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We study automated intrusion response for an IT infrastructure and formulate the interaction between an attacker and a defender as a partially observed stochastic game. To solve the game we follow an approach where attack and defense…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
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…
The paper studies ways in which the sets of a partition of a lattice in $\RR^n$ become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in $\RR^n$ gives rise to…
Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…
We develop an abstract axiomatic theory of tie-breaking. A tie-breaking input consists of a finite set N of players, a weak order on N representing the standings to be refined, and an auxiliary information item drawn from a set on which the…
Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…
Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart…
We study the recursive structure of P-positions in the chocolate game $C_{m,m}$, an impartial game played on an $m \times m$ chocolate bar. We show that the set of P-positions exhibits self-similar patterns that can be described and…
We consider a restricted game on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components obtained with a specific…
A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is…
We study impartial take away games on 2 unordered piles of finite nonnegative numbers of tokens $(x,y)$. Two players alternate in removing at least one and at most all tokens from the respective piles, according to certain rules, and the…
Interacting particle systems of interest in evolutionary game theory introduced in the probability literature consist of variants of the voter model in which each site is occupied by one player. The goal of this paper is to initiate the…
We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference…
We study a three-state Potts model extended by allowing cyclic dominance between the states as it appears for the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice when varying the temperature and the…
We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score,…
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic games (zero-sum and…
In this article, we study the evolution of the strategies in a sort of weighted three cornered game, Glico Game. This game has three strategies in each agent and three parameters in the payoff matrix. We divide the parameter region into 8…
This is a preprint of Chapter 2 in the following work: Marta Lewicka, A Course on Tug-of-War Games with Random Noise, 2020, Springer, reproduced with permission of Springer Nature Switzerland AG. We present the basic relation between the…
Subtraction games are a classical topic in Combinatorial Game Theory. A result of Golomb~(1966) shows that every subtraction game with a finite move set has an eventually periodic nim-sequence, but the known proof yields only an exponential…