Information Theoretic cutting of a cake

Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions the cake based on some fairness criterion. Fair division may be accomplished in a distributed or centralized way. Due to its natural and practical appeal, it has been a subject of study in economics. To best of our knowledge the role of partial information in fair division has not been studied so far from an information theoretic perspective. In this paper we study two important algorithms in fair division, namely "divide and choose" and "adjusted winner" for the case of two agents. We quantify the benefit of negotiation in the divide and choose algorithm, and its use in tricking the adjusted winner algorithm. Also we analyze the role of implicit information transmission through actions for the repeated divide and choose problem by finding a trembling hand perfect equilibrium for an specific setup. Lastly we consider a centralized algorithm for maximizing the overall welfare of the agents under the Nash collective utility function (CUF). This corresponds to a clustering problem of the type traditionally studied in data mining and machine learning. Drawing a conceptual link between this problem and the portfolio selection problem in stock markets, we prove an upper bound on the increase of the Nash CUF for a clustering refinement.Comment: Submitted to IEEE Transactions on Information Theor

Competitive division of a mixed manna

A mixed manna contains goods (that everyone likes) and bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale–Eisenberg): hence it is welfarist (determined by the set of feasible utility profiles), unique, continuous, and easy to compute. We show that the competitive division of a mixed manna is still welfarist. If the zero utility profile is Pareto dominated, the competitive profile is strictly positive and still uniquely maximizes the product of utilities. If the zero profile is unfeasible (for instance, if all items are bads), the competitive profiles are strictly negative and are the critical points of the product of disutilities on the efficiency frontier. The latter allows for multiple competitive utility profiles, from which no single-valued selection can be continuous or resource monotonic. Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods

State of New York Public Employment Relations Board Decisions from September 27, 1974

9_11_1975_PERB_BD_DecisionsOCR.pdf: 78 downloads, before Oct. 1, 2020