“In 1989, the Serbs commemorated their defeat at the hands of the Turks in the Battle of Blackbird Field, in 1389, and it formed the starting point for the Balkans wars of the 1990s.”
— Baumeister and Hastings (1997)

“You know the Spanish crusade against Muslims and the expulsions from Al Andalus [in 1492] are not so long ago.”
— Al Qaeda spokesman
(after claiming responsibility for the 2004 Madrid bombing)

It seems unlikely that remote events from over 500 years ago could have contemporary relevance to the groups above. Strange as it may seem, memory may matter - sometimes in a way that induces profoundly disturbing responses.
The “memories” that induced such horrific behavior — a self destructive war in one case and terrorism in another — were obviously not direct. Instead, they were shaped by oral or written accounts of history that were passed on through the generations. Our work explores a mechanism for memory creation of this kind, which social scientists in various fields refer to as social memory. According to anthropologist Carole L. Crumley, social memory is defined as follows:
“Social memory is the means by which information is transmitted among individuals and groups and from one generation to another. Not necessarily aware that they are doing so, individuals pass on their behaviors and attitudes to others in various contexts but especially through emotional and practical ties and in relationships among generations [...]”
Crumley’s definition is obviously neutral about how social memory is to be used. Societies do not always use their “practical ties and relationships among the generations” to create war, genocide, and terrorism. In some cases, however, it does appear that way. Historian William McNeill has this to say about the aftermath of World War I:
“The suddenness with which the tide of victory reversed directions after June 1918 gave Germans little time to adjust to defeat [...] The German army was still on French soil and its leaders could claim with enough plausibility to be convincing to those who wished to believe it that German soldiers had never been defeated in battle but lost the war because they had been betrayed by Social Democrats and other social revolutionaries in the rear [...] The Nazi movement founded itself on this myth [...]”
Our work attempts to develop these ideas formally. We investigate how destructive behavior can arise from social memory. In particular, we focus on how incorrect social memory can arise in equilibrium, even in the face of contrary physical evidence, and how it is critical in creating and perpetuating destructive conflict on a large scale.
Clearly, not all conflicts are universally destructive. Some yield clear winners and losers. Moreover, traditional equilibrium theories can account for at least some “moderately bad” outcomes without social memory having any special role. For instance, conflicts yielding long run payoffs above each player’s stage game minmax can be sustained in a standard repeated game if the players are patient enough. Alternatively, conflict can arise in a standard signalling model as a rational response to a partially revealing strategy.
Our interest in this work, however, lies in conflicts with no winners and losers; conflicts that are, in fact, so destructive that existing theories have trouble explaining them. In standard repeated games, for instance, the stage game minmax payoff builds in a modicum of self protection. A player can do no worse than to choose a stage game best response against anything that other players can conceivably do to him. Consider, for instance, the Battle of Verdun in 1916 in which hundreds of thousands of French and German soldiers died and where the final position of these armies at the end of the battle was no more than a few kilometers away from what it was at the beginning. It seems unlikely that such an outcome was above these countries’ minmax, and so a simple repeated game explanation would then require that both countries would be well compensated in the long run for carnage suffered in battle. Similarly, a drawback of signalling games is that they require agents to assign large likelihood to objective states of the world in which the conflict is desirable from at least one country’s point of view. Yet in some conflicts, World War I again being a case in point, decision makers are often aware at the outset that the hostilities are undesirable.1 
The goal of our work is not to discredit these models but rather to expand them in a way that can accommodate a formal definition and role for social memory in conflicts. We therefore posit a model that abstracts away from scenarios in which there are positive incentives for conflict, for instance because one social stratum stands to gain from what is an overall destructive conflict with another society. Consider a repeated game faced by two nations each period in which all out conflict is catastrophically bad for all involved in a way that everyone understands. Each nation in this conflict is a “dynastic” placeholder for individual decision makers who are finitely lived but care about what happens to future generations who inhabit the same nation-dynasty. Families, tribes, and ethnic groups are all ongoing entities with similar features.