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A directed graph where there is exactly one edge between every pair of vertices is called a tournament. Finding the “best” set of vertices of a tournament is a well studied problem in social choice theory. A tournament solution takes a tournament as input and outputs a subset of vertices of the input tournament. However, in many applications, for example, choosing the best set of drugs from a given set of drugs, the edges of the tournament are given only implicitly and knowing the orientation of an edge is costly. In such scenarios, we would like to know the best set of vertices (according to some tournament solution) by “querying” as few edges as possible. We, in this paper, precisely study this problem for commonly used tournament solutions: given an oracle access to the edges of a tournament T , find f(T) by querying as few edges as possible, for a tournament solution f. We first show that the set of Condorcet non-losers in a tournament can be found by querying 2n−⌊log n⌋−2 edges only and this is tight in the sense that every algorithm for finding the set of Condorcet non-losers needs to query at least 2n−⌊log n⌋−2 edges in the worst case, where n is the number of vertices in the input tournament. We then move on to study other popular tournament solutions and show that any algorithm for finding the Copeland set, the Slater set, the Markov set, the bipartisan set, the uncovered set, the Banks set, and the top cycle must query Ω(n2) edges in the worst case. On the positive side, we are able to circumvent our strong query complexity lower bound results by proving that, if the size of the top cycle of the input tournament is at most k, then we can find all the tournament solutions mentioned above by querying O(nk + n log n / log(1− 1 / k ) ) edges only.
Standard (offline) control scenarios in elections (such as adding, deleting, or partitioning either voters or candidates) have been studied for many voting systems, natural and less natural ones, and the related control problems have been classified in terms of their complexity. However, for one of the most important natural voting systems, the Borda Count, only a few such complexity results are known. We reduce the number of missing cases by pinpointing the complexity of three control scenarios for Borda elections, including some that arguably are among the practically most relevant ones. We also study online candidate control, an interesting dynamical, partial-information model due to Hemaspaandra et al. (2012a), who mainly focused on general complexity bounds by constructing artificial voting systems—only recently they succeeded in classifying four problems of online candidate control for one natural voting system: sequential plurality (Hemaspaandra et al. 2016). We settle the complexity of another four natural cases: constructive and destructive online control by deleting and adding candidates in sequential Borda elections.
Before engaging in a group venture agents may seek commitments from other members in the group and, based on the level of participation (i.e. the number of actually committed participants), decide whether it is worth joining the venture. Alternatively, agents can delegate this costly process to a (beneficent or non-costly) third-party, who helps seek commitments from the agents. Using methods from Evolutionary Game Theory, this paper shows that, in the context of Public Goods Game, much higher levels of cooperation can be achieved through such centralized commitment management. It provides a more efficient mechanism for dealing with commitment free-riders, those who are not willing to bear the cost of arranging commitments whilst enjoying the benefits provided by the paying commitment proposers. We show that the participation level plays a crucial role in the decision of whether an agreement should be formed; namely, it needs to be more strict in terms of the level of participation required from players of the centralized system for the agreement to be formed; however, once it is done right, it is much more beneficial in terms of the level of cooperation and social welfare achieved. In short, our analysis provides important insights for the design of multi-agent systems that rely on commitments to monitor agents' cooperative behavior.
This paper studies a criteria-based mechanism for nurturing and enhancing agents' group-benefiting individual efforts whenever the agents are self-interested. The idea is that only those agents that meet the criteria get to benefit from the group effort, giving an incentive to contribute even when it is otherwise individually irrational. Specifically, the paper provides a comprehensive equilibrium analysis of a threshold-based criteria mechanism for the common cooperative information gathering application, where the criteria is set such that only those whose contribution to the group is above some pre-specified threshold can benefit from the contributions of others. The analysis results in a closed form solution for the strategies to be used in equilibrium and facilitates the numerical investigation of different model properties as well as a comparison to the dual mechanism according to only an agent whose contribution is below the specified threshold gets to benefit from the contributions of others. One important contribution enabled through the analysis provided is in showing that, counter-intuitively, for some settings the use of the above-threshold criteria is outperformed by the use of the below-threshold criteria as far as collective and individual performance is concerned.
