In this paper, we establish some estimates of the global/local error bounds for the sets \(S^{\mathrm{Pareto}}_{\bar{y}}\), \(S^{\mathrm{W}}_{\le \bar{y}}\) and \(S^{\mathrm{W}}\), where \(S^{\mathrm{Pareto}}_{\bar{y}}\) is the set of efficient solutions of a unconstrained set-valued optimization problem (\(\mathcal {SP}\)) corresponding to an efficient value \(\bar{y}\) of a unconstrained set-valued optimization problem (\(\mathcal {SP}\)), \(S^{\mathrm{W}}_{\le \bar{y}}\) is the set of weakly efficient solutions of (\(\mathcal {SP}\)) corresponding to weakly efficient values smaller than a weakly efficient value \(\bar{y}\) and \(S^{\mathrm{W}}\) is the set of all weakly efficient solutions of (\(\mathcal {SP}\)). These estimates are expressed in terms of the approximate coderivative, the limiting Frechet/basic coderivatives and the coderivative of convex analysis. Thus, we establish conditions ensuring the existence of weak sharp minima for (\(\mathcal {SP}\)). We also extend the concept of the good asymptotic behavior to a convex or cone-convex set-valued map.