This paper studies theoretically and experimentally how the possibility of a negative payoff to one player in 2-by-2 hawk-dove games affects the strategic behavior of both players. Exposing column players to a possibility of negative payoff allows us to examine if row players can anticipate the column players' loss aversion. A level-k model with loss averse agents predicts treatment effects across two versions of hawk-dove games with and without losses. Our data support a direct effect of loss aversion and fail to support the anticipation of loss aversion. Specifically, the column players in the treatment group are more likely to play Dove when they face losses; while, only few untreated participants acting as row players seem to anticipate such increased propensity of choosing Dove by their opponents. Further, a time effect is documented and found to be explained by increases in participants' depths of strategic reasoning over time.