A finite-state, finite-memory minimum principle, part 2

In part 1 of this paper, a minimum principle was found for the finite-state, finite-memory (FSFM) stochastic control problem. In part 2, conditions for the sufficiency of the minimum principle are stated in terms of the informational properties of the problem. This is accomplished by introducing the notion of a signaling strategy. Then a min-H algorithm based on the FSFM minimum principle is presented. This algorithm converges, after a finite number of steps, to a person - by - person extremal solution

Assessing the Impact of Game Day Schedule and Opponents on Travel Patterns and Route Choice using Big Data Analytics

The transportation system is crucial for transferring people and goods from point A to point B. However, its reliability can be decreased by unanticipated congestion resulting from planned special events. For example, sporting events collect large crowds of people at specific venues on game days and disrupt normal traffic patterns. The goal of this study was to understand issues related to road traffic management during major sporting events by using widely available INRIX data to compare travel patterns and behaviors on game days against those on normal days. A comprehensive analysis was conducted on the impact of all Nebraska Cornhuskers football games over five years on traffic congestion on five major routes in Nebraska. We attempted to identify hotspots, the unusually high-risk zones in a spatiotemporal space containing traffic congestion that occur on almost all game days. For hotspot detection, we utilized a method called Multi-EigenSpot, which is able to detect multiple hotspots in a spatiotemporal space. With this algorithm, we were able to detect traffic hotspot clusters on the five chosen routes in Nebraska. After detecting the hotspots, we identified the factors affecting the sizes of hotspots and other parameters. The start time of the game and the Cornhuskers’ opponent for a given game are two important factors affecting the number of people coming to Lincoln, Nebraska, on game days. Finally, the Dynamic Bayesian Networks (DBN) approach was applied to forecast the start times and locations of hotspot clusters in 2018 with a weighted mean absolute percentage error (WMAPE) of 13.8%

A Continuation Method for Nash Equilibria in Structured Games

Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact algorithms for computing Nash equilibria in structured game representations, including both graphical games and multi-agent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normal-form and extensive-form games due to Govindan and Wilson; they follow a trajectory through a space of perturbed games and their equilibria, exploiting game structure through fast computation of the Jacobian of the payoff function. They are theoretically guaranteed to find at least one equilibrium of the game, and may find more. Our approach provides the first efficient algorithm for computing exact equilibria in graphical games with arbitrary topology, and the first algorithm to exploit fine-grained structural properties of MAIDs. Experimental results are presented demonstrating the effectiveness of the algorithms and comparing them to predecessors. The running time of the graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. The algorithm for MAIDs can effectively solve games that are much larger than those solvable by previous methods

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201