GAMES OF INCOMPLETE INFORMATION AND NATIONAL SECURITY

Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. GAMES OF INCOMPLETE INFORMATION AND NATIONAL SECURITY Pál Koudela Abstract The game theory of incomplete information was developed by John Harsányi in 1967/68. The mathematical model was created to meet the new needs of the Cold War and soon became the standard in national security, military analysis, security policy and economic strategic research and using applied methods it is inevitable to find a game theory solution to a difficult situation and follow it in the footsteps of Harsányi. Since its birth many weapons competition, deterrence, optimal threat, crisis instability verification, disarmament talks and other international and security conflicts were analyzed, we discuss here the Cuban Missile Crisis and the Iranian Hostage Crisis in details. Along with the development of security analysis many new models based on Harsányi’s contribution were created, we follow up the evolution of the original thought and the role of Harsányi himself in it. Keywords: John Harsányi, game theory, incomplete information, national security, international conflicts How Security Demanded the Evolution of Game Theory While game theory first appeared as a tool to interpret and predict economic situations, soon after the Second World War it became the standard framework in military analysis. General Oliver Haywood used game theory as a means of understanding, while descripted two battles of the war in France and another in Southeast Asia.1 Although Haywood’s models became core elements in the military higher education curriculum since, the Cold War created a situation of even more incomplete information with an emerging need for a more sophisticated mathematical model in national security. The Mutual Assured Destruction required open recognition of the strengths and vulnerabilities of individual nations, in fact, neither side trusted the seemingly established balance, and military developments have since focused on the defense side of nuclear attack. By the 1960s, China, Britain and France already had nuclear weapons too, creating an even more complicated situation in understanding of international power relations. In such an environment, Reinhard Selten and John Harsányi started to deal with the nature of balance in the sixties. John Nash has developed a criterion for the mutual consistency of player strategies, called Nash equilibrium, which can be applied more broadly than the previous set of criteria proposed by Neumann and Morgenstern. Harsányi's answer was different: in 1967/68 he created a model of incomplete information games based on Bayesian equilibrium.2 Game theory of incomplete information was developed for the US defense institution: the Arms Control and Disarmament Agency,3 and transformed the entire scientific security policy soon. 1 Haywood, Oliver G., JR. (1950) Military Decision and the Mathematical Theory of Games. Air University Quarterly Review, 4(1): 17–30.; Haywood, Oliver G., JR. (1954) Military Decision and Game. Journal of the Operations Research Society of America, 2(4): 365–385. 2 Harsanyi, John (1967) Games with Incomplete Information Played by Bayesian Players. Prt I. The Basic Model. Management Science, 14(3): 159–182. 3 Breit, William – Barry T. Hirsch (2004) Lives of the laureates. Eighteen Nobel economists. Cambridge: MIT Press. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Harsányi’s influence on military strategic analysis By the 1980s military strategy analysis incorporated the incomplete information game theory developed by John Harsányi. George Downs4 outlined possible models for strategic misunderstandings and imperfect intelligence, compared to the perfect information situation in which decommissioning negotiations necessarily lead to mutual agreement (i.e. cooperation), since this is the most profitable solution for both parties, knowing each other's decisions. Until the end of the Brezhnev era, US intelligence had always generously estimated the Soviet military potential, despite the fact that technical conditions did not usually justify it. An overestimation of military power led to further weaponry. Unknown factors gave rise to uncertainty, to which the US military leadership responded with "assurance". Dagobert Brito and Michael Intriligator5 analyzed the circumstances in which conflict led to the outbreak of war. They used a formal model that included both redistribution of resources and alternatives to war and imperfect information. Countries with rational decision mechanism are considering the consequences of both economic consumption and war. In the first phase of the game, both countries focus on either consumption or armament, while in the second phase, either the threat or the need to use force may lead to a reallocation of resources. If both countries are fully informed, no war will break out, and voluntary redistribution of resources is much more likely. However, in an asymmetric information situation, war can break out if an uninformed country adopts a dividing balance strategy, anticipating the possibility of war in order to prevent potential bluffing of the opponent. This game results in a Bayesian perfect equilibrium situation, where the first step is always taken by the one who has more information, and with this step, he reveals all available knowledge to the other player. In their analysis, Brito and Intriligator have developed a formal model in which conflicts, wars and redistribution are equally likely. Rational state decision-making in the two-step model cares about the economic law of consumption, and uses its military power to enforce that right. If both parties are fully informed, there will be no war-forced redistribution; voluntary redistribution of resources is much more likely, and neither side will encourage the fight. However, in the case of asymmetric information, war can occur when the uninformed party applies a separating equilibrium strategy, but even then, it does not apply the equilibrium aggregation strategy. In fact, it is a dynamic Bayesian game based on Harsányi's incomplete information model, the signaling game, which results in a state of equilibrium.6 The information sent does not tell you anything about the sender's position, but it does provide a guide to a possible strategic imitation. In such cases, the aim is not to prevent bluffing, but to adapt. Usually it occurs when neither party is interested in the conflict due to the distribution of resources, or if the country lacking information has enough resources to bribe the other country by cession or any valuable transfer. Of course, even if resources are scarce on both sides, no conflict is expected. Conflict is most likely to occur when the information-deficient party has sufficient resources for a separating equilibrium strategy, but not enough for the pooling equilibrium. With such a pooling equilibrium, armament rivalry leads to a much larger arsenal of weaponry, its purpose is Downs, George W. – Rocke, David M. – Siverson, Randolph M. (1985) Arms Races and Cooperation. World Politics, 38(1): 118–146. 