1,346 research outputs found
On Iterated Dominance, Matrix Elimination, and Matched Paths
We study computational problems arising from the iterated removal of weakly
dominated actions in anonymous games. Our main result shows that it is
NP-complete to decide whether an anonymous game with three actions can be
solved via iterated weak dominance. The two-action case can be reformulated as
a natural elimination problem on a matrix, the complexity of which turns out to
be surprisingly difficult to characterize and ultimately remains open. We
however establish connections to a matching problem along paths in a directed
graph, which is computationally hard in general but can also be used to
identify tractable cases of matrix elimination. We finally identify different
classes of anonymous games where iterated dominance is in P and NP-complete,
respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical
Aspects of Computer Science (STACS
An O(nlogn) algorithm for the two-machine flow shop problem with controllable machine speeds
Production Planning;Scheduling;produktieleer/ produktieplanning
The computational complexity of rationalizing Pareto optimal choice behavior
We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.
The computational complexity of rationalizing Pareto optimal choice behavior.
We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.
Sequential voting and agenda manipulation
We study the possibilities for agenda manipulation under strategic voting for two prominent sequential voting procedures: the amendment procedure and the successive procedure. We show that a well known result for tournaments, namely that the successive procedure is (weakly) more manipulable than the amendment procedure at any given preference profile, extends to arbitrary majority quotas. Moreover, our characterizations of the attainable outcomes for arbitrary quotas allow us to compare the possibilities for manipulation across different quotas. It turns out that the simple majority quota maximizes the domain of preference profiles for which neither procedure is manipulable, but at the same time neither the simple majority quota nor any other quota uniformly minimizes the scope of manipulation once this becomes possible. Hence, quite surprisingly, simple majority voting is not necessarily the optimal choice of a society that is concerned about agenda manipulation
Implementation Theory
This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered
Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas
Games provide fertile research domains for algorithmic research. Often, game research helps solve real-world problems through the testing and refinement of search algorithms in game domains. Other times, game research finds limits for certain algorithms. For example, the game of Go proved intractable for the Min-Max with Alpha-Beta pruning algorithm leading to the popularity of Monte-Carlo based search algorithms. Although effective in Go, and game domains once ruled by Alpha-Beta such as Lines of Action, Monte-Carlo methods appear to have limits too as they fall short in tactical domains such as Hex and Chess. In a continuation of this type of research, two new games, Crossings and Epaminondas, are presented, analyzed and used to test two Monte-Carlo based algorithms: Upper Confidence Bounds applied to Trees (UCT) and Heuristic Guided UCT (HUCT). Results indicate that heuristic knowledge can positively affect UCT\u27s performance in the lower complexity domain of Crossings. However, both agents perform worse in the higher complexity domain of Epaminondas. This identifies Epaminondas as another domain that poses difficulties for Monte Carlo agents
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