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A Model of Asymmetric Information Due to Government Change

GUO Gang
December 20, 1999

Abstract

Incomplete information is omnipresent in international relations. A common source of such incomplete information is the change of government in one or more countries. This paper attempts to provide some insight into the international interaction under such circumstances. First, a specific case - that of the Strategic Arms Limitation Talks (SALT II) between the United States and the Soviet Union in early 1977, when Jimmy Carter had just became the US president, was considered. I constructed a game theoretic model of incomplete information for this negotiation. In this game, the Soviet Union is uncertain about the new US administration's "toughness". I argued that there exists an "ambiguous" outcome that the Soviet Union has different utilities for, depending on the "type" of the US administration that she believes she is dealing with. Then, as a generalization, I argued that such "ambiguous" outcomes, that is, outcomes for which one player has different utilities depending on its opponents' types, often exist in games with asymmetric information between nations. In the last part I illustrated this generalized model by examining another case of international negotiation under asymmetric information - that between the Soviet Union and the West on German unification in early 1954, when Khrushchev just came to power.

Introduction

International negotiations are rarely conducted under complete or symmetric information. States always keep certain information secret, and cases of deliberate misrepresentation also abound in foreign relations. However, one of the most common sources of incomplete information in the interaction between nations has been the change of government. In a democracy, major shifts in policy stand normally come about when a new administration takes office. In a non-democracy, although generally speaking it's less costly for a regime to make major policy changes due to the lack of a large constituency, important deviations from established policy lines still have to await a new generation of leaders. Especially in long-standing negotiations between states on issues that would recur repeatedly in the future, the coming onto stage of a new government, whether in a democracy or a non-democracy, can have dramatic effects. As a consequence, in such occasions, the country or countries that have to deal with a new government are often uncertain about their counterpart, whereas their own preferences and characteristics are already common knowledge after the previous rounds of negotiations. The situation under such asymmetric incomplete information is certainly worth looking at. In practice countries look on with great eagerness when pre-election campaigns in a democracy send out various signals about the policy stand of a prospective government, or during black-box power struggles after the demise of the previous dictatorship in a non-democracy, in particular when these happen in a country they have to repeatedly deal with down the road. After the leadership transition is already settled, there is still a short period of time when the real political profile of the new administration is not clear. Therefore, in this paper I shall try to formalize this kind of situation, using the Harsanyi (1967 - 68) transformation of incomplete information into imperfect information. The game model will be constructed in light of the Strategic Arms Limitation Talks (SALT II) between the United States and the Soviet Union in early 1977, when Jimmy Carter had just became the US president, but I shall show later that this model is actually general enough to be applied to other situations of international negotiations with asymmetric incomplete information.

Historical Background

Although the idea of achieving mutual restraint of strategic nuclear arsenals through negotiations between the United States and the Soviet Union can be traced to a series of U.S. and Soviet gestures in the wake of the Cuban missile crisis (Labrie 1979:3), real negotiations started much later than that. The first round of the Strategic Arms Limitation Talks, SALT I, lasted two and a half years (from November 17, 1969 to May 26, 1972, when the Treaty on Anti-Ballistic Missile Systems and Protocol to the Interim Agreement were signed in Moscow) and consisted of seven negotiating sessions alternating between Helsinki and Vienna. In November 1972, U.S. and Soviet SALT negotiators reconvened in Geneva to begin a new round of talks aimed at achieving a comprehensive limit on strategic offensive arms. Two years later, President Ford and General Secretary Brezhnev reaffirmed, at the Vladivostok summit, "the intention to conclude a new agreement on the limitation of strategic offensive arms, to last through 1985". The Joint U.S.-Soviet Statement also includes the following stipulation:

"Agreement was reached that further negotiations will be based on the following provisions.

...