5 Brito, Dagobert – Michael Intriligator (1985) Conflict, War, and Redistribution. American Political Science Review, 79(4): 943–957. 6 Fudenberg, Drew – Jean Tirole (1991) Game Theory. Cambridge: MIT Press. 326–331. 4 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. deterrence rather than actual armed conflict – roughly covering the US-Soviet relationship of the eighties.7 By the early seventies, it was clear to military operations research that sequential games could not be described with the Nash model. In repetitive, incomplete or incomplete games, negotiations and conflicts also serve as sources of information for both parties. The problem was that in such a game – in contrary to traditional game theory –, participants tended to overestimate (or considers it beneficial) their own determination. What is more, they judge the relative effectiveness of their own military power in a completely different way, which results in both of them perceiving the other as irrational and the negotiations failing. If the threat-based game remains ineffective, there will be an armed conflict that narrows the differences in understanding the game. Losses are gradually accumulating, and the actual output becomes clearer to both parties than the total loss would occur. The nuclear threat game outlined above is thus fundamentally different from the real conflict experience. In the Arab-Israeli conflict of the seventies, the only factor that could not be predicted in advance was the speed of the steps. It was then not determined by the participants in the conflict, but by the intensity of the strategies played.8 Even a limited war at nuclear power level could be ruled out, based on game theory, as long as strategic games are available, they will always take precedence over actual warfare. Part of this is the negotiated solution. The decades that have passed since then have justified mathematical interpretation, although historical reality has often shown itself to be contrary to logical solutions. Thus, Harsányi's work not only became the basis of mathematical game theory, but also gained particular importance in military strategic analysis, as the basis of deterrence / threat was based on the lack of information, which then became one of the determining contexts of modern international tensions. Stability based on mutual deterrence is linked to the credibility of the threat. While authenticity used to be credibility, in post-Harsányi game theory, it was already linked to rationality, since in an incomplete information model, no one can be sure how his opponent will react to his attack on stability. Of course, much of the uncertainty surrounding deterrence remained for decades to come. Strategic analyzes of the 1980s expressed doubts about this.9 By the time of the Gulf War and the dissolution of the Soviet Union, it had also become clear that, contrary to earlier beliefs,10 there was no linear relationship between war costs and deterrence-based stability; moreover, the rise in war costs beyond a certain point increases the likelihood of conflict, as opposed to deterrence.11 This made the need for disarmament between the two world powers clear and explicit. As players' credibility decreases, the likelihood of deterrence stability increases again because deterrence-failure costs increase. In principle, the dismantling of medium-range missiles in Europe in the 1990s reduced the level of threat, in reality, however, the existence of an independent British and French nuclear force bypassed this effect, and the aforementioned game theory step was omitted. If the role of players in a deterrent game is disproportionate, this model is just as unsustainable as in Afghanistan. Nor can stability based on mutual deterrence 7 Powell, Robert (1993) Guns, Butter and Anarchy. The American Political Science Review, 87(1):115–132. Pugh, George E. – John P. Mayberry (1973) Theory of Measures of Effectiveness for General-Purpose Military Forces: Part I. A Zero-Sum Payoff Appropriate for Evaluating Combat Strategies. Operations Research, 21(4): 867–885. 9 Intriligator – Brito (1981) i.m.; Mueller, John (1989) Retreat from Doomsday: The Obsolescence of Major War. New York: Basic Books.; Mueller, John (1989) Retreat from Doomsday: The Obsolescence of Major War. New York: Basic Books. 10 Lebow, Richard Ned (1984) Windows of Opportunity: Do States Jump through Them? International Security, 9(1):147– 186. 11 Kilgour, D. Marc – Frank C. Zagare (1991) Credibility, Uncertainty, and Deterrence. American Journal of Political Science, 35(2): 305–334. 8 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. be maintained in areas of major interest to one party – essentially a change in the balance of basic conditions – as happened in 1956 in Hungary or in 1968 in Czechoslovakia. Crisis Research - The Cuban Missile Crisis In zero-sum games, unpredictability can pay off, even if you have to choose strategies at random. The risk of bluffing is when it turns out, as the opponent's informational advantage may decide the game. However, international relations are rarely a zero-sum game. War will inevitably lead to surplus destruction, which will essentially mean a loss for everyone. The nations therefore encourage mutual trade and coordinate peace efforts rather than trying to obtain each other's resources through costly warfare. In national security, efficiency is what determines the right strategy, and it is never the only ever working model of the world. The prerequisite for choosing the right strategy is determining the leader's position. Whether unpredictability could be an effective strategy under any circumstances in international relations first became the focus of attention and public interest in relation to Nixon’s politics. Long decades have passed since the first military analyzes of the 1950s, and the Cold War deterrence strategy was intertwined with the issue of national security. For the United States, not only military blocs and spheres of interest were important, but most of all, the emphasis was on the defense of its own country, which could also be the bases of the legitimacy of the leadership. By the end of the eighties, however, all this remained within the bipolar framework: the conflicts between the two sides were essentially