on posterior beliefs of prior beliefs and new information is much easier to see than the effect shown in (5).

On the left side of (6), P(HID)IP(-HID) is the posterior odds that the


Round Prior Odds Likelihood Ratio Posterior Odds

hypothesis H is true, conditional on having observed the data D. On the right side of (6), P(H)IP(-H) is the prior odds that the hypothesis H is true, and P(DIH)IP(DI-H) is the likelihood ratio that the data D would be observed if H were true rather than false. The posterior odds are equal to multiplying the prior odds and the likelihood ratio.

In 1989, the demonstrators' prior odds changed in every round, but the likelihood ratio was a constant because the government repeatedly played the suboptimal strategies in the first and second rounds, and its words and deeds that the demonstrators observed in the different rounds were the same. The likelihood ratio, P(DIH)IP(DI-H) < 1 because the proba- bility that D (the government showed force but did not use it) would be observed if the government were tough was always smaller than the prob- ability that the data would be observed if the government were weak.

According to (6), in the first round, P(H) = P(-H) = 50% (i.e., the students believed that there was a 50-50 chance for the government to suppress by force), then P(H)IP(-H) = 1. The likelihood was P(D1H)I P(D1-H). Therefore, the demonstrators7 posterior odds were equal to P(DIH)IP(DI-H), which became their prior odds in the second round. While the likelihood was a constant, the demonstrators' posterior odds in the second round were equal to [P(DIH)IP(DI-H)12. Table 4 summarizes this discussion.

Equation (7) shows that the demonstrators' beliefs about the probability of governmental suppression by force decrease in the second round of the repeated game, and table 4 contains evidence that there are two reasons for the decrease. First, the likelihood ratio (new information) is constant and always smaller than "1." Second, the posterior odds in every round are smaller than the prior odds.




Probability of Substantive Gain Success Expected Gain Round (c'> 0) (0 iP < 1) (G > 0)

1 ......................... G 1' P1 = 50% G1 = Gl'x P1
2 ......................... G2'>G1' P2 > P1 G2 = G2' X P2


G2 > G1

An Increase in the Demonstrators7 Expected Gain

As mentioned before, the demonstrators' expected gain is equal to multi- plying a substantive gain and the probability of the success of their re- sisting. Table 5 shows how the expected gain changes in the repeated game.

In table 5, P2 >P1 because the demonstrators7 beliefs about the proba- bility of governmental suppression by force decrease, which means that the demonstrators believe that the probability of the success of their resis- tance increases.

As a consequence of the government's suboptimal strategies, G2' >Gl'. In 1989, GI' was the students demands in the first round that were the legitimation of the first unofficial student organization. After the military police withdrew, the government was forced to negotiate with the unoffi- cial student organization for the first time because no unofficial organiza- tions were allowed to exist after the Communist party took control of China in 1949. In the second round, intellectuals, factory workers, private businessmen, and government officials participated in the movement. Substantive gain in the second round is greater than that in the first round because all of the demonstrators asked to have the political rights to estab- lish their own unofficial organizations. The government, anxious about losing political power, threatened the movement by imposing martial law, which was much harsher than the first threat. But again the government backed down.

In sum, the 1989 movement occurred because the demonstrators tried to change the allocation of political rights in China. The movement's de- velopment was a process in which power and rights were reallocated. In each round, the government lost power when it backed down, and the demonstrators demanded more after they had obtained some political rights, which increased their substantive gain.




Probability of Substantive Loss Failure Expected Loss Round (-L'< 0) (O<P<l) (-L< 0)

1 ......................... -L1' Pl = 50% -Ll = -L1' X P1
2 ......................... -L2' < -L1' P2 < P1 -L2 = -L2' X P2


-L2 = -L1

Constant Value of the Demonstrators7 Expected Loss

Table 6 shows how the demonstrators' expected loss changes in the re- peated game. Numbers 1 and 2 denote the number of the round, -Lf is a substantive loss, and p is the probability of failure of the demonstrators7 resistance. We see that P2 <P1 because the demonstrators' beliefs about the probability of governmental suppression by force decrease, which means that the probability of the failure of the demonstrators' resistance decreases. If the substantive loss is constant, the value of the expected loss in the number axis is moving to the right toward 0when P2 < PI in the repeated game.

