The "joint costs" model states that the incentive to strike is inversely related to the total costs associated with workers' and firms' strike activities. Not only has this model been tested with mixed results, but also the joint costs model is problematic in explaining several stylized facts in the strike literature because higher strike costs do not always yield a lower incidence of strike activity. This paper illustrates how the joint cost model can yield these counterintuitive results. It shows that strike incidence need not decrease when joint strike costs increase. The innovation is to raise union and firm joint strike costs in an asymmetric way. Increasing a particular side's strike costs necessarily decreases its incentive to strike. However, in response, the other side's incentive can increase, since under a number of circumstances it holds out with a higher probability in order to collect the relatively larger expected rents coming about because the other side's implicit threat point decreases. To illustrate this, we model contract negotiations as a simple one-period game. (No need for more complex repeated games such as attrition since our point is only to show as simply as possible why the joint-costs model yields ambiguous results.) We use standard Hicksian concession curves to derive a payoff matrix. The payoff matrix results in contract negotiations following along the lines of a "game of chicken". The solution to the game yields no one stable pure Nash-equilibrium strategy, but instead a mixed strategy so that choices become probabilistic depending upon union and firm concession curve parameters. The results indicate that increasing either party's strike costs can have ambiguous effects on strike incidence. This ambiguity may explain why higher strike costs need not always lead to fewer strikes, and thus may account for the mixed success observed in studies that empirically test the joint costs model with strike incidence data. Although couched in terms of strikes, the results are equally applicable to other negotiation situations.