Our results demonstrate the possibility that participants, even in the face of imperfect but mounting evidence pointing to the truth, rely exclusively on intra−dynastic messages to gauge the best course of action. Weighing the various possible intentions and mistakes that may generate their predecessors’ behavior, we show that it is possible that the beliefs of the current participants may stray very far from what is actually taking place. In other words, social memory within and across societies can be systematically incorrect. Catastrophic and perpetual all out conflicts may then actually materialize in a variety of ways provided everyone making decisions today is sufficiently concerned about the future.
To illustrate the mechanism by which this occurs, consider a world in which there are two dynasties, France and Germany. These countries are engaged in a repeated “Game of Conflict”. In a Game of Conflict, there is at least one “destructive” action profile which takes both countries below their “individually rational” (minmax) payoff levels in the stage game. We refer to this profile as “all out war.” Notice that if both countries had perfect memory of the past then all out war could not occur with high frequency since, with perfect memory, long-run equilibrium payoffs must lie above the stage game minmax.
Consider an equilibrium in which all out war occurs with arbitrarily high frequency. Each war epoch starts at a predetermined date (but the logic easily extends to a war epoch brought about by some, possibly random, exogenous payoff irrelevant event like the assassination of an Archduke). A war epoch continues until some possibly distant point in the future at which time the slaughter will be over, and peace will prevail again. To rationalize this scenario each side believes that plunging into war is in the long run interest of their country. The question in the mind of both sides is: how good will peace be for them once it prevails? Critically, both sides must think that peacetime will be a lot worse for them if they fail to wage war today.
This is possible in the dynastic Game of Conflict because peaceful epochs come in three very different varieties: one that is good for both sides (“cooperation”), one that is bad for one side and good for the other (“domination” by one country over the other), and a third one in which the two sides are reversed. Suppose, then, that France did not wage war. Then the equilibrium entails that peace in that case simply consists of domination of France by Germany. This asymmetric peace continues for a short time until the next war epoch, at which point a long phase of all out war resumes. But why should France engage in such costly slaughter? After all, it does not have anything more to lose during peace times: these are already good for Germany and bad for France . Indeed, if France had full memory about the past history, it would have an incentive not to choose the war option since it would then see clearly that this option places its long run payoff below its stage game minmax.
This is where the possibility of systematically incorrect social memory becomes critical. We demonstrate how France, relying on its own historiography (passed down from one generation to the next) rather than on available evidence, suffers from the illusion that peace times are not asymmetrically biased against it. If such an illusion can be maintained for long enough in the face of mounting evidence against it, and if the future matters a lot for everyone, then our argument is complete and a world with very frequent destructive all out wars is compatible with rational equilibrium behavior.
To summarize, we show that there exist equilibria in the dynastic Game of Conflict with the following properties. (1) All out war occurs with arbitrarily high frequency. (2) Physical evidence is ignored−i.e., neither beliefs nor actions condition on evidence from the past.  (3) Social memory following counterfactual histories may be incorrect; in fact, there are certain possible histories after which social memory is maximally incorrect in the following sense. Using a standard hypothesis testing procedure, and given any level of confidence, the null hypothesis that a certain event took place is rejected by a statistician who observes the accumulated evidence. However, all participants’ beliefs assign probability 1 to the very same event.
It is worth noting that our construction does not depend on anyone’s failure to understand the consequences of war. Everyone in this model correctly anticipates that it will be horrific.2  Rather, what matters is the failure of future leaders to comprehend some of the various counterfactual options off path available to present leaders. Hence, moving forward, current leaders are led to the inescapable conclusion that war is necessary. This logic and its ugly consequences do not arise in standard repeated games with infinitely−lived players.
Crucially, messages can in principle convey more information than any imperfect physical evidence. This is because they are sent after the current action profile is observed. It turns out that this is suffcient to make viable equilibria in which physical evidence is ignored, but the messages convey the “wrong” information to future individuals. To underscore this point, we examine a variation of the dynastic model in which information is further degraded so that present actions of the rival country are not directly observed. All dynastic members observe the same imperfect evidence about the rival. We show that, in any pure strategy equilibrium, messages would be useless in this case, and so participants would be forced to confront the evidence. The perpetual state of frequent all out war sketched above cannot arise in this case.