3. Based on the principle of equality and equal security, the new agreement will include the following limitations:

a. Both sides will be entitled to have a certain agreed aggregate number of strategic delivery vehicles;"

The mutual understanding achieved in Vladivostok set the aggregate numerical ceiling of the above category "a" at 2400. Also, according to U.S. Secretary of State Kissinger at the press conference in Vladivostok, bombers are included under the above-mentioned category "a" (U.S. Department of State 1974:898). At this time, it seemed very likely that a U.S.-Soviet SALT II agreement could be reached very soon. However, around that time and later, innovations in military technology presented two issues that became highly contentious, and the negotiations gradually ground to a halt in early 1976. These two issues are on the Soviet Backfire bombers and on the American cruise missiles, and can be explained in a much simplified way as the following. The U.S. wanted, and the Soviet Union refused, to include Backfire, a new kind of Soviet medium-range bombers that have strategic potential, in the 2400 aggregate ceiling agreed on at Vladivostok. On the other hand, the Soviet Union wanted, and the U.S. refused, to include the U.S. cruise missiles, a kind of practically "pilotless aircraft" still under development that can be launched from various bases, in the tight restraints on strategic delivery vehicles. Despite these difficulties, in early 1976, U.S. Secretary of State Kissinger's last attempt in Moscow produced "considerable progress" when the Soviet leaders showed encouraging signs of interest in the latest U.S. proposal, which would retain the Vladivostok 2400 aggregate ceiling, exclude Backfire from the ceiling, and put limitations on U.S. cruise missiles. However, when the U.S. Joint Chiefs of Staff made clear their opposition to any SALT agreement along this line, President Ford gave up and concluded that they "could not be able to achieve a SALT agreement in 1976", largely due to domestic political considerations. Despite these difficulties, it is still safe to say that a SALT treaty was "ninety percent complete" at that time, as the SALT delegations from both countries continued to work on the less contentious part of the draft treaty text throughout 1976 in Geneva, and as late as President Ford's last State of the Union address to Congress on January 12, 1977, he still believed that a SALT agreement based on the Vladivostok accord was "well within reach this year". A week later, Jimmy Carter was inaugurated into office as the new President of the United States.

Asymmetric information

When President Carter took office, the Soviet Union had no clear idea of what the new U.S. administration's preferences on the SALT II agreement would be, although in both the United States and the Soviet Union there were genuine belief that the SALT negotiations would be started again under the new president. After eight years of political détente policy carried out in a generally consistent way by Republican President Nixon, Ford, and Secretary Kissinger, the inauguration of Carter signified the first real transition in leadership since 1969 (Garthoff 1994:623). From the Soviet Union's perspective, their uncertainty was about whether the new administration's preference profile on the long-standing issue of SALT II negotiations would be a more or less continuation of the Nixon-Ford-Kissinger political détente or a generally toughened stand that had just emerged in American domestic political scene in the previous years. Carter's public remarks on the issue of SALT II negotiations before and immediately after he took office sent out at best mixed, if not confusing, signals about his position on that issue. At some occasions, it seemed that he would take a tough and aggressive position in limiting the nuclear arsenal of both the United States and the Soviet Union and would demand that the Soviet Union make more substantial reductions in her strategic capacity. During the election campaign of 1976, he criticized president Ford in an interview and said that "the policy of détente has given up too much to the Russians and gotten too little in return", and in another interview he said that the United States should be "tougher" in pursuing détente (Garthoff 1994:624). In his inauguration address on January 20, 1977, Carter announced to the world his ambitious "ultimate goal - the elimination of all nuclear weapons from this earth". As Carter's Secretary of State Cyrus Vance observed, the "Soviets, always edgy when confronted by a new American administration, were uneasy about Carter's well-publicized desire for sharp reductions in nuclear weapons and uncertain about his intentions regarding détente." (Vance 1983:46) In other occasions, though, Carter would make speeches as though he would continue on the path of political détente and would conduct SALT II negotiations in alignment with the approach developed by the previous administration, based on the Vladivostok accord. Brzezinski observed that when Carter "came to the White House ... he firmly supported the concept of détente" (Brzezinski 1983:147). In a personal letter to the Soviet leader Brezhnev sent a week after the presidential inauguration, Carter stressed that "it is my goal to improve relations with the Soviet Union" and that the first of the "three areas where progress can be made toward this goal" was the rapid conclusion of SALT (Brzezinski 1983:152). On February 8, 1977, in reply to questions asked at a news conference in Washington, D.C., president Carter announced that "I would be willing to go ahead with the Soviet Union, conclude a quick agreement, if they think it advisable, and omit the Backfire bomber and the cruise missile from the negotiations at this stage." (Department of State 1983:154) Later he stated clearly that "Now, I believe in détente with the Soviet Union. To me, it means progress toward peace" (Garthoff 1994:624). As Carter himself remembers, when taking office he thought he "would follow the path that had been established by [his] predecessors." (Carter 1982:215) So, at the time the new Carter administration made initial proposals to the Soviet Union on the SALT negotiations, the Soviet leaders were uncertain about the preference profile on the U.S. side concerning the SALT negotiations.