analyzed as a game of decision-makers in two countries. October 1962 also marked a turning point in the history of science. The first game theory analysis of the Cuban missile crisis was published in 1966 by Thomas Schelling, 12 who was awarded the Nobel Prize in Economics in 2005. Although Schelling was the first to apply game theory to international crisis analysis, he used the Cuban crisis itself as an illustration only. In the following half century, however, his work has provoked many reassessments and debates. All versions of the analysis were based on an incomplete information model, and in the seventies, Harsanyi, if indirectly, engaged himself in the analysis of the Cold War with his game theory debate with Nigel Howard.13 Today, the game theory analysis of the missile crisis has gone through many variations, and greater or lesser changes, refinements, and debates have had an effect on game theory itself, and even the subject is seen as a stand-alone element in the history of science.14 However, in the context of multiple analyzes of historical conflict, at least two important components need to be highlighted: on the one hand, historiography and the majority of game theory authors see the resolution of the conflict as a compromise. This, in turn, requires more complex modeling than games with clear victory and defeat. On the other hand, all models include the assumption that the state of equilibrium – persistence in the decisions made until further changes – presupposes rational actors. This results in the definition of the equilibrium itself, distinguishing between static or dynamic and complete or incomplete information situations.15 The two-player strategy games of the sixties were built on risk-based competition, with complete information, with two non-interchangeable and unequal Nash equilibrium points. In 12 Schelling, Thomas C. (1966) Arms and Influence. New Haven: Yale University Press. Harsanyi, John C. (1973) Review of paradoxes of rationality. American Political Science Review, 67(2): 599–600.; Harsanyi, John C. (1974) Communications. American Political Science Review, 68(2): 731–732. and 68(6): 1694–1695. 14 Zagare, Frank C. (2014) A Game-Theoretic History of the Cuban Missile Crisis. Economies, 2(1): 20–44. 15 Morrow, James D. (1994) Game Theory for Political Scientists. Princeton University Press: Princeton. 13 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. games with these two equilibrium situations, especially with balanced power, Harsányi 16 was right to ask on what basis one could make a prediction, or even later explain how one player achieved what the other did not, once there is more than one rational decision result? Schelling left the threat-based games a chance not to upset the delicate balance, based on rational insight, and the actual steps were replaced by threats and engagements, such as Kennedy's October 22 televised speech. The first game theory analysis specifically for the missile crisis was written by Nigel Howard.17 Harsányi18 wrote a review of this book two years later, which then led to years of debate in the American Political Science Review’s Communication section. In Howard's view, the game was still a strategy game described in a two-by-two matrix. The first step was for the United States on October 16, when Kennedy announced the discovery of Soviet-installed missiles. There are only two choices left for the US: either to cooperate and proclaim blockade against Cuba, or to compete and measure air strikes on Soviet missiles. On October 22, following the announcement of the blockade, the Soviets had only two strategic choices, according to Howard: either to cooperate and withdraw their missiles, or not to cooperate and continue to maintain them. According to Howard, the second best solution, the cooperation was realized, that is, a compromise was reached. Although Schelling had assumed this, Howard was the first to describe it openly. (Table 1.) Table 1. The decision-making situation for the Cuban missile crisis in a pure strategic game Soviet Union US Withdraw (cooperation) Maintain (competition) Blockade (cooperation) Compromise (3,3) Soviet Victory (2,4) Air Strike (competition) US Victory (4,2) Conflict (1,1) (Source: Zagare (2014) A Game-Theoretic History., own editing P.K.) Howard realized that even when analyzed in the traditional matrix, the missile crisis is best described as a mixed strategy, and compromise is not a Nash equilibrium situation. To solve this dilemma, he introduced the so-called meta-game theory, in the path of John Neumann. He changed the basic game in such a way that decisions were based on the likelihood of expectations of the opponent, so the meta-game takes place in the head before real decisions. Howard thus moved the meta-game to a communication level, saying that the consequences of communicating forward steps stabilize the situation. Meta games unveil the opponent's strategies by communication, so unlike the previous 2X2 matrix, a 4X4 decision situation is created, which results a 64-output meta game based on the original 2X2 version. In this model, Harsanyi, John C. (1977) Advances in Understanding Rational Behavior. In Robert E. Butts – Jaakko Hintikka (eds.) Foundational Problems in the Special Sciences. D. Reidel: Dordrecht. 293–296.; Harsanyi, John C. (1977) Rational Behavior and Bargaining Equilibrium in Games and Social Situations. Cambridge University Press: Cambridge. 17 Howard, Nigel (1971) Paradoxes of Rationality. Theory of Metagames and Political Behavior. Cambridge: The MIT Press. 18 Harsanyi, John C. (1973) Review of paradoxes of rationality. American Political Science Review, 67(2): 599–600. 16 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. there is a Nash equilibrium for the (3,3) compromise situation, but only if both parties work together, because they both presuppose a cooperative action from the other side. In this model, which of the four equilibrium situations actually occurs depends on what the actors assume and how they communicate. In the case of the missile crisis, the compromise was that both major powers openly stated that they would be ready for a full war in case of an attack from the other side. Howard, however, did not answer why any party (in this case the US) would choose the meta-strategy, and denied that there could be any specific explanation or reason for it. Harsányi responded to this point by pointing out that any dominant meta-strategy is irrational and therefore unreliable; choosing any meta-strategy assumes its maximum usefulness and makes it unreasonable to assume the choice of other options for the opponent. It follows that, in the case of a dominant strategy, a player would