The Role of Social Memory in All-Out War

Recall McNeill’s discussion of the Nazi myth. The problem was not so much that the Germans did not know what happened. Rather, it was that they misunderstood why it happened. The catastrophe of the German defeat was interpreted by many, including Hitler, as a betrayal or a lack of will by civilians: “a deep distrust of civilian steadfastness, based on Hitler’s memories of 1918, governed Germany’s domestic policy during the first phases of World War II.”3 
But would Hitler have believed a message that exonerated civilians in the rear? In the model, the message deviating from the expected plays this role. This message indicates that the German civilian leadership chose the protective action D instead of the self-destructive action W. If the deviating message were sent, however, it would have been discounted completely by Hitler, who would have concluded instead that the message was sent in error, despite the fact that message is an equilibrium response to the self protective action D. In these circumstances, the German civilian leadership opts for W instead of D since the latter entails that a distrustful future German decision maker would unwittingly hurt Germany following the choice of D. In sum, the future German leader’s belief that his predecessor chose W on path is correct, but his understanding of why it was chosen is not.

Conclusion

Social memory is embodied in a society’s vicarious beliefs about the past. These beliefs are shaped by both intergenerational communication and the imperfect physical evidence from the past. To formalize it entails a detailed model of the intergenerational communication within dynastic societies.
We show that there exist equilibria in a canonical Game of Conflict in which “all out war” occurs with arbitrarily high frequency. In these equilibria physical evidence is ignored and, in fact, beliefs of one or both parties are maximally incorrect after certain events.
Significantly, these equilibria can occur despite the fact that there are no objective states of the world in which the conflict is desirable from anyone’s point of view. These outcomes could not be attained in a standard infinitely repeated game. Because messages can, in principle, convey more information than any imperfectly informative physical evidence, there are equilibria in which the current generation focuses only on the messages. Ironically, social memory can be maximally incorrect precisely because it relies on sources that can be more informative than hard evidence.
Two further issues bear mentioning here. The first concerns a critical robustness test for sequential equilibrium. The strategies used in this equilibrium remain sequentially rational even if we consider the trembles that generate the equilibrium beliefs when they are arbitrarily small, but before they have completely shrunk to zero. Intuitively, the robustness property we have just claimed tells us that the equilibrium on which we have focused throughout the paper survives the possibility that play does in fact stray off the equilibrium path with positive (albeit arbitrarily small) probability.
Second, we have focused our attention entirely on “bad” equilibria with frequent all out wars. The implication is that systematically wrong social memory is a bad thing. But there is a flip-side to this which highlights the possible “good” consequences of wrong social memory. Precisely because very bad payoffs can be sustained on path, these payoffs can be used as “punishments” off it.
Whether cooperation can in general be sustained more easily in the dynastic game is an open question at this point. The question of how the possibility of systematically inaccurate social memory might lead to the emergence of better equilibria is clearly both interesting and potentially important. We leave this issue for future research.

Luca Anderlini is Professor of Economics, Georgetown University.
Dino Gerardi is Associate Professor of Economics, Yale University.
Roger Lagunoff is Professor of Economics, Georgetown University.
This paper is an adaptation of “Social Memory and Evidence from the Past”, of the Yale Cowles Foundation Working Papers Series. The original paper may be read at http://cowles.econ.yale.edu/P/cd/d16a/d1601.pdf.