In contrast to the Soviet Union's uncertainty about the new U.S. administration, there was much less uncertainty on the U.S. side about the Soviet leaders. There had been only one leadership circle since the removal of Khrushchev in the mid-1960's - that around General Secretary Brezhnev. What is more important, after years of negotiation with the Brezhnev administration conducted under president Nixon, Ford and Secretary Kissinger, the Soviet preference on strategic arms limitation was made very clear. Various U.S. proposals had been tried on the Soviets, and the Soviet Union's replies and reactions had been consistent in terms of basic guidelines. As Carter later recalled in his memoir: "it is much easier to negotiate a SALT treaty in a totalitarian society with a relatively consistent policy, where the voices of news media and opposition political forces are either stilled or heard only in a closed room. The Politburo "can make a decision, and the nation's propaganda apparatus can then proclaim the 'unanimously agreed upon' new policy essential to self-defense" (Carter 1982:213). Therefore we can regard the Soviet stand on SALT II as common knowledge to both sides when the U.S.-Soviet negotiations started in early 1977.

Preference Orderings

1 Possible U.S. preferences in Soviet Perspective

From the Soviet point of view, before real interactions in the negotiations made things clearer, the new U.S. government could be either "tough" or "détente". If the new administration was tough, it would most want sharp and comprehensive reductions on the Soviet nuclear arsenal, in the name of reaching the "ultimate goal of elimination of all nuclear weapons". As Brzezinski recalled, at the first meeting of the Special Coordination Committee on SALT on February 3, 1977, the "President underlined his commitment to deep cuts, a position with which all the principals were now familiar" (Brzezinski 1983:157). Vance also hinted that "others in the administration, calculating that our long-term arms control and security objectives justified the risks of pressing at once for deep reductions and qualitative restraints on weapons modernization, argued for the comprehensive deep-cut approach" (Vance 1983:48). Other than this aggressive reduction, a tough U.S. administration should have no preference for a SALT agreement to the then deadlock. Therefore, in contrast to the détente approach, a tough administration would not regard an early agreement on nuclear disarmament as a desirable outcome that is conducive to creating a better political atmosphere between the United States and the Soviet Union. As Garthoff observed, Carter did not put improvement of relations with the Soviet Union in the forefront of his foreign policy agenda (Garthoff 1994:625). So in the Soviet perspective, a tough U.S. administration would prefer the impasse to any SALT agreement under the framework of the Vladivostok accord.

On the other hand, if the new administration was pro-détente, it would most want a quick and limited SALT agreement. In this sense, a "détente" U.S. administration would have a similar preference structure to that of the Nixon-Ford-Kissinger Administration. The previous administration believed that "the more we try to cram into a single agreement, the longer it will take to negotiate; and the more drawn out the negotiations, the greater the risks of exacerbating the very competition we seek to avoid" (Iklé 1975:325). At the time of the SALT negotiations in early 1977, this would be translated into a preference for a SALT II agreement without the contentious Backfire and cruise missile issues, as president Carter told Anatoly Dobrynin, the Soviet Ambassador, in February, before the negotiation started.