have to choose one and only that one, otherwise, conflict would arise.19 In the eighties, the series of game theory analyzes of the missile crisis continued. Howard's meta-games have also been enhanced to become an early theory of equilibrium.20 This model assumes three options for both actors, considering that the United States could not only respond by blockade or air strike to the deployment of Soviet missiles, but also by diplomacy, and the Soviet Union could not only maintain or withdraw its missiles, but could also increase their number. The decision matrix was decimalized, an unjustified order of preference was established for each state's decision options, and the outputs were divided into four groups: rational, sanctioned, unstable and stable by simultaneity. However, Fraser and Hipel were unable to substantiate the equilibrium point of their own dynamic model, and this may have contributed to Steven Brams21 developing his own dynamic decision theory model of the crisis. Brams actually iterated the game, assuming that when it starts, both players can make decisions regardless of their original state and then react to the other, resulting in a series of steps. The game is over when none of the players responds, and if they have no intention of taking any further action in the long run, this output is a non-short-sighted equilibrium.22 In the eighties, the game theory analysis of international relations underwent a major change. They have moved away from the static environment visualization previously used in strategic models, and the former Nash equilibrium has been replaced by Selten's23 model for perfect equilibrium of dynamic subgames. In this theoretical context, incomplete information analysis has become the decisive factor, replacing the previous complete information analysis.24 The first application of Harsányi's incomplete information to the Cuban missile crisis was carried out by Harrison Wagner.25 In his model he builds the equilibrium state in stages, or more precisely, builds a decision graph from a set of strategies based on rational decisions. Each equilibrium situation is characterized by whether or not it has provided sufficient information for the particular situation. 19 Harsanyi, John C. (1974) Communications. American Political Science Review, 68(6): 1694–1695. Fraser, Niall M. – Hipel, Keith W. (1982) Dynamic modelling of the Cuban missile crisis. Conflict Management and Peace Science, 6(2): 1–18. 21 Brams, Steven J. (1985) Superpower Games. Yale University Press: New Haven.; Brams, Steven J. (2011) Game Theory and the Humanities: Bridging Two Worlds. MIT Press: Cambridge. 22 Brams, Steven J. (1994) Theory of Moves. Cambridge: Cambridge University Press. 23 Selten, Reinhard (1975) Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory, 4(1): 25–55. 24 Harsanyi, John (1967) Games with Incomplete Information Prt I.; Harsanyi, John C. (1968) Games with Incomplete Information Played by “Bayesian” Players. Part II. Bayesian Equilibrium Points. Management Science, 14(5): 320-334.; Harsanyi, John C. (1968) Games with Incomplete Information Played by ‘Bayesian’ Players. Part III. The Basic Probability Distribution of the Game. Management Science, 14(7): 486–502. 25 Wagner, R. Harrison (1989) Bargaining in the Cuban Missile Crisis. In Ordeshook, P.C., (ed.) Models of Strategic Choice in Politics. Ann Arbor: University of Michigan Press. 20 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Since Kennedy had refused to halt works on the rocket base, Khrushchev has gained valuable insight into what the American side was preferring. Thus, Wagner's model broke with earlier risk-based competing games, and saw the missile crisis as a bargaining and informationgathering practice based on incomplete information of the two Cold War parties. It is also irrelevant to the end result that Wagner relied in 1989 on sources26 which suggested that the Soviet missiles were not armed. It was revealed only after the dissolution of the Soviet Union, in 1997, that this had actually happened on October 26th.27 Wagner, based on Harsányi's work, derived preferences from choices, which was a significant step forward compared to earlier models that assumed them in advance. However, he did not develop a general behavioral model to determine the conditions under which equilibrium could be established. The practical application of Harsányi's theory was accomplished by Frank Zagare.28 Zagare's asymmetric escalation game extends John Harsányi’s incomplete information game theory, based on the perfect Bayesian equilibrium, to a comprehensive spectrum of preferences and choices and integrates it into a simple strategy game. In his work with Mark Kilgour, Zagare also provides a clear answer to the basic questions unanswered by earlier models, why did the Soviet Union deploy missiles at all in Cuba? They came to the conclusion that Khrushchev may have assumed that the US would either not want to act violently or that it would be too late for such a move to be made before Soviet missiles were discovered. The strategy of the American response is also clear from Zagare's work: the US sought to achieve the goal of removing the missiles at the lowest cost.29 All of these sequential games, illustrated with organizational charts and a decision trees, were based on a peculiar model of the extensive-form games30 first formulated by John Harsányi.31 Of particular interest in the development of game theory is that Zagare, although consistently mistaken for references, refers in his book to a work by Harsányi related to the utilitarian philosophical work of the Hungarian-American scientist rather than to the mathematical analysis of game theory.32 Here Harsányi relied on the utilitarian view that social welfare functions should be defined as a linear combination, which is, actually, the arithmetic mean of the Neumann-Morgenstern utility functions.33 His argumentation is based on the following mathematical theorem.34 If (a) members of society behave according to Bayesian rationales; and if (b) our moral choices between alternative social policies follow these axioms similarly; and if (c) we are morally indifferent to the choice between two social policies, if, to our knowledge, everyone in our society will be indifferent to the effects of those two policies; then the welfare function of individuals will be a linear combination of the Neumann-Morgenstern utility functions of all individuals. Surprisingly, in terms of rationality / irrationality, however, 26 Betts, Richard K. (1987) Nuclear Blackmail and Nuclear Balance. Brookings: Washington. Fursenko, Aleksandr – Naftali, Timothy (1997) “One Hell of a Gamble”: Khrushchev, Castro, and Kennedy, 1958– 1964. Norton: New York. 28 Zagare, Frank C. (2014) A Game-Theoretic Explanation of the Cuban Missile Crisis. Department of Political Science, University at Buffalo: Buffalo.; Zagare, Frank C. (2014b) A Game-Theoretic History of the Cuban Missile Crisis. Economies, 2(1): 20–44.; Zagare, Frank C. (2016) A General Explanation of the Cuban Missile Crisis. International Journal of Peace Economics and Peace Science, 1(1): 91–118.; especially: Zagare, Frank C. – Kilgour, D.M. (2000) Perfect Deterrence. Cambridge: Cambridge University Press. 