Related papers: Refining Constructive Hybrid Games
We present a self-contained introduction to the theory of chip-firing games on metric graphs, as well as the more recent theory of tropical Prym varieties. We briefly discuss the connection between these notions and their algebraic…
We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
We extend a smooth dynamical systems averaging technique to a class of hybrid systems with a limit cycle that is particularly relevant to the synthesis of stable legged gaits. After introducing a definition of hybrid averageability…
We present constructive provability logic, an intuitionstic modal logic that validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and…
An important class of differential interactive games, namely, one of the laced interactive games is considered. A posteriori analysis of such games (including the virtual a posteriori decomposition of a collective control) is discussed.…
We propose a definition of the category of hybrid systems in which executions are special types of morphisms. Consequently morphisms of hybrid systems send executions to executions. We plan to use this result to define and study networks of…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two…
We study combinatorial games under mis\`ere convention. Several sets of games have been considered earlier to better understand the behaviour of mis\`ere games. We here connect several of these sets. In particular, we prove that comparison…
There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…
Productive societies feature high levels of cooperation and strong connections between individuals. Public Goods Games (PGGs) are frequently used to study the development of social connections and cooperative behavior in model societies. In…
Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq…
Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions,…
In this paper, we consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect…
We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal…
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…