For an administration that takes the détente approach to the SALT negotiations, besides the most preferred outcome of a quick agreement, it should also prefer an agreement that would place limit on both Backfire bombers and cruise missiles under the aggregate ceiling of the Vladivostok accord, to the current stalemate. Also, such administration would prefer a comprehensive deep cut in nuclear arms to no agreement at all. As Vance explained, "I did not disagree in principle with those who favored the comprehensive approach. In the long term, this was clearly where we had to go. ... It might be that the Soviets ... would be willing to take a bold step. We could not know unless we tried. And success would mean a dramatic breakthrough in turning around the arms race" (Vance 1983:49). So it is clear that for a pro-détente administration, a comprehensive deep-cut SALT treaty, if realized, would be a preferred outcome to the status quo. Even Kissinger believed that "the deep cut proposal we had put together on SALT had a good chance to be accepted by the Soviets if they are sincere and want to make progress on disarmament" (Carter 1982:219).

2 The Soviet preference orderings and the "ambiguous" outcome

As had been made clear by the interaction between the United States and the Soviet Union during SALT negotiations since 1972, the Soviets would most of all want to conclude an agreement based on their version of the understanding reached at Vladivostok. The basic points of this outcome are, the numerical aggregate ceiling of 2400 strategic delivery vehicles would be implemented, the Soviet Backfire bombers would be excluded from such ceiling, and limitations would be placed on the testing and deployment of U.S. cruise missiles. The least preferred outcome for the Soviet Union is, of course, the comprehensive deep cut in nuclear arsenal that would require substantial reduction on the Soviet side.

The Soviet preference on the above two outcomes are clear, while a third kind of SALT agreement would have ambiguous meaning to the Soviet Union, depending on the "type" of the new U.S. administration that the Soviets had to deal with for the next four years or even eight years. And that is the agreement with neither Backfire nor cruise missiles included in the aggregate limitation. The Soviet Union was uncertain about what kind of a U.S. administration she had to deal with in the future, and this would affect its own preference over the agreement that had "ambiguous" meanings. If the new U.S. administration would take the détente path, then a SALT agreement excluding both Backfire bombers and cruise missiles would be conducive to generating a general political atmosphere of détente between the Soviet Unions and the United States. Under this circumstances, such an outcome would be preferable to the then status quo of no agreement at all. If the new U.S. administration was tough, on the other hand, a SALT agreement that failed to limit U.S. cruise missiles would pose problems for the Soviet Union down the road, from the Soviet perspective. In this scenario, the tough U.S. administration would value competition over cooperation with the Soviet Union, and the generally worsened political setting between the two countries would make such a SALT agreement undesirable to the Soviets. As Brzezinski said, he would see in such a SALT agreement "an opportunity to halt or reduce the momentum of the Soviet military buildup" (Brzezinski 1983:146). If the Soviet Union was to deal with such a U.S. administration, then she would rather remain uncommitted under the current deadlock than being chained by such an agreement in the coming competition and confrontation with a tough U.S. administration in the next four or possibly even eight years. Therefore, in this situation of asymmetric incomplete information, the Soviet Union would have different payoffs for this same outcome when dealing with different kinds of U.S. administration, even if the agreement reached by the U.S. and the Soviet Union might be the same and even if the agreement was carried out to the letter.

The Structure of the Game Model

Now I will reconstruct the first round of SALT negotiations in March 1977 between the Soviet Union and the United States as a game of incomplete information. First of all, I shall specify the sequence of moves and sets of possible actions at each node for each player: the United States and the Soviet Union.

1 Sequence of moves and sets of actions

In this round, the U.S. administration moves before the Soviet Union. It offers to the Soviet Union three possible proposals on the SALT agreement. The first, which I shall call V (Vladivostok) in this paper for simplicity, is a proposal based on the Vladivostok framework, with three essential features: the aggregate number of strategic delivery vehicles was limited to 2400, as agreed on in Vladivostok; the inclusion but in effect exemption of the Backfire bombers from such ceilings; the limitation on U.S. cruise missiles. This is the proposal that is most accommodating and favorable to the Soviet side, and is also favored by the State Department and the Arms Control and Disarmament Agency, according to Brzezinski (1983:158).

