In this thesis we study the optimal role assignment in jury voting. Jurors have to decide between two states of nature. Jurors cannot directly observe the state of nature, but only a noisy signal, that is correlated with the true state of nature. Some jurors are better than the other, and higher ability jurors receive signals that more likely lead to the correct choice. Not all jurors vote simultaneously, and jurors that vote later are informed on what previous jurors have voted. We want to know what the optimal role assignment, if we have jurors with different ability levels. In a two juror advisor-decider scheme, the first juror has the role of advisor and the second juror is the decider. The advisor passes his vote to the decider, and the decider’s choice is the final decision the of the whole decision process. For random signals with linear-, β- and Gaussian probability densities, the best jurors should be the decider. For three member casting vote schemes, the first two jurors vote simultaneously. If the decision is not unanimous, then there is no majority decision, and the casting juror breaks the tie. Besides receiving his own signal, the casting juror is informed on what the other jurors have voted. For random signals with linear-, β - and Gaussian densities, reliability is maximised, when the median ability juror has the casting vote.

A principal-agent problem is a mathematical framework for modelling contractual relationships, where a principal delegates tasks to an agent in exchange for reward. Many real life contracts are of this type. The agent does not have the same objectives as the principal and he possesses hidden information. Two types of hidden information is generally considered: moral hazard (hidden action) and adverse selection (hidden type). This asymmetry of information can be exploited by the agent for his own benefits, which can reduce the principal's utility. The goal is find a mechanism, in the form of a contract, that aligns the principal's and agent's objectives and maximises the principal's utility. Previous economic studies focuses on finding analytical solutions on specific cases. In this study we consider numerical solution approaches for a principal agent-problem with moral hazard, and a generalised principal-agent problem with moral hazard and adverse selection problem. The moral hazard problem is a bi-level programming problem and it is solved by assuming the agent's optimal effort is an implicit function dependent on the contract. The generalised principal agent problem is an infinite programming problem. For that we propose two numerical solution methods: the discretisation method and the basis function method. Both are tested on a option contract problem with moral hazard and adverse selection. From the experiment, the discretisation method seems to be the better performer.