Related papers: The $k$-flip Ising game
A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…
We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method,…
This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on…
Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…
We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th…
In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates…
We investigate how the time evolution of different kinetic Ising models depends on the initial conditions of the dynamics. To this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise. We…
This paper presents an in-depth statistical analysis of an experiment designed to measure the extent to which players in a simple game behave according to a popular behavioral economic model. The p-beauty contest is a multi-player number…
This paper addresses the problem of steering a discrete-time linear dynamical system from an initial Gaussian distribution to a final distribution in a game-theoretic setting. One of the two players strives to minimize a quadratic payoff,…
We consider a network of N noisy bistable elements with global time-delayed couplings. In a two-state description, where elements are represented by Ising spins, the collective dynamics is described by an infinite hierarchy of coupled…
We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this paper we consider the scenario when Maker plays randomly and Breaker is "clever", and…
Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In Statistical Physics the Kinetic Ising Model has been introduced to describe…
This paper deals with N-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected…
A deck of $n$ cards is shuffled by repeatedly moving the top card to one of the bottom $k_n$ positions uniformly at random. We give upper and lower bounds on the total variation mixing time for this shuffle as $k_n$ ranges from a constant…