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In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies…
In this work, an abstract and general language for the fundamental objects underlying dynamic games under probabilistic uncertainty is developed. Combining the theory of decision trees by Al\'os-Ferrer--Ritzberger (2005) and a Harsanyian…
Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the…
Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific…
This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space…
The Principle of Least Action has evolved and established itself as the most basic law of physics. This allows us to see how this fundamental law of nature determines the development of the system towards states with less action, i.e.,…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
Game-theoretic approaches are envisioned to bring human-like reasoning skills and decision-making processes for autonomous vehicles (AVs). However, challenges including game complexity and incomplete information still remain to be addressed…
Trust models are widely used in various computer science disciplines. The main purpose of a trust model is to continuously measure trustworthiness of a set of entities based on their behaviors. In this article, the novel notion of "rational…
In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two…
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…
We propose a new framework for imitation learning -- treating imitation as a two-player ranking-based game between a policy and a reward. In this game, the reward agent learns to satisfy pairwise performance rankings between behaviors,…
The paper explores the nature of risk, providing a characterization using the categories of the Basic Formal Ontology (BFO). It argues that the category Risk is a subclass of BFO:Role, contrasting it with a similar view classifying Risk as…
In this paper, we study a famous discrete dynamical system, the Chip Firing Game, used as a model in physics, economics and computer science. We use order theory and show that the set of reachable states (i.e. the configuration space) of…
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
In this paper an interesting application of mathematics in economics is presented: the formulation of the theory of consumer basic problem, grounded on the concept of preferences relation and operationalized with optimization tools.
In this work we continue the study of non-chaotic asymptotic correlations in many element systems and discuss the emergence of a new notion of asymptotic correlation -- partial order -- in the Choose the Leader (CL) system. Similarly to the…