Related papers: Partizan Subtraction Games

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any two initial…

For a poset $P$, an Ungar move sends $P$ to $P\setminus T$, where $T$ is some subset of maximal elements of $P$. With these Ungar moves, Defant, Kravitz, and Williams define the Ungar games, where two players alternate making nontrivial…

We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…

Parrondo's coin-tossing games comprise two games, $A$ and $B$. The result of game $A$ is determined by the toss of a fair coin. The result of game $B$ is determined by the toss of a $p_0$-coin if capital is a multiple of $r$, and by the…

In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is…

We present a deterministic algorithm, solving discounted games with $n$ nodes in $n^{O(1)}\cdot (2 + \sqrt{2})^n$-time. For bipartite discounted games our algorithm runs in $n^{O(1)}\cdot 2^n$-time. Prior to our work no deterministic…

The ability of a deterministic, plastic system to learn to imitate stochastic behavior is analyzed. Two neural networks -actually, two perceptrons- are put to play a zero-sum game one against the other. The competition, by acting as a kind…

Let $S_n$ be the total gain in $n$ repeated St.\ Petersburg games. It is known that $n^{-1}(S_n-n\log_2n)$ converges in distribution to a random element $Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with…

The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call…

There are $n$ independent Bernoulli random variables with parameters $p_i$ that are observed sequentially. Two players, A and B, act in turns starting with player A. Each player has the possibility on his turn, when $I_k=1$, to choose…

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to…

The triangle game introduced by Chv\'{a}tal and Erd\H{o}s (1978) is one of the most famous combinatorial games. For $n,q\in\mathbb{N}$, the $(n,q)$-triangle game is played by two players, called Maker and Breaker, on the complete graph…

We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the…

We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order sqrt(n) from the naive law-of-large numbers…

Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the…

I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only…

We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…

We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The…

We introduce achievement positional games, a convention for positional games which encompasses the Maker-Maker and Maker-Breaker conventions. We consider two hypergraphs, one red and one blue, on the same vertex set. Two players, Left and…