The relationship between the U.S. and the Soviet Union is of crucial importance for world affairs. Despite changing political climates and technological capabilities, the overall tenor of this relationship has remained remarkably stable. Periods of harsh rhetoric and intense crises have alternated with periods of improving relations, but direct war between the superpowers has been avoided while efforts to establish sustained cooperation have not, thus far, been successful. Similarly, the arms race has proceeded at different speeds at different times, but the overall level of effort devoted to the military by each state has remained within a fairly narrow range. In this project the investigators use mathematical models and time series data in an effort to understand the underlying sources of this long term stability. Previous quantitative research on U.S.-Soviet relations has focused on arms race models first developed by Lewis Frye Richardson after World War I. Surprisingly, statistical tests have not revealed much hard evidence of the existence of reaction between the superpowers, and this puzzle has generated several lines of research. Some have offered more detailed models of the political processes of budgeting or procurement or more differentiated measures of military effort, but in this project the researchers develop a more general model meant to capture, at the aggregate level, the overall structure of superpower relations. The researchers argue that this "rivalry system" is stable essentially because of the "sophisticated reactions" occurring within each state. That is, important political actors in both states put forth great efforts to obtain information about the likely future behavior of the other state, and they use this information to inform and justify their policy proposals. Since policy makers are also concerned about the detrimental economic consequences of the arms race, each state's foreign and security policies are determined by competition between actors with different expectations of the level of threat and economic costs. It is this explicit focus on the expectational basis of rivalry that is most distinctive about the models to be examined in this proposed research. To estimate and analyze these models the investigators use data on such aggregate level characteristics as military budgets, weapons stocks, overall diplomatic relations, military interventions and other uses of force, economic conditions, and public and elite opinion. The researchers compile a vast amount of data on these topics and, since most previous policy analyses have focused on short term changes, they convert short data series from different sources (or from the same source at different times) into consistent long term data series. Once these data are collected and the properties of the various models compared, the investigators examine the rivalry system's likely response to hypothetical policy changes. The investigation should provide a more objective assessment of the natural dynamics of superpower rivalry.