Related papers: On the Foundations of Dynamic Games and Probabilit…
The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of potential function for discrete-space stochastic systems. It is based on a…
Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we…
Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…
Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. Few studies focus on two-stage stochastic programs with this type of…
Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and…
Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…
In this paper we introduce the reactivity in decision-form games. The concept of reactivity allows us to give a natural concept of rationalizable solution for decision-form games: the solubility by elimination of sub-reactive strategies.…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
It is well known that reinforcement learning can be cast as inference in an appropriate probabilistic model. However, this commonly involves introducing a distribution over agent trajectories with probabilities proportional to exponentiated…
We revisit and reinterpret Selten's concept of subgame perfectness in the context of single agent normal form sequential decision making, which leads us to the concept of subtree perfectness. Thereby, we extend Hammond's characterization of…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…
Despite increasing attention paid to the need for fast, scalable methods to analyze next-generation neuroscience data, comparatively little attention has been paid to the development of similar methods for behavioral analysis. Just as the…
In this paper, we extend the Descent framework, which enables learning and planning in the context of two-player games with perfect information, to the framework of stochastic games. We propose two ways of doing this, the first way…
In \cite{ CLEVACKTHI, CLEVACK} an attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness, asymptotic analysis and parameter estimation for fully nonlinear evolutionary game…
Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice.…