Pareto Optimal Allocation under Uncertain Preferences

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under two natural uncertainty models: (1) the lottery model in which each agent has an independent probability distribution over linear orders and (2) the joint probability model that involves a joint probability distribution over preference profiles. For both of the models, we present a number of algorithmic and complexity results.Comment: Preliminary Draft; new results & new author

Stable marriage with general preferences

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP-complete, showing this way that a natural attempt to resolve the existence (or not) of 3D stable matchings is bound to fail.Comment: This is an extended version of a paper to appear at the The 7th International Symposium on Algorithmic Game Theory (SAGT 2014

The Private Value of Public Pensions

Individual retirement savings accounts are replacing or supplementing public basic pensions. However at decumulation, replacing the public pension with an equivalent private sector income stream may be costly. We value the Australian basic pension by calculating the wealth needed to generate an equivalent payment stream using commercial annuities or phased withdrawals, but still accounting for investment and longevity risks. At age 65, a retiree needs an accumulation of about 8.5 years earnings to match the public pension in real value and insurance features. Increasing management fees by 1% raises required wealth by about one year's earnings. Delaying retirement by 5 years lowers required wealth by about one half year's earnings. Phased withdrawals have money's worth ratios close to 0.5 suggesting that private replacement costs are high.social security; longevity risk; phased withdrawal; stochastic present value