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We analyse assignment problems in which not every agent is controlled by the central planner. The free agents search for vacant tasks autonomously, guided by their own preferences. The central planner, aiming to maximise the total value of the assignment, must take into account the behaviour of the uncontrolled agents. We model this situation as an n + 1-player game played between n free agents and the central planner. We show that it is a weakly dominant strategy for the free agents to choose tasks according to their true preferences. Contrarily, the strategy of the central planner in the resulting Nash Equilibrium is highly complex – we prove that it corresponds to the solution of a mixed integer bilevel optimisation problem. Finally, we demonstrate how this program can be reduced to a computationally much more manageable disjoint bilinear program.

The temperature based algorithm known as the Nomogram Method for the determination of a 95.45% death-time interval can be combined with non-temperature based (NTB) findings in the so called Compound Method (CM). The impact of such integration on the probability yielded by the resulting interval has however neither been described nor exploited. In fact the interval after integration of NTB findings rarely yields 95.45% probability. We present a technique, based on the conditional probability distribution that can be calculated if the NTB findings are taken into account, which ensures the probability inside the interval to be 95.45%. The technique was successfully applied to a set of 53 cases published by Henssge et al. and led to a reduction of the interval width up to more than 15% compared to the CM interval, whereas in other cases the interval width increased due to probability content of the CM intervals below 95.45%. A spreadsheet file in which the method proposed in this paper is implemented can be obtained upon email request from the author S. Potente