The second, which I shall call Vp (Vladivostok plus) in this paper for simplicity, is the comprehensive deep-cut proposal, again with three essential features: the Vladivostok aggregate ceiling is lowered to around or even below 2000; exemption of Backfire bombers in return for Soviet assurance not to increase their strategic potentials; partial limitation on U.S. cruise missiles. According to Brzezinski (1983:158), this action was most favored by the Defense Department and the Joint Chiefs of Staff, although apparently it's the least favored by the Soviet side.

The third, which I shall call Vm (Vladivostok minus) in this paper for simplicity, is the proposal that, if made agreement, would have ambiguous significance to the Soviet Union. This proposal suggests that the two sides reach a quick but limited SALT II agreement and defer the contentious issues of Backfire bombers and cruise missiles to the SALT III negotiations.

After the U.S. administration makes the move, the Soviet Union observes the U.S. action and decides whether to accept the proposal or not.

2 Incomplete information

In this round of negotiation, as above mentioned, the Soviet Union was uncertain about the new U.S. administration's payoff structure. The Soviet Union also had uncertainty over the "ambiguous" outcome, that is, the agreement that excludes Backfire bombers and cruise missiles from the Vladivostok framework. Therefore, if the new U.S. administration is tough, the strategic form of the game would be:

Soviet Union
Accept Don't Accept
"tough" type US Administration

Vladivostok minus

U2(Vm)

U1(Vm)

U2(SQ)

U1(SQ)

Vladivostok

U2(V)

U1(V)

U2(SQ)

U1(SQ)

Vladivostok plus

U2(Vp)

U1(Vp)

U2(SQ)

U1(SQ)

Whereas if the new U.S. administration will take the détente path, then the strategic form of the game would become:

Soviet Union
Accept Don't Accept
"détente" type US Administration

Vladivostok minus

U'2(Vm)

U'1(Vm)

U2(SQ)

U1(SQ)

Vladivostok

U2(V)

U'1(V)

U2(SQ)

U1(SQ)

Vladivostok plus

U2(Vp)

U'1(Vp)

U2(SQ)

U1(SQ)

Following the common practice of transforming games of incomplete information into games of imperfect information, devised by Harsanyi (1967 - 1968), I will let Nature moves at the initial node. Nature chooses whether the new U.S. administration is of the "tough" type or of the "détente" type. This initial move is observed by the U.S., but not by the Soviet Union, who assigns a prior probability p to Nature's choice of a "tough" type U.S. administration. At the second stage of the game, the United States chooses from one of three actions described above: Vm, V, and Vp. The Soviet Union observes the U.S. action, but doesn't know which type of U.S. administration she is dealing with, hence the three information sets in the extensive form game presented in figure 1 in the following page.

As shown in the extensive form game, at each of these information sets, the Soviet Union chooses whether to accept the U.S. proposal or not. If the Soviet Union doesn't accept the U.S. proposal, then the outcome is the status quo, which I assume to have zero payoff for both players. If the Soviet Union accepts the Vm proposal, the outcome will be the agreement Vm, for which the "tough" type and the "détente" type U.S. administration have payoffs of M1 and M1' respectively. For the Soviet part, if she is facing the "tough" type, then her payoff for the outcome Vm will be M2, while if she faces the "détente" type, then her payoff will be M2'. According to my previous discussion of the U.S. and Soviet preference orderings, M1 < 0 < M1' and M2 < 0 < M2'.

If the Soviet Union accepts the V proposal, the outcome will be the agreement V, for which the "tough" type U.S. administration, the "détente" type administration, and the Soviet Union have payoffs of V1, V1' and V2, respectively. Again, according to my previous discussion of preference orderings, V1 < 0 < V1' and V2 > M2'> 0 > M2.

If the Soviet Union accepts the Vp proposal, the outcome will be the agreement Vp, for which the "tough" type U.S. administration, the "détente" type administration, and the Soviet Union have payoffs of P1, P1' and P2, respectively. Again, according to my previous discussion of preference orderings, both P1 and P1'are greater than 0, and both P2 and P2'are smaller than 0. The overall preference orderings for both players are presented in the following table 1.