In 1989, the demonstrators7 substantive loss increases in the repeated game, that is, -L2' < -Lll because the government's threats escalated step by step. In the first round, the government threatened the movement by erecting seven police blockade lines. The second threat was much harsher than the first, when thousands of troops with tanks were deployed around Beijing. This indicates that the harsher the threat, the greater the demonstrators7 substantive loss. If the probability of the failure of the demonstrators' resisting is constant, the value of the expected loss in the number axis is moving away from 0to the left when -L2' < -Llf. In the repeated game, the demonstrators' expected loss is almost constant because their substantive loss increases, while the probability of the failure of their resistance decreases.

In sum, this section shows the dynamics of the repeated game. After the government played the suboptimal strategies in the first round, the demonstrators7 beliefs about the probability that the government would use force decreased, and their expected gain increased in the second round. Due to these dynamics the two conditions under which the demonstrators resist the threat still existed in the second round. The demonstrators be- lieved that the chance for the government to use force was 50% in the first round, but less than this in the second round. While their expected gain exceeded their expected loss in both rounds, the difference between the gain and the loss in the second round was greater than that in the first round. Therefore, the demonstrators resisted again in the second round, even though the government's threat was much harsher than that in the first round.



According to Bayes's rule, in the third round, the demonstrators' prior

beliefs about the probability that the government would use force were

lower than they had been in the second round. Therefore, the dynamics

of the repeated game did not change. Why did the movement end in a

military crackdown?

The third round began with a hunger strike on June 2, 1989. Most of the student leaders decided, contrary to their earlier position, to pressure the government by occupying Tiananmen Square until June 20, when the standing committee of the National People's Congress was expected to convene. On June 3, the government warned that troops enforcing martial law were ready to pounce, but the demonstrators did not withdraw. When they tried to stop the troops, a tragedy occurred.

There were two significant differences in the third round: first, the gov- ernment decided "to use force"; second, it did not conceal this preference as private information because it tried to avoid a major confrontation. Why did the government's strategies change, and why did the demonstra- tors continue to resist? I would say it was because both sides were affected by "interdependent choice." In his discussion of this concept, Kreps ex- plains that "the action taken by any individual depends on the opportuni- ties that are presented to the individuals. Those opportunities, in turn, often depend on the collective actions of others" (1990, p. 5).

What were the "opportunities" presented to the government when it chose "to use force"? In the third round, hundreds of tanks and thousands of soldiers were blocked by barricades around Beijing, and the demonstra- tors started their second hunger strike at Tiananmen Square. At this stage, the government was desperate. After backing down twice, it had lost its credibility, and some of its political power was shifting to the demonstra- tors. The best indicator of this shift was that the demonstrators7 expected gain had gradually increased (as shown above). In the first round, the students simply demanded official recognition of the first unofficial stu- dent organization. In the second round, organizations for intellectuals, workers, and private businessmen were conceived. In the third round, the demonstrators questioned the legitimacy of the government, criticized some of its top leaders, and asked them to resign.

The Demonstrators

Resist Back Down







FIG.3.-A strategic form of the subgame

The possible emergence of a new "society" threatened party officials. Tsou (1992) observed that, in China, before the 1989 movement, "the party-state, through various instrumentalities, occupied most of the social spaces. Society had no institutions or organizations that spoke for it freely and authentically. One can safely come to the conclusion that civil society as such did not exist" (p. 271). In the repeated game, a new "society" was conceived and the government lost political power. In the third round, the government could either continue to lose power or reverse this trend. Since it opposed the emergence of any new "society," it rejected the subop- timal strategies and decided to use force.

The preceding argument suggests a causal relationship between the shift in'political power and the change in the government's strategies. One way to test this is to present a strategic form of the main model.

In figure 3 ,after the government threatened the movement and showed force, each side had two choices. The demonstrators could either resist or back down, and the government could play either the suboptimal or the optimal strategies. If it played suboptimal, it would not use force; other- wise, it would use force. Note that Y2, X2, Y3, X3, Y4 and X4 are the same payoffs as those in figure 2. Thus, Y2' is the government's payoff if it uses force when the demonstrators back down; U(Y2) > U(Y2') > U(Y3), and U(Y2) > U(Y2') > U(Y4). Here, m is the probability that the government plays the suboptimal strategies in the repeated game, and 1 -m is the probability that it plays the optimal strategies.

