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Algorithmic Decision-Making in Multi-Agent Systems: Votes and Prices
178 Seiten, Dissertation Universität Köln (2018), Softcover, A5
In the first part of this thesis, we study pricing problems to maximize revenue. Our model is known as leader-follower games or Stackelberg pricing games introduced by the economist von Stackelberg. A distinguished player, the leader, chooses prices for a set of items, and the other players, the followers, each seek to buy a minimum cost feasible subset of the items.
The goal of the leader is to maximize her revenue, which is determined by the sold items and their prices. Most previously studied cases of such games can be captured by a combinatorial model where we have one follower, a base set of items, some with fixed prices, some priceable, and constraints on the subsets that are feasible for the follower.
In the second part of this thesis, we study committee election. In committee elections it is often assumed, that voters only approve or disapprove each candidate, or that they rank all candidates as it is common for single-winner elections. We propose an intermediate approach where the voters rank the candidate into a fixed number of groups. This allows more diverse votes as approval votes but leaves more freedom than in a strict total order. As a generalization, we introduce cardinal preferences: Voters specify a dissatisfaction value towards both membership and non-membership of a candidate in a committee.