Figure 1: the game theoretic model of early 1977 SALT II negotiation in extensive form

Table 1: the U.S. and the Soviet payoff ordering for the game model

Payoff ordering for both players

If U.S. administration is "tough"

If U.S. administration is "détente"

U.S. payoff ordering

P1 > 0 > M1 > V1

M1' > V1'> P1' > 0

Soviet payoff ordering

V2 > 0 > M2 > P2

V2 > M2'> 0 > P2

Perfect Bayesian Equilibrium

The basic features of this game theoretic model resemble those of a signaling game, which is the simplest kind of game in which the issue of updating and perfection both arise (Fudenberg and Tirole 1991:324). A perfect Bayesian equilibrium for a signaling game is a set of strategies and beliefs such that, at any stage of the game, strategies are optimal given the beliefs, and the beliefs are obtained from equilibrium strategies and observed actions using Bayes' rule.

First of all, several strategies can be ruled out as strictly dominated strategies. The Soviet Union will never reject a U.S. proposal of V, regardless of the types of U.S. administration she is dealing with. Also the Soviet Union will never accept a U.S. proposal of Vp, regardless of the types of U.S. administration she is dealing with. Given that the Soviet Union will always accept V and always reject Vp, the "tough" type U.S. administration will never propose V, and the "détente" type administration will never propose Vp.

Second, the notations for the beliefs specified as follows. Let mm be the Soviet belief that the U.S. administration is of the "tough" type if the Soviet Union observes a U.S. proposal of Vm. Let m be the Soviet belief that the U.S. administration is of the "tough" type if the Soviet Union observes a U.S. proposal of V. Let mp be the Soviet belief that the U.S. administration is of the "tough" type if the Soviet Union observes a U.S. proposal of Vp.

After examining the payoff structure and each of the remaining possible strategy and belief profiles, I found three perfect Bayesian equilibria, all of which are separating equilibria, in which the two types of U.S. administration choose two different actions.

First, consider the following strategy profile: the "tough" type U.S. administration offers Vm, and the "détente" type offers V. The Soviet Union accepts V and doesn't accept Vp, as always. Bayesian updating would assign probability 1 to the "tough" type administration if the Soviet Union observes Vm, and so the Soviet equilibrium strategy is "don't accept if Vm".

Second, consider the following strategy profile: the "tough" type U.S. administration offers Vp, and the "détente" type offers Vm. The Soviet Union accepts V and doesn't accept Vp, as always. Bayesian updating would assign probability 1 to the "détente" type administration if the Soviet Union observes Vm, and so the Soviet equilibrium strategy is "accept if Vm".

Third, consider the following strategy profile: the "tough" type U.S. administration offers Vp, and the "détente" type offers V. The Soviet Union accepts V and doesn't accept Vp, as always. If the Soviet Union observes Vm, his belief mm is out of equilibrium path, so it can not be updated by the Bayes' rule. In this case, "accept if Vm" can't be an equilibrium strategy for the Soviet Union, because if the Soviet Union plays "accept if Vm", then the "détente" type U.S. administration would rather play Vm instead of V and get M1'> V1' So the only remaining possible equilibrium strategy for the Soviet Union is "don't accept if Vm", which would be a better response to the above U.S. strategies than "accept if Vm" for the Soviet Union if the following condition is satisfied:

Eu2(accept if Vm) < Eu2(don't accept if Vm)
M2*mm + M2'* (1 - mm) < 0 * mm + 0 * (1 - mm)
mm > M2' / (M2' - M2)

So the third perfect Bayesian equilibrium is, the "tough" type U.S. administration offers Vp, the "détente" type offers V, the Soviet Union accepts V and doesn't accept Vp or Vm, mm > M2' / (M2' - M2).

The first two perfect Bayesian equilibria each involve one type of U.S. administration offering Vm, the proposal that, if accepted, would have ambiguous outcome for the Soviet Union. Therefore when the Soviet Union observes the proposal Vm, she knows for sure what type of U.S. administration she is dealing with. The third perfect Bayesian equilibrium is more interesting, because the ambiguous proposal Vm is out of the equilibrium path. In this equilibrium, the prospect of Vm being rejected by the Soviet Union prevented the "détente" type U.S. administration from deviating to offering Vm, its most preferred proposal if realizable. As to the "tough" type, the best payoff it can hope for is zero (since Vp will never be accepted), so the Soviet action here doesn't change its best response. The belief condition that mm be larger than a certain cut-point shows that the Soviet Union will reject Vm only if she has a sufficiently high probability assigned to the U.S. administration being a "tough" type. Since this belief mm can not be derived from Bayes' rule, in practice it might come from anywhere. A more reasonable guess, though, would be that it might have some relationship with the Soviet prior probability p.

