Related papers: Multiplayer Games of War

We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…

We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor…

Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…

In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed…

We consider various probabilistic games with piles for one player or two players. In each round of the game, a player randomly chooses to add $a$ or $b$ chips to his pile under the condition that $a$ and $b$ are not necessarily positive. If…

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

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 introduce a two-player model of reinforcement learning with memory. Past actions of an iterated game are stored in a memory and used to determine player's next action. To examine the behaviour of the model some approximate methods are…

We consider a scenario where N users try to access a common base station. Associated with each user is its channel state and a finite queue which varies with time. Each user chooses his power and the admission control variable in a dynamic…

We consider the dynamics of player's strategies in repeated market games, where the selection of strategies is determined by a learning model. Prior theoretical analysis and experimental data show that after large number of plays the…

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…

Basically, in (one-player) war Real Time Strategy (wRTS) games a human player controls, in real time, an army consisting of a number of soldiers and her aim is to destroy the opponent's assets where the opponent is a virtual (i.e.,…

This paper analyzes a simple game with $n$ players. We fix a mean, $\mu$, in the interval $[0, 1]$ and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the…

In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at…

Log-linear learning has been extensively studied in both the game theoretic and distributed control literature. It is appealing for many applications because it often guarantees that the agents' collective behavior will converge in…

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…

$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and…

Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…