We propose Kont, a formal framework for comparing normative multiagent systems (nMASs) by computing tradeoffs among liveness (something good happens) and safety (nothing bad happens). Safety-focused nMASs restrict agents' actions to avoid undesired enactments. However, such restrictions hinder liveness, particularly in situations such as medical emergencies. We formalize tradeoffs using norms, and develop an approach for understanding to what extent an nMAS promotes liveness or safety. We propose patterns to guide the design of an nMAS with respect to liveness and safety, and prove their correctness. We further quantify liveness and safety using heuristic metrics for an emergency healthcare application. We show that the results of the application corroborate our theoretical development.
The Cooperative Target Observation (CTO) problem has been of great interest in the multi-agents and robotics literature due to the problem being at the core of a number of applications including surveillance. In CTO problem, the observer agents attempt to maximize the collective time during which each moving target is being observed by at least one observer in the area of interest. However, most of the prior works for the CTO problem consider the targets movement to be Randomized. Given our focus on surveillance domain, we modify this assumption to make the targets strategic and present two target strategies namely Straight-line strategy and Controlled Randomization strategy. We then modify the observer strategy proposed in the literature based on the K-means algorithm to introduce five variants and provide experimental validation. In surveillance domain, it is often reasonable to assume that the observers may themselves be a subject of observation for a variety of purposes by unknown adversaries whose model may not be known. Randomizing the observers actions can help to make their target observation strategy less predictable. As the fifth variant, we therefore introduce Adjustable Randomization into the best performing observer strategy where the observer can adjust the expected loss in reward due to randomization depending on the situation.
Multiagent sequential decision making has seen rapid progress with formal models such as decentralized MDPs and POMDPs. However, scalability to large multiagent systems and applicability to real world problems remain limited. To address these challenges, we study multiagent planning problems where the collective behavior of a population of agents affects the joint-reward and environment dynamics. Our work exploits recent advances in graphical models for modeling and inference with a population of individuals such as collective graphical models and the notion of finite partial exchangeability in lifted inference. We develop a collective decentralized MDP model where policies can be computed based on counts of agents in different states. As the policy search space over counts is combinatorial, we develop a sampling based framework that can compute open and closed loop policies. Comparisons with previous best approaches on synthetic instances and a real world taxi dataset modeling supply-demand matching show that our approach significantly outperforms them w.r.t. solution quality.
Decentralized Markov Decision Process (Dec-MDP) provides a rich framework to represent cooperative decentralized and stochastic planning problems under transition uncertainty. However, solving a Dec-MDP to generate coordinated yet decentralized policies is NEXP-Hard. Researchers have made significant progress in providing approximate approaches to improve scalability with respect to number of agents. However, there has been little or no research devoted to finding guarantees on solution quality for approximate approaches considering multiple (more than 2 agents) agents. We have a similar situation with respect to the competitive decentralized planning problem and the Stochastic Game (SG) model. To address this, we identify models in the cooperative and competitive case that rely on submodular rewards, where we show that existing approximate approaches can provide strong quality guarantees ( a priori, and for cooperative case also posteriori guarantees). We then provide solution approaches and demonstrate improved online guarantees on benchmark problems from the literature for the cooperative case.
We define a class of parameterised infinite state multi-agent systems (MAS) that is unbounded in both the number of agents composing the system and the domain of the variables encoding the agents. We analyse their verification problem by combining and extending existing techniques in parameterised model checking with predicate abstraction procedures. The resulting methodology addresses both forms of unboundedness and provides a technique for verifying unbounded MAS defined on infinite-state variables. We illustrate the effectiveness of the technique on an infinite-domain variant of an unbounded version of the train-gate-controller.