Historical Play of the Game

Now I shall look at how this game of asymmetric information between the U.S. and the Soviet Union actually worked out in the SALT II negotiations in March 1977. By doing so it is hoped that some insights can be gained about the perfect Bayesian equilibrium strategies and beliefs.

On the U.S. side, at the Special Coordination Committee meetings on SALT from February to March, 1977, the new Administration's proposals took shape. Before Secretary of State Vance went to Moscow at the end of March, Carter instructed him that the deep-cuts proposal is the preferred proposal, and the National Security Council stressed to him "that the Soviets are likely to reject and ridicule our proposals" (Brzezinski 1983:160). When the negotiations started in the Kremlin on March 28, the U.S. had two proposals to make, with the comprehensive deep cuts (the action Vp in the game model) made clear to both sides as the preferred one to the "deferral" proposal (the action Vm in the game model). Therefore I modeled the U.S. action as single proposals instead of a bundle of two proposals, for two reasons. First, it was not common knowledge before the two sides started the negotiation that the U.S. action would be a bundle of two proposals. Second, even though the two proposals are made together, they were given separate and independent considerations by both sides, as if they were each offered individually. (And Vm was apparently included just as an "also-run").

The Soviet rejection of Vp was quite dramatic, with Foreign Minister Gromyko thumping the podium and calling the U.S. package a "cheap and shady maneuver" (Brzezinski 1983:164). Apparently here the equilibrium being played is the third perfect Bayesian equilibrium that I discussed in the last section: a "tough" type U.S. administration offered Vp and the Soviets rejected it; Vm was off the equilibrium path, but the Soviets rejected it when they saw it. We can also infer that the Soviet belief mm that the U.S. administration is "tough" is sufficiently high. From the historical accounts, the Soviet Union's prescience might have come from two sources, Carter's personal correspondence with Brezhnev (Brzezinski 1983:161) and Carter's speech at the UN General Assembly on the comprehensive proposal (Vance 1983:53), although as I explained before, the Soviets still had uncertainty about the new Administration when the negotiations started.

Generalized Model

Although I have gone into fairly fine historical detail in developing this game theoretic model of asymmetric incomplete information, this shouldn't prevent the model from being generalized to be applicable to other situations of asymmetric information due to government change. The key features of such situation that this game theoretic model attempts to capture are that at the beginning of the game one government has uncertainty about the new government's payoff structure, and that as one government considers its future interactions with the new government, it can have different payoffs for the same outcome, depending on the "type" of new government it will deal with in the future. Therefore with necessary changes in the specifications of the game theoretic model that I used in this paper, it can be applied to a class of cases where a government interacts with another new government, with asymmetric incomplete information.

In the new, generalized version of the model, nature moves at the initial choice node and decide whether the new government, called player 1, will be a "friendly" or "unfriendly" type of administration. The prior probability of nature choosing "friendly" type is common knowledge to both players. Then each type of the new government moves and choose from three possible actions to offer to its opponent: "accommodate", "prey" or "equivocate". The opponent of the new government, called player 2, observes the action taken by player 1, but doesn't know which type of player 1 it is dealing with, hence there are three information sets after each of the three actions taken by player 1. Player 2 can either accept or reject the offer. If it rejects the offer, the outcome is the status quo. If it accepts "accommodate", "prey", or "equivocate", the outcome will be "accommodation", "prey", or "equivocation", respectively. Player 2 prefers the outcome "equivocation" to the status quo if it faces the "friendly" type of player 1, but would prefer the status quo to "equivocation" if player 1 is of the "unfriendly" type. Under this generalized setting, this game theoretic model can have much broader applicability, which I shall illustrate by the following example.

