Related papers: Compactification of Extensive Game Structures and …
Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is…
Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem…
We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad…
Simple adaptive procedures that converge to correlated equilibria are known to exist for normal form games (Hart and Mas-Colell 2000), but no such analogue exists for extensive-form games. Leveraging inspiration from Zinkevich et al.…
Heifetz, Meier, and Schipper (2013) introduced dynamic game with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form…
Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play,…
Complex environments and tasks pose a difficult problem for holistic end-to-end learning approaches. Decomposition of an environment into interacting controllable and non-controllable objects allows supervised learning for non-controllable…
This paper studies scenarios of cyclic dominance in a coevolutionary spatial model in which game strategies and links between agents adaptively evolve over time. The Optional Prisoner's Dilemma (OPD) game is employed. The OPD is an extended…
NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
We introduce an order-invariant reinforcement learning framework for black-box combinatorial optimization. Classical estimation-of-distribution algorithms (EDAs) often rely on learning explicit variable dependency graphs, which can be…
Higher-order interactions are prevalent in real-world complex systems and exert unique influences on system evolution that cannot be captured by pairwise interactions. We incorporate game transitions into the higher-order prisoner's dilemma…
Behavior trees (BTs) are an optimally modular framework to assemble hierarchical hybrid control policies from a set of low-level control policies using a tree structure. Many robotic tasks are naturally decomposed into a hierarchy of…
In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing…
We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show…
Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain and has been long discussed in…
We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…
Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning…
The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are…
Modern chess engines achieve superhuman performance through deep tree search and regressive evaluation, while human players rely on intuition to select candidate moves followed by a shallow search to validate them. To model this…