In figure 3, the demonstrators' preferences are common knowledge, that is, U(X3) > U(X2) > U(X4). The government's preferences are private information, but it has been known that for the tough government U(Y2) > U(Y2') > U(Y4) > U(Y3), and for the weak government U(Y2) > U(Y2') > U(Y3) > U(Y4). There is no pure strategy Nash equilibrium in figure

3. In the mixed strategies Nash equilibrium, and

In (8), in the repeated game, the probability m that the government chooses the suboptimal strategies is determined by the demonstrators' payoffs X2, X3, and X4. Taking a comparative-static approach (Chiang 1984), the effect of X2, X3, and X4 on m could be examined.

The results from comparative-static analysis are summarized in table 7.

In table 7, X2 is the demonstrators' payoff when they back down, X2 = -F. And X3 is their payoff when they resist and the government does not use force, X3 = H + G. Their payoff when they do resist and the government uses force is X4 (X4 = -L + H).

It has been demonstrated that the dynamics in the 1989 movement were G1 < G2 < G3, and -L1 = -L2 = -L3. The honor bestowed on the demonstrators in the nth round is Hn (n = 1, 2, 3). When they resist, they run a risk because of the expected loss. The greater the expected loss, the greater the risk, and the greater the honor. If the expected loss is constant, that is, if -L1 = -L2 = -L3, then H1 = H2 = H3. Therefore, X3 (X3 = H + G) is increasing, and X4 (X4 = -L + H) is constant in the repeated game. What about X2? Here, X2 = -F, and -F is a general cost for the demonstrators when they lose face by backing down. The greater the expected loss, the smaller the cost of losing face. If the expected loss is


Independent Variable Dependent Variable


IN THE PROBABILITY Independent Variable Dependent Variable

constant, -F will also be constant. In 1989, the effect of the demonstra- tors' payoffs X2, X3, and X4 on m is summarized in table 8.

In table 8, an increase in the demonstrators' expected gain G is a condi- tion under which the probability that the government plays the subopti- mal strategies decreases. This is because X3 = H + G, and H is constant. The causal relationship between the shift in political power and the change in the government's strategies is confirmed in table 8. Although the government tried to maximize the sum of its utility in a two-level game in the first two rounds, it lost its game with the international community in the third round. As a result of the demonstrators' gains in political power, the government chose "to use force."

To avoid a major confrontation, the government warned the demon- strators of its plan to use force. The first warning was issued at about

2:00 P.M. on June 3, 1989, at an intersection near Tiananmen Square. More than 1,000 soldiers and armed police attacked the crowds, firing tear gas and clubbing any opposition. This was the first time the govern- ment had acted with force to suppress the demonstrators since the emer- gence of the movement. The second warning was sent about five hours later. Government-controlled radio and television stations repeatedly warned that, if the people entered the streets, "they should bear responsi- bility for their own fates." The government also sent out vehicles to broad- cast this warning. This was the first time the government had issued a serious warning by official broadcast since the emergence of the move- ment.

News that the government was planning to use force spread quickly, and the demonstrators clearly received the message. It is paradoxical that when they perceived that a crackdown was least likely, the government was clearly signaling its plan to use force.

How would the demonstrators be expected to respond? Most of them did not heed the warning, primarily because not only had the government backed down twice, but had also refrained from using force to suppress popular demonstrations since Liberation. Most of the demonstrators be- lieved that the people's army would never harm the people. Some scholars

who studied the 1989 movement noticed a difference between the govern-

ment's message and the demonstrators' beliefs. Mu and Thomson argue

that "despite the government warning, most people still did not believe

that the people's army would really fire on the people" (1989, p. 81). Tsou

stated: "At that time, there was a widespread belief that the People's Lib-

eration Army would not turn its guns on the people. It is impossible to

know who first began promoting that opinion and how it became so

widely accepted. But it is true that many students and Beijing residents

believed that the army was 'the people's army' and would not carry out

any orders to harm the people" (1992, p. 313).