1954 Soviet-Western Negotiation on German Unification

On March 5, 1953, Soviet dictator Stalin died, and after intense power struggle within the Kremlin, Khrushchev ascended to the top of the Soviet leadership. At this point, the West had uncertainty about the new Soviet rulers. There were genuine hope and sign that the new leaders would break away from Stalin's legacy and take on a new, conciliatory approach toward the West. There were also signs that the new leadership might be as heavy-handed as Stalin was, as shown, for instance, by the quick suppression of the June 1953 uprising in East Germany. Therefore, as four-power talks on German unification approached early in 1954, the Soviet Union and the West had asymmetric incomplete information. As to the set of possible actions, according to Gaddis (1997:133), the Soviet could offer one of three proposals on German unification: Stalin's March 1952 offer, Beria's May 1953 plan, or a more assertive proposal. Here Beria's plan was apparently the "accommodate" offer, the assertive proposal was the "prey" offer, and the Stalin's offer was the "equivocate" action. Beria's plan called for a unified and neutral Germany, and "it makes no difference whether or not it is socialist" (Gaddis 1997:130). It also called for West Germany to pay the Soviet Union substantial reparations in order to have East Germany demoted to some kind of subordinate status within a single German state. This plan, if realized, was of course the most favorable outcome to the West, but an "unfriendly" type Soviet leadership would never propose it. The assertive proposal, on the other hand, would take a much more rigid position on German unification, demanding withdrawal of Western troops from Germany. This is certainly the Soviet Union's favorite but unattainable outcome, since the West would reject it, no matter how "friendly" the new Soviet leaders were. Stalin's offer called for a four-power conference to arrange free elections throughout Germany, which would in turn establish an independent, reunified, rearmed, but neutral state. This would be the "equivocal" proposal in the sense that it is the idea of proceed from a position of strength in the East to project Soviet influence over West Germany (Gaddis 1997:134). If the West was to deal with a "friendly" type of Soviet leadership for the next 10 or 20 years, such an outcome would be preferable to the status quo, as it would create better political atmosphere in Europe in the long term. On the other hand, if the Soviet leaders are of the "unfriendly" type, this outcome would not look so rosy, as an expansionary and aggressive Soviet leadership would very likely turn this unified and rearmed Germany into a source of instability in Europe. Therefore, according to the results of section 6 in this paper, if the Western belief that the new Soviet leadership is "unfriendly" when they observe the "equivocal" proposal is sufficiently high, the West will reject it when they see it. In the real play of the game in history, the Soviet Union took the "prey" action and made such an aggression offer during the four-power talk that the U.S. Secretary of State Dulles stated that "Molotov made [his] German proposal so extreme, calling in effect for complete sovietization [of] all Germany and withdrawal [of] US, UK and French forces, that we believe Western position has been greatly strengthened by exhibition of his uncompromising approach." (Gaddis 1997:134) On the other hand, as Gaddis observed, "[h]ad the Russians at this moment renewed Stalin's March 1952 offer", the West might possibly have accepted it. So the perfect Bayesian equilibrium being played in this case is similar to the second one I found in section 6 of this paper, that is, the "friendly" type of player 1 offers "prey", the "unfriendly" type of player 1 offers "equivocal", and player 2 rejects "prey" and accepts "equivocal".

Conclusions

In this paper, I first constructed a game theoretic model of asymmetric information based on the SALT II negotiations in early 1977, when the U.S. had a new administration. Then I showed that this model is more broadly applicable to a class of cases of strategic interaction with a new government, which was illustrated by the example of the Soviet-West negotiations on German unification in early 1954, when the Soviet Union had a new leadership circle. These two examples showed results that are generally consistent with the simple formal analysis in this paper, although much remains to be done for this game model. It would be desirable, for example, to look at the effects of both players' time horizon on the equilibria, as a key feature of the model is that the calculations of the player 2 as regards the "ambiguous" outcome are affected by its expectation about future plays with a certain type of player 1. It would also help, of course, to look at more historical cases that can be categorized into this class of games of asymmetric information.

References