 In this context, an outcome (or its associated payoff vector) is Pareto optimal if there are no other outcomes that are better for some agents without being worse for  others.[10]  A solution is symmetric if the payoffs that agents receive from identical shares of a good are equivalent when those agents have equivalent utility functions, nonagreement points, and  strategies.[11]  It is scale invariant if the solution does not depend on how the payoffs are  represented.[12]  And it is reapplication stable if the application of a solution concept to a bargaining problem does not generate downstream bargaining problems among subsets of agents over the relative shares of a good they can  claim.[13]  While a solution is individually monotone if an agent is guaranteed to do at least as well when a bargaining problem is modified by expanding the feasible set to include new outcomes that are all more favorable to the agent. And it is population monotone if, for a given set of claimants, none lose while others gain merely because some members of the set depart and/or new claimants arrive.