Adversarial risk analysis (ARA) provides decision-theoretic arguments to manage uncertainty in competitive decision-making environments. This paper introduces efficient algorithmic approaches to approximate ARA solutions in multi-stage games, covering both sequential and simultaneous settings, through augmented probability simulation. Two examples concerning international piracy and air combat illustrate the proposed methodology.
To make a choice in the presence of multiple criteria, we generally use an aggregation function which determines, for each alternative, the balance of its strengths and weaknesses and its overall evaluation. The aggregation function uses weights to adapt the model to the decision-maker's value system, by specifying the importance of the criteria and possibly their interactions. In this paper, we propose a noise-tolerant active learning method for these parameters, which not only effectively reduces the indeterminacy of the weights to identify an optimal or near-optimal decision among a given set of alternatives, but also simultaneously determines a predictive model of preferences capable of making relevant choices for the decision-maker on new instances. These outcomes are achieved by leveraging a general disagreement-based active learning approach that is theoretically guaranteed to be tolerant to noisy answers. The proposed method applies to various weighted aggregation functions, linear or not, classically used in decision theory.
Conditional preference networks (CP-nets) have received significant attention for modeling preferences over combinations of features. However, dominance testing, the problem of inferring from a CP-net whether one outcome is always preferred over another, is NP-hard, requiring exponential time in practice. In this paper, we introduce the use of independent relaxed subproblems as a heuristic for faster inference from CP-nets. We show how to relax the constraints in the conditional preference tables and partition the network, yielding smaller subproblems that can be solved easily. The lengths of these solutions can then be added together to provide a heuristic for informed search algorithms such as A* and applied to dominance testing in CP-nets. We prove that the resulting additive heuristic function is admissible and consistent, guaranteeing optimality and completeness. We show from experiments on randomly generated binary and multivalued CP-nets that our method performs better than the state of the art, and can further be combined with other pruning techniques, resulting in greatly improved performance for dominance testing.
Electoral control is a scenario where an election chair changes the structure of an election by actions such as adding or deleting either candidates or voters with the goal of either making a favorite candidate win or precluding a despised candidate's victory. Much work has been done on the computational complexity of controlling elections for single-winner voting rules, yet much less work on the control complexity for multiwinner voting rules which aim at electing not only a single winner but a winning committee of candidates. Meir et al. [20] initiated the investigation of electoral control for multiwinner voting rules, including single nontransferable vote (SNTV) and bloc voting. We study these two rules with respect to control by adding, deleting, or replacing candidates.
In Subset Sum Game as studied by Pieterse and Woeginger [Theory of Computing Systems, 2021], two players alternatingly fill a common knapsack each with items from a private collection. The goal of Player A is to reach a value of at least T_ , whereas Player B may follow different strategies. Subset Sum Game is NP-complete and solvable in pseudopolynomial time if Player B greedily selects the biggest available item in each turn; the game is PSPACE-complete, however, if Player B plays a hostile strategy where the only aim is to avoid that Player A wins. We continue the study of the game with these two strategies for Player B. First, we provide a faster pseudopolynomial-time algorithm for a greedy Player B and show that the problem with a hostile Player B is fixed-parameter tractable with respect to the knapsack capacity C. Moreover, we study the influence of further parameters such as T_ , the number of rounds in the game, and the number of different numbers in the input on the complexity of the problem. Second, we consider a further variant of the game, called Protective Subset Sum Game, where Player A additionally has the goal that Player B reaches a value of at least T_ . In a nutshell, we show that most algorithms for the nonprotective variant can be transferred to Protective Subset Sum Game.
