Domestic Violence : Credible Threats and the Use of Services as Signals

Previous work on domestic violence has focused on the woman's threat point to leave violent relationships, and the impact of variables such as income on this threat point. She has a credible threat to leave if her utility outside the relationship is at least as great as that achieved by staying. This paper considers the possibility that her threat point is known only to her, and, therefore, she may have strategic incentives to signal that she will leave when in fact she may or may not. This strategic interaction is modeled in a game-theoretic sorting model in which she may bluff and he may or may not call her bluff. Services such as police intervention, shelters, and counseling may provide her with a signaling mechanism, and the model illustrates that the use of such signals may improve her situation even if she returns to the relationship. Thus, measuring the success of services by only the number of women who leave violent relationships may underestimate their value by ignoring the benefits offered to women who stay in their relationships. This model provides a rational explanation for why many battered women use services and/or call the police only to return to their relationships after a few days or weeks. In addition, the model illustrates that the overall power of women in the economy can provide external benefits for all women, regardless of their particular situation