263–272. 29 Zagare – Kilgour (2000) Perfect Deterrence. 178. 30 The extensive form summarizes the game's order of choice, the possible outputs, the usefulness of the players' decisions associated with these outputs, and the information available to each player at the time of the decision. 31 Harsanyi (1967) Games with Incomplete Information. Prt. I. 32 Harsanyi, John (1955) Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility. Journal of Political Economy, 63(4): 309–321.; Harsanyi, John (1975) Nonlinear Socal Welfare Functions. Theory and Decision, 6(3): 311–332. 33 In decision theory, the Neumann-Morgenstern utility principle shows that among certain axioms of rational behavior, decision-makers, faced with the probabilistic outcome of different decisions, must behave as they maximize the expected value of a function, while potential outcomes will be determined at specific points in the future. 34 Harsanyi (1955) Cardinal Welfare. 27 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. we see a connection between Harsányi's analysis of utilitarianism and the critical axiom of decision-making, which are essentially based on the Neumann-Morgenstern utility principle. National security strategies based on incomplete information Political scientist Steven Brams and mathematician Mark Kilgour built a complete model of national security by the end of the 1980s, based on incomplete information game theory.35 Brams also developed a new game theory scheme following Harsányi, called Theory of Moves.36 The starting point of the theory is a payoff matrix or game configuration in which the game order is not defined, which is followed by a switch to the extensive form, the game-tree analysis within the matrices. The players do not choose strategies, but take steps and responds to specific situations and the opponent's actions. In all cases, they look forward to drawing conclusions from actions already taken. In traditional game theory, players are assumed to choose strategy at the same time, so the question of whether or not their moves are rational during the game is only important when choosing a strategy with Nash equilibrium in mind. In the Brams’s model, the initial status quo can thus be reconfigured at every step and, in the long run, may deviate from the original strategy. In essence, this is a dynamic multi-step model that creates four rules that determine the chances of a given situation in a two-by-two game. Each player's initial state is determined by the row and column value of the matrix, but players can change strategy one-sided at any time, and the opponent can also react unilaterally to create a new state. Strategy changes take place until somebody actually steps, which actually creates the output and final state of the game. So Brams inserted a parallel or alternate game in which participants speculated what the other player would do if he knew what we knew, what the opponent would react to and speculate what he would do if he knew, what we know about what he knows. Assuming that players think not only of the immediate consequences of their action, but also of the consequences of their action’s reaction, and of the response to their action over the reaction, etc., this extends the strategic analysis of conflicts to the distant future. From weapons competition, deterrence, optimal threat, crisis instability verification, disarmament talks to Reagan's Star Wars plan, Brams and Kilgour analyze countless international conflicts. These include, of course, the Cuban missile crisis, but for us, the game between the US and Iran between 1979 and 1982, in which Carter had incomplete information about Khomeini's preferences, is more interesting here. Carter, misunderstanding the Iranian side, made wrong decisions. According to Brams and Mattli37, this crisis was not basically an armed conflict but a game. As far as the hostage drama is concerned, the interests of both parties seem simple: the conflict has given Khomeini the opportunity to permanently dismantle US relations built by Reza Pahlavi and gain more support from the extremist revolutionary forces. Carter wanted primarily the immediate release of the hostages, but he also wanted to negotiate with the newlyestablished religious forces, since he had a direct security and economic interest in renewing Iran-US relations. Of course, if the hostages had been executed, he could not have ignored the military response, since protecting the honor of the United States would have come first. So there were two options for Carter. One is to negotiate with the help of the Security Council or the International Court of Justice, or even through informal diplomatic channels, including Brams, Steven – D. Mark Kilgour (1988) Game Theory and National Security. New York: Blackwell. Brams (1994) Theory of Moves. 37 Brams, Steven J. – Walter Mattli (1993) Theory of Moves: Overview and Examples. Conflict Management and Peace Science, 12(2): 50–54. 35 36 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. economic sanctions, while the other is through military strike: rescue and/or punishment attacks against strategically important targets. For Khomeini, negotiation as a strategy was also possible, but it would have meant transferring all the assets of the Shah and reaching the end of American intervention. Another option was obstruction, including bogus negotiations. Thus, the United States' primary goal was to reach negotiations, and the situation was exacerbated by the Soviet invasion of Afghanistan in December. This further increased the risk of military intervention and made possible Soviet cooperation through the UN completely impossible. Carter speculated that Iran's serious troubles: lack of professionals, demonstrations, internal fighting with the Kurds and invasions of Iraq along the western border, and of course power struggles, all forced Khomeini to opt for negotiations, thereby retreating with dignity from the problems of his rule.38 As a result, according to Carter, Khomeini most wanted the US to retreat by initiating and refusing to negotiate. Second, he wanted to reach a negotiated compromise, so the two worst options would have both been military intervention for Iran. But Carter misunderstood the situation: Khomeini sought complete Islamization and wanted to close all ties with the US, because for him it was Satan himself. Khomeini knew no compromise, so for him there was only obstruction, whatever the US planned. Even those Iranian leaders ready to negotiate fared ill. (see Tables 2 and 3) Table 2. Game as misperceived by Carter Khomeini Negotiate Negotiate Obstruct I. Compromise II. Carter surrenders (4,3) Carter Intervene militarily (2,4) [4,3] [4,3] ↑ ↓ impediment IV. Khomeini surrenders III. Disaster (3,2) [4,3]/[2,4] 38 → ← ← (1,1) [2,4]/[4,3] Carter, Jimmy (1982) Keeping Faith: Memoirs of a President. New York: Bantam. 