Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach

This thesis examines settings where multiple decision makers with conflicting interests benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in joint single-source shortest path problems and joint weighted minimum colouring problems. The primary focus of the thesis are problems where each agent corresponds to a vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the shortest paths from the supplier to all other vertices in the graph. The optimal solution is a shortest path tree of the graph and the aim is to allocate the cost of this shortest path tree amongst the agents. The thesis defines shortest path tree problems, proposes allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core allocations for shortest path tree games are introduced and polyhedral properties of the core are studied. Moreover, computational results on finding the core and the nucleolus of shortest path tree games for the application of cost allocation in Wireless Multihop Networks are presented. The secondary focus of the thesis are problems where each agent is interested in having access to a number of facilities but can be in conflict with other agents. If two agents are in conflict, then they should have access to disjoint sets of facilities. The aim is to allocate the cost of the minimum number of facilities required by the agents amongst them. The thesis models these cost allocation problems as a class of cooperative games called weighted minimum colouring games, and characterises total balancedness and submodularity of this class of games using the properties of the underlying graph

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Identification of gene-gene interactions for Alzheimer's disease using co-operative game theory

Thesis (Ph.D.)--Boston UniversityThe multifactorial nature of Alzheimer's Disease suggests that complex gene-gene interactions are present in AD pathways. Contemporary approaches to detect such interactions in genome-wide data are mathematically and computationally challenging. We investigated gene-gene interactions for AD using a novel algorithm based on cooperative game theory in 15 genome-wide association study (GWAS) datasets comprising of a total of 11,840 AD cases and 10,931 cognitively normal elderly controls from the Alzheimer Disease Genetics Consortium (ADGC). We adapted this approach, which was developed originally for solving multi-dimensional problems in economics and social sciences, to compute a Shapely value statistic to identify genetic markers that contribute most to coalitions of SNPs in predicting AD risk. Treating each GWAS dataset as independent discovery, markers were ranked according to their contribution to coalitions formed with other markers. Using a backward elimination strategy, markers with low Shapley values were eliminated and the statistic was recalculated iteratively. We tested all two-way interactions between top Shapley markers in regression models which included the two SNPs (main effects) and a term for their interaction. Models yielding a p-value<0.05 for the interaction term were evaluated in each of the other datasets and the results from all datasets were combined by meta-analysis. Statistically significant interactions were observed with multiple marker combinations in the APOE regions. My analyses also revealed statistically strong interactions between markers in 6 regions; CTNNA3-ATP11A (p=4.1E-07), CSMD1-PRKCQ (p=3.5E-08), DCC-UNC5CL (p=5.9e-8), CNTNAP2-RFC3 (p=1.16e-07), AACS-TSHZ3 (p=2.64e-07) and CAMK4-MMD (p=3.3e-07). The Shapley value algorithm outperformed Chi-Square and ReliefF in detecting known interactions between APOE and GAB2 in a previously published GWAS dataset. It was also more accurate than competing filtering methods in identifying simulated epistastic SNPs that are additive in nature, but its accuracy was low in identifying non-linear interactions. The game theory algorithm revealed strong interactions between markers in novel genes with weak main effects, which would have been overlooked if only markers with strong marginal association with AD were tested. This method will be a valuable tool for identifying gene-gene interactions for complex diseases and other traits

Quality and Investment Decisions in Hospital Care when Physicians are Devoted Workers

This paper analyses the decision to invest in quality by a hospital in an environment where doctors are devoted workers, i.e. they care for specific aspects of the output they produce. We assume that quality is the result of both an investment in new technology and the effort of the medical staff. Hospital services are paid on the basis of their marginal cost of production while the number of patients treated depends on a purchasing rule which discriminates for the level and timing of the investment. We show that the presence of devoted doctors affects the trade-off between investment and the purchasing rule so that for the hospital it is not always optimal to anticipate the investment decision.Hospital technology, Devoted worker, Quality, Irreversible investment, Real options

Marginal contribution, reciprocity and equity in segregated groups: Bounded rationality and self-organization in social networks

We study the formation of social networks that are based on local interaction and simple rule following. Agents evaluate the profitability of link formation on the basis of the Myerson-Shapley principle that payoffs come from the marginal contribution they make to coalitions. The NP-hard problem associated with the Myerson-Shapley value is replaced by a boundedly rational 'spatially' myopic process. Agents consider payoffs from direct links with their neighbours (level 1) which can include indirect payoffs from neighbours' neighbours (level 2) and up to M-levels that are far from global. Agents dynamically break away from the neighbour to whom they make the least marginal contribution. Computational experiments show that when this self-interested process of link formation operates at level 2 neighbourhoods, agents self-organize into stable and efficient network structures that manifest reciprocity, equity and segregation reminiscent of hunter gather groups. A large literature alleges that this is incompatible with self-interested behaviour and market oriented marginality principle in the allocation of value. We conclude that it is not this valuation principle that needs to be altered to obtain segregated social networks as opposed to global components, but whether it operates at level 1 or level 2 of social neighbourhoods. Remarkably, all M>2 neighbourhood calculations for payoffs leave the efficient network structures identical to the case when M=2.

Strategic Regulators and the Choice of Rulemaking Procedures: The Selection of Formal vs. Informal Rules in Regulating Hazardous Waste

The selection of decisionmaking procedures by regulatory agencies is examined, using the EPA and its implementation of the Resource Conservation and Recovery Act as a source of data. The role that congressional selection of agency procedures plays in the efforts of Congress to control agency policy is refined

Ageism & Cooperation

Discrimination based on age can affect same-aged and intergenerational interactions, presenting socially and economically undesirable phenomena. To investigate the effects of age stereotypes on cooperation, we presented older adults (over age 50) and younger adults (under age 25) with belief elicitation tasks (about anticipated interactions) and then a series of same, different, and unknown-aged group interactions in a Sender-Receiver game. Compared to the in-group (the age group they belong to) both younger and older participants stereotyped the out-group (the age group they did not belong to) as relatively different and more uncooperative than observed to be. We have only partial support for the notion that stereotypers behaved strategically: while younger stereotypers acted relatively uncooperatively and earned more, older stereotypers acted relatively cooperatively (despite out-group beliefs) and earned less. We discuss the implications of these findings for social identity theory, stereotype theory, and intergenerational interactions in an aging society