Seminar by Arijit Sen (IIM Calcutta)

Motivated by the writings of Thomas Schelling, and by records of various ‘armed transgressions’ in world history, we formulate a Transgression Game of asymmetric information between a Transgressor and a Responder – where the former is privately informed about his value of farther transgression, and the latter might have private information about her cost of confronting transgression. In this adversarial game, played over a (possibly) large but finite potential transgression positions, we identify the Transgressor’s equilibrium transgression strategy – whether he will transgress in a Salami-esque manner (by escalating transgression via a sequence of hops) or in a Whole-Hoggish manner (by transgressing in one large leap), and the corresponding equilibrium confrontation strategy of the Responder (who, in principle, can confront at every position that the Transgressor progresses to).

We clarify that it is easy to justify Salami Tactics as a ‘behavioural equilibrium’ strategy in our game (especially when the Responder’s only option is to confront transgression by a disproportionately large response). In contrast, in the set of Perfect Bayesian Equilibria (especially ones that satisfy an ‘obvious’ belief refinement), the Transgressor either employs: (a) a Whole-Hoggish strategy of leaping from the initial status quo position to the final position, or (b) a mildly Salami-esque strategy of hopping / jumping from the status quo to a ‘specific’ intermediate position, and then (if he ‘survives’) jumping to the final position. In equilibrium, the Responder certainly confronts the Transgressor at the final position; but if she does confront him at the intermediate position, she does so with a ‘low enough’ probability.