459–489. Dominant strategy Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Table 3. Real game Khomeini Negotiate Negotiate Obstruct I. Carter succeeds II. Khomeini succeeds (4,2) (2,4) [2,4] [2,4] ↑ ↓ impediment IV. Carter adamant ← III. Khomeini adamant (3,1) impediment (1,3) Carter Intervene militarily → [2,4] ← Dominant strategy [2,4] (x,y) = (payoff to Carter, payoff to Khomeini) [x,y]= [[payoff to Carter, payoff to Khomeini] in anticipation game 4 = best; 3 = next best; 2 = next worst; 1 = worst Nash-equilibria underscored Non-myopic equilibria with bold Arrows in matrices indicate direction of cycling (Source: Brams, Steven (2011) Game Theory and the Humanities: Bridging Two Worlds. Cambridge: The MIT Press.) Thus, in Brams's39 interpretation, there were two games of different logic: one in Carter's head and the other in reality, the most important difference being that the former had two non-shortsighted equilibrium states,40 whereas the latter had only one. Carter therefore believes that the preferred compromise (4.3) can be reached at any point in the game, as shown by the anticipation game. Moreover, in this fiction the equilibrium (4,3) is so stable that the change of power, that is, who owns it, has no influence on it. So if Carter can move, he can force Khomeini to stop at either (4,3) or (1,1). (Horizontal arrows show Khomeini's response.) Carter thought that since Khomeini prefers (4,3), he should stop there. Had Khomeini had a deployable resource, he would have made Carter stop at either (3,2) or (2,4). (Vertical arrows show Carter's response.) Carter prefers (3,2) so he'll probably stop there. Because both of them prefer Carter- 39 40 Brams (2011) Game Theory and the Humanities. This is Brams' model derived from the Theory of Moves. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. induced (4,3) state to Khomeini-induced (3,2), they both have a common interest in stopping the series of step-counter-step at the previous one – so having the available forces irrelevant. Thus, Carter thought he had an effective deterrent while not in real play, so the only non-myopic balance favored Khomeini (2,4). Due to the cyclical nature of the game, the movable forces also remained ineffective. Carter consequently chose the optimum negotiation he could, and when he failed, deployed his supposedly effective resource, Kitty Hawk. However, this still did not change Khomeini's strategy and would have led to state (1,3) due to Khomeini's response, obstruction. A successful hostage rescue could have deprived Khomeini of his main asset (1,3), but with the failure of American action, only the same (2,4) situation arose again. Most interestingly, US Department of State analysts were aware in the week following the hostage that there was no chance of a negotiation with the Iranian side or of successfully rescuing the hostages,41 whether through economic or military action. All this was later expressed politically by the resignation of Cyrus Vance, Secretary of State for Foreign Affairs in April. The above analysis by Steven Brams also reveals the distinction between strategic action by individual decision makers and a team of management professionals. When we think about the situation, Harsányi himself was such a specialist, and the 1980s conflict could already be perfectly understood following his work. After the turn of the millennium, Akan Malici42 compared two specific leadership strategies following Brams: a resilient by Gorbachev, and an inflexible by Kim Ir Sen. Nowadays, the use of game theory in strategic analysis has become commonplace, even when analyzing reckless or selfish, provocative or strategically illconsidered leadership behavior. The "madman" leader as a strategist was a thoughtful idea in Nixon's time, or at least an existing public opinion.43 Many people imagined that there was a thoughtful plan behind it, though the incomplete information modeling of game theory made it clear that there was no such thing. The fact that Ariel Sharon visited Temple Mount in September 2000 or that Japanese leaders regularly visit the Yasukuni Shrine is symbolic. The former triggered the Second Intifada and significantly hampered the Israeli-Palestinian peace process, the latter is regularly poisoning the relationship between Japan and South Korea and between Japan and China.44 Harsányi45 has clearly demonstrated that the Nash equilibrium of each complete information game is the ultimate limit to the Bayes-Nash equilibrium, approaching any series of incomplete information games. Following in his footsteps, it now appears that there are situations of communication failure where only a complete lack of Pareto efficiency results in a Bayes-Nash equilibrium in an incomplete information game, even if it is really effective in uncertainty.46 Just as Brams and many others47 have sought to develop playable situations from secondary strategic speculation behind real games, in real conflicts the third actor, who can be interpreted as a subordinate and complementary strategy, has become an important factor in game theory. 41 Sick, Gary (1985) All Fall Down. New York: Penguin. 246. Malici, Akan (2008) When Leaders Learn and When They Don’t: Mikhail Gorbachev and Kim Il Sung at the End of the Cold War. Albany: State University of New York Press. 43 Haldeman, Harry R. (1978) The Ends of Power. New York, Times Books. 44 Etzioni, Amitai (2014) Japan Should Follow – Germany. The Diplomat, February 06, 2014. https://thediplomat.com/2014/02/japan-should-follow-germany/; Hefetz, Nir – Gadi Bloom (2006) Ariel Sharon: A Life. New York: Random House. 45 Harsanyi, John C. (1973) Games With Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points. International Journal of Game Theory, 2(1): 1–23. 46 Baliga, Sandeep – Tomas Sjöström (2004) Arms Races and Negotiations. Review of Economic Studies, 71(2): 351–369. 