Related papers: Guessing about Guessing: Practical Strategies for …
The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a…
An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…
Quitting games are one of the simplest stochastic games in which at any stage each player has only two possible actions, continue and quit. The game ends as soon as at least one player chooses to quit. The players then receive a payoff,…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
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…
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this…
We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…
We study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an…
Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
We empirically analyze a simple heuristic for large sparse set cover problems. It uses the weighted greedy algorithm as a basic building block. By multiplicative updates of the weights attached to the elements, the greedy solution is…
In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their…
We show the existence and effective computability of optimal winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their…
We analyze the following version of the deterministic \hats game. We have a graph $G$, and a sage resides at each vertex of $G$. When the game starts, an adversary puts on the head of each sage a hat of a color arbitrarily chosen from a set…
People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or…
The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, using such an agent involves the user exposing themselves to the risk that the…
Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…
It is noted that some unusual moves against a strong chess program greatly weaken its ability to see the serious targets of the game, and its whole level of play... It is suggested to create programs with different weaknesses in order to…