There was an information gap, which might be defined as the difference between the government's message and the demonstrators' beliefs. How did this gap originate? Did it reflect the demonstrators' subjective wishes or misperceptions? Here misperceptions are defined as "the distorted be- liefs and unjustified inferences produced by psychological biases" (Fearon 1992, p. 101).

The information gap between the student movement and the Chinese government resulted from a learning process in which the demonstrators formed new beliefs based on their prior beliefs and on new information, according to Bayes's rule. In order to show how this happened, let

P(H) = probability (the government is tough) X = probability (the government shows force but does not use it I the government is tough) 1 -X = probability (the government shows force but does not use it I the government is weak) Y = probability (the government not only shows force but uses it I the government is weak) 1 -Y = probability (the government not only shows force but uses it I the government is tough)

In the first two rounds, the likelihood ratio (new information) P(D(H)I P(D(-H) = Xl(1 -X) and (1 -X) > X. In the third round, P(D1H)I P(D1-H) = (1 -Y)IY and (1 -Y) > Y.

According to Bayes's rule, the demonstrators' prior beliefs in the third round were equal to their posterior beliefs in the second round, which were [P(DIH)IP(DI-H)I2 in table 4, and can be expressed as [X/(1 -X)]'. The likelihood in the third round, P(D1H) IP(D1-H), can be expressed as (1 -Y)/Y. Then after the government signaled its intentions, the demon- strators' posterior beliefs would be

In (1 I), X = Y, because in principle the probability that the tough gov- ernment does not use force is very close to the probability that the weak government uses force. In (ll), (1 -Y)/Y > 1, which means that the probability of governmental suppression by force is greater than SO%, based on the message sent by the government. But the posterior beliefs X/(1 -X) are still smaller than 1, which meant that the demonstrators continued to believe that the probability of governmental suppression by force was less than 50%. This reflects their prior beliefs. According to (1 1), the demonstrators' beliefs were not subjective wishes or misperceptions. Let Z denote the information gap, then

Thus, Z resulted from the process of disclosing and acquiring private information in the repeated game. The government clearly signaled its intention to use force. The demonstrators received and revised the mes- sage, based on their prior beliefs. When the government began to use force, the demonstrators still resisted because they perceived that the probability of governmental suppression by force was less than SO%, and their expected gain was much greater than their expected loss. In this game, the unintended outcome of the movement was a perfect Bayesian equilibrium.

Following the government's broadcast on June 3, hundreds of thou- sands of demonstrators, sensing that the people's army would never hurt the people, appeared on Changan Boulevard to block the troops. At about

10:30 P.M. armed with tanks, assault rifles, and machine guns, the troops arrived at West Changan Boulevard. When the demonstrators confronted them, a military crackdown occurred, and the confrontation was costly for both sides. Many demonstrators died defending their ideal, economic sanctions from other nations ensued, and more than 40,000 intellectuals and students left China. For both sides, the cost was predictable before the crackdown, therefore, both sides wanted very much to avoid it, but the information gap between the government and the demonstrators led to an unintended outcome, even when both sides behaved rationally. The cost of this outcome was the price of proving and acquiring private infor- mation.


By applying game theory to the study of the 1989 Chinese student move- ment's development and outcome, this article explains why threats made by the Chinese government, backed by a strong military, could not deter the demonstrators in 1989, and why the outcome was unexpected. The interactive framework-who does what when and with what informa- tion-is a principal focus of this study, and information is the most impor- tant element in this framework. The demonstrators' actions, which were based on incomplete information, were different from those based on more complete information. The information was incomplete because the gov- ernment concealed its preferences as private information in a two-level game. Intertemporal dependency of strategy sets was another important element in the framework. Decisions made by the Chinese government at the beginning of the movement affected its strategic choices in the final round; the demonstrators' expectations of the government's strategies, firmed in the first round, resulted in the information gap in the third round when the message sent by the government failed to influence the demon- strators' beliefs. The unintended outcome of the movement resulted from rational interaction between the two sides. The cost of the unintended outcome was the price of disclosing and acquiring the government's pri- vate information that the Communist Party did not want to relinquish any political power, even though there had been a successful economic reform in China.


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