47 For example, complementary and subordinate strategies were revealed when analyzing the Israeli-Palestinian conflict by Berrebi, Claude – Esteban F. Klor (2006) On Terrorism and Electoral Outcomes: Theory and Evidence from the IsraeliPalestinian Conflict. Journal of Conflict Resolution, 50(6): 899–925.; Berrebi, Claude – Esteban F. Klor (2008) Are Voters Sensitive to Terrorism? Direct Evidence from the Israeli Electorate. American Political Science Review, 102(3): 279–301. 42 Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Political extremism may not only appear in a dominant position, as we have seen with Nixon or Carter. A subordinate position may also trigger an unexpected provocation aimed at gaining the opponent's capitulation, while apparently merely trying to increase his willingness to compromise. (Carter assumed the latter about Khomeini - erroneously.) In international relations theory pre-WWI fear spirals and conflicts such as World War II., where most of all, the lack of deterrence encouraged Hitler, are clearly distinguished.48 Games with strategic additions or substitutes are stylized representations of two types of strategic interaction. A dominant extremist can cause conflicts if his actions are a strategic complement, and if he wants to use his plan as a secondary or subordinate strategy, he will be ineffective. This toolbar tends to favor the subordinate in convincing, often successfully forcing his dominant opponent to retreat. In other words, a provocateur can gain extra power if his strategy is not clearly separated from the decisions of the management environment. Such provocative attempts were made in February 1965 during the Gulf of Tonkin Incident when the warships were re-assigned to the Gulf.49 Baliga and Sjöström50 also modeled that a third actor could provoke successfully even if his actions were clearly separate from the domestic leadership. A fine example is the following: after the 2008 Mumbai terrorist attack, Indian government officials were fully aware that the Pakistani civilian government was not involved in the attacks and that the decision was taken independently by the Pakistani secret service. While Pakistan's secret service is generally believed to have a strategy to make India's presence in Kashmir costly, consequently in the long run to induce India to hand over the disputed territory, it can hardly be a goal without governmental and military forces. If Pakistani leaders are aggressive enough, the role of the secret service may be to prepare the ground for an effective military action through a network of insurgents. As they do not want to provoke, they send a neutral message to India in this case. Of course, if India reveals this strategy, the lack of provocation will by no means be reassuring to Pakistan. However, if the secret service speculates on the insecurity of the Pakistani leadership, provocation will be the best way to increase tension between the two countries. And if the secret service assumes that the Pakistani leadership will not be able to take any action at all, they will be neutral again, pending a more decisive leadership in Pakistan in the future. This situation is very similar to the Iranian hostage drama. In many cases, such analyzes use only general models of incomplete information games, such as Brams, while others, like Baliga, refer directly to Harsányi. However, incomplete information-based game theory modeling has become the basis for national security analyzes. Nowadays it is inevitable to find a game theory solution to a difficult situation and follow it in the footsteps of Harsányi. Decisions and plans affecting national security or regional economic stability, such as Donald Trump's withdrawal from the Trans-Pacific Partnership Agreement, the renegotiation of the North American Free Trade Agreement, trade tariffs on China, or even plans to exit the World Trade Organization, they affect the international economic and political balance. The tense relationship between 48 Lieber, Keir A. (2007) The New History of World War I and What It Means for International Relations Theory. International Security, 32(2): 155–191. 49 Bamford, James (2001) Body of secrets: anatomy of the ultra-secret National Security Agency: from the Cold War through the dawn of a new century. New York: Doubleday.; Ellsberg, Daniel (2002) Secrets: A Memoir of Vietnam and the Pentagon Papers. New York: Penguin. 66. 50 Baliga, Sandeep – Tomas Sjöström (2012) The Strategy of Manipulating Conflict. American Economic Review, 102(6): 2897–2922. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Trump and the US leadership clearly implies third-party modeling, whereas hard-to-understand China requires double modeling.51 Conclusions Connecting the starting point of today's game theory to John von Neumann, the most important turning point of the period since then is the three-part work of John Harsányi from 1967-68. National security, military analysis, security policy and economic strategic research and applied methods are still based on incomplete information game theory methods. In fact, historical conditions created the backdrop for incomplete information-based modeling in the Cold War, but in the decades that followed, these circumstances became more and more determinative not only of the actors involved but also of their technical tools. The most enduring work of John Harsányi was that he remained alive despite his high mathematical abstraction. This is evident in his later work and in discussions with others. It was not so much a theory for itself and a technocratic application as so many experts had in the field. Harsányi has never forgotten that even the most abstract mathematical model should help in understanding and simulating reality, in itself is worthless. This pragmatic attitude also puts a mark on the subsequent applied theoretical research, and it also noticeably selects successful and unsuccessful works. There were other great researchers who were significant in applied game theory. For example, before Harsányi, it was General Oliver Haywood, who was accepted even by the uncompromising Ede Teller. At the time of his analysis of the battles of World War II, he was not familiar with incomplete information game theory, and based his work on Neumann's foundations. After 1967, however, all significant contributions and applications followed in Harsányi's footsteps and continue to do so today. References Baliga, Sandeep – Tomas Sjöström (2004) Arms Races and Negotiations. Review of Economic Studies, 71(2): 351–369. Baliga, Sandeep – Tomas Sjöström (2012) The Strategy of Manipulating Conflict. American Economic Review, 102(6): 2897–2922. Bamford, James (2001) Body of secrets: anatomy of the ultra-secret National Security Agency: from the Cold War through the dawn of a new century. New York: Doubleday. Berrebi, Claude – Esteban F. Klor (2006) On Terrorism and Electoral Outcomes: Theory and Evidence from the Israeli-Palestinian Conflict. Journal of Conflict Resolution, 50(6): 899–925. Berrebi, Claude – Esteban F. Klor (2008) Are Voters Sensitive to Terrorism? Direct Evidence from the Israeli Electorate. American Political Science Review, 102(3): 279–301. Betts, Richard K. (1987) Nuclear Blackmail and Nuclear Balance. Brookings: Washington. Brams, Steven – D. Mark Kilgour (1988) Game Theory and National Security. New York: Blackwell. Brams, Steven J. – Walter Mattli (1993) Theory of Moves: Overview and Examples. Conflict Management and Peace Science, 12(2): 50–54. 