Related papers: Combinatorial Games with a Pass: A dynamical syste…
We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution is varied, a game can undergo a phase transition, in which…
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…
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…
Committed individuals, who features steadfast dedication to advocating strong beliefs, values, and preferences, have garnered much attention across statistical physics, social science, and computer science. This survey delves into the…
Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs. It is closely…
In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
Commitment devices are powerful tools that can influence and incentivise certain behaviours by linking them to rewards or punishments. These devices are particularly useful in decision-making, as they can steer individuals towards specific…
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…
Modern control systems are featured by their hierarchical structure composing of cyber, physical, and human layers. The intricate dependencies among multiple layers and units of modern control systems require an integrated framework to…
A new combinatorial game is given. It generalizes both Substraction and Nim. It is proved the computation of Nash equilibrium points in this new game is NP-hard.
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn,…
We study the effectiveness of iterated elimination of strictly-dominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore,…
Elucidating the mechanisms that lead to cooperation is still one of the main scientific challenges of current times, as many common cooperative scenarios remain elusive and at odds with Darwin's natural selection theory. Here, we study…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…
Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…