Related papers: Guessing about Guessing: Practical Strategies for …

The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…

We present a couple of adaptive learning models of poker-like games, by means of which we show how bluffing strategies emerge very naturally, and can also be rational and evolutively stable. Despite their very simple learning algorithms,…

Since Pokemon Go sent millions on the quest of collecting virtual monsters, an important question has been on the minds of many people: Is going after the closest item first a time-and-cost-effective way to play? Here, we show that this is…

Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…

We consider a problem of guessing, wherein an adversary is interested in knowing the value of the realization of a discrete random variable $X$ on observing another correlated random variable $Y$. The adversary can make multiple (say, $k$)…

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…

Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…

We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the…

Deep Reinforcement Learning combined with Fictitious Play shows impressive results on many benchmark games, most of which are, however, single-stage. In contrast, real-world decision making problems may consist of multiple stages, where the…

We consider multiplayer stochastic games in which the payoff of each player is a bounded and Borel-measurable function of the infinite play. By using a generalization of the technique of Martin (1998) and Maitra and Sudderth (1998), we show…

Poker is a large complex game of imperfect information, which has been singled out as a major AI challenge problem. Recently there has been a series of breakthroughs culminating in agents that have successfully defeated the strongest human…

Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

Most people struggle with prioritizing work. While inexact heuristics have been developed over time, there is still no tractable principled algorithm for deciding which of the many possible tasks one should tackle in any given day, month,…

In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears,…

We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…

In multi-player card games such as Skat or Bridge, the early stages of the game, such as bidding, game selection, and initial card selection, are often more critical to the success of the play than refined middle- and end-game play. At the…

Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…

The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to different groups. We concentrate on two types of generalization:…

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…