Long-term competition: A game-theoretic analysis

There have been continuing expressions of interest from a variety of quarters in the development of techniques for modelling national behavior in a long-term context of continuing international rivalry --- for short, ``long term competition''. The most characteristic feature of these models is that they extend over time in a fairly regular or repetitive manner. The underlying structure of possible actions and consequences remains the same, though parameters may vary and balances shift, and the decisions and policies of the national decision makers are by no means constrained to be constant or smoothly-varying, or even ``rational'' in any precisely identifiable sense. The use of game theory or an extension thereof is obviously indicated, and considerable theoretical progress has been made in this area. But the ability of the theory to handle real applications is still far from satisfactory. The trouble lies less with the descriptive modelling, --- i.e., formulating the ``rules of the game'' in a dynamic setting, than with the choice of a solu-tion concept that will do dynamic justice to the interplay of motivations of the actors. (Game theoreticians, like mathematical economists, have always been more comfortable with static than dynamic models.) Since any predictions, recommendations, etc. that a mathematical analysis can produce will likely be very sensitive to the rationale of the solution that is used, and since the big difficulties are conceptual rather than technical, it seems both possible and worthwhile to discuss salient features of the theory without recourse to heavy mathematical apparatus or overly formal arguments, and thereby perhaps make the issues involved accessible to at least some of the potential customers for the practical analyses that we wish we could carry out in a more satisfactory and convincing manner.