51 It is illuminating that this can be read as a university paper: MccGwire, Jake (2018) A Game Theory Analysis of Donald Trump’s Proposed Tariff on Chinese Exports. Student Economic Review, 31(1): 69–77. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Brams, Steven J. (1985) Superpower Games. Yale University Press: New Haven. Brams, Steven J. (1994) Theory of Moves. Cambridge: Cambridge University Press. Brams, Steven J. (2011) Game Theory and the Humanities: Bridging Two Worlds. MIT Press: Cambridge. Breit, William – Barry T. Hirsch (2004) Lives of the laureates. Eighteen Nobel economists. Cambridge: MIT Press. Brito, Dagobert – Michael Intriligator (1985) Conflict, War, and Redistribution. American Political Science Review, 79(4): 943–957. Carter, Jimmy (1982) Keeping Faith: Memoirs of a President. New York: Bantam. pp. 459– 489. Downs, George W. – Rocke, David M. – Siverson, Randolph M. (1985) Arms Races and Cooperation. World Politics, 38(1): 118–146. Ellsberg, Daniel (2002) Secrets: A Memoir of Vietnam and the Pentagon Papers. New York: Penguin. 66. Etzioni, Amitai (2014) Japan Should Follow – Germany. The Diplomat, February 06, 2014. https://thediplomat.com/2014/02/japan-should-follow-germany/ Fraser, Niall M. – Hipel, Keith W. (1982) Dynamic modelling of the Cuban missile crisis. Conflict Management and Peace Science, 6(2): 1–18. Fudenberg, Drew – Jean Tirole (1991) Game Theory. Cambridge: MIT Press. 326–331. Fursenko, Aleksandr – Naftali, Timothy (1997) “One Hell of a Gamble”: Khrushchev, Castro, and Kennedy, 1958–1964. Norton: New York. Haldeman, Harry R. (1978) The Ends of Power. New York, Times Books. Harsanyi, John (1955) Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility. Journal of Political Economy, 63(4): 309–321. Harsányi, John (1967) Games with Incomplete Information Played by Bayesian Players. Prt I. The Basic Model. Management Science, 14(3): 159–182. Harsanyi, John (1975) Nonlinear Socal Welfare Functions. Theory and Decision, 6(3): 311– 332. Harsanyi, John C. (1968) Games with Incomplete Information Played by “Bayesian” Players. Part II. Bayesian Equilibrium Points. Management Science, 14(5): 320-334. Harsányi, John C. (1968) Games with Incomplete Information Played by ‘Bayesian’ Players. Part III. The Basic Probability Distribution of the Game. Management Science, 14(7): 486–502. Harsanyi, John C. (1973) Games With Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points. International Journal of Game Theory, 2(1): 1–23. Harsanyi, John C. (1973) Review of paradoxes of rationality. American Political Science Review, 67(2): 599–600. Harsanyi, John C. (1974) Communications. American Political Science Review, 68(2): 731– 732. and 68(6): 1694–1695. Harsanyi, John C. (1974) Communications. American Political Science Review, 68(6): 1694– 1695. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Harsanyi, John C. (1977) Advances in Understanding Rational Behavior. In Robert E. Butts – Jaakko Hintikka (eds.) Foundational Problems in the Special Sciences. D. Reidel: Dordrecht. 293–296. Harsanyi, John C. (1977) Rational Behavior and Bargaining Equilibrium in Games and Social Situations. Cambridge University Press: Cambridge. Haywood, Oliver G., JR. (1950) Military Decision and the Mathematical Theory of Games. Air University Quarterly Review, 4(1): 17–30. Haywood, Oliver G., JR. (1954) Military Decision and Game. Journal of the Operations Research Society of America, 2(4): 365–385. Hefetz, Nir – Gadi Bloom (2006) Ariel Sharon: A Life. New York: Random House. Howard, Nigel (1971) Paradoxes of Rationality. Theory of Metagames and Political Behavior. Cambridge: The MIT Press. Intriligator – Brito (1981) i.m.; Mueller, John (1989) Retreat from Doomsday: The Obsolescence of Major War. New York: Basic Books. Kilgour, D. Marc – Frank C. Zagare (1991) Credibility, Uncertainty, and Deterrence. American Journal of Political Science, 35(2): 305–334. Lebow, Richard Ned (1984) Windows of Opportunity: Do States Jump through Them? International Security, 9(1):147–186. Lieber, Keir A. (2007) The New History of World War I and What It Means for International Relations Theory. International Security, 32(2): 155–191. Malici, Akan (2008) When Leaders Learn and When They Don’t: Mikhail Gorbachev and Kim Il Sung at the End of the Cold War. Albany: State University of New York Press. MccGwire, Jake (2018) A Game Theory Analysis of Donald Trump’s Proposed Tariff on Chinese Exports. Student Economic Review, 31(1): 69–77. Morrow, James D. (1994) Game Theory for Political Scientists. Princeton University Press: Princeton. Mueller, John (1989) Retreat from Doomsday: The Obsolescence of Major War. New York: Basic Books. Powell, Robert (1993) Guns, Butter and Anarchy. The American Political Science Review, 87(1):115–132. Pugh, George E. – John P. Mayberry (1973) Theory of Measures of Effectiveness for GeneralPurpose Military Forces: Part I. A Zero-Sum Payoff Appropriate for Evaluating Combat Strategies. Operations Research, 21(4): 867–885. Schelling, Thomas C. (1966) Arms and Influence. New Haven: Yale University Press. Selten, Reinhard (1975) Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory, 4(1): 25–55. Sick, Gary (1985) All Fall Down. New York: Penguin. Wagner, R. Harrison (1989) Bargaining in the Cuban Missile Crisis. In Ordeshook, P.C., (ed.) Models of Strategic Choice in Politics. Ann Arbor: University of Michigan Press. Zagare, Frank C. – Kilgour, D.M. (2000) Perfect Deterrence. Cambridge: Cambridge University Press. pp. 263–272. Koudela, Pál (2019). Game of Incomplete Information and National Security. Central European Political Science Review CEPSR 20(78) 73-96. Zagare, Frank C. (2014) A Game-Theoretic History of the Cuban Missile Crisis. Economies, 2(1): 20–44. Zagare, Frank C. (2014) A Game-Theoretic Explanation of the Cuban Missile Crisis. Department of Political Science, University at Buffalo: Buffalo. Zagare, Frank C. (2016) A General Explanation of the Cuban Missile Crisis. International Journal of Peace Economics and Peace Science, 1(1): 91–118.