Related papers: The minimum size required of a solitaire army

In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…

2048 is a single player video game, played by millions mostly on mobile devices. We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256…

We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of…

Minimal balanced collections are a generalization of partitions of a finite set of n elements and have important applications in cooperative game theory and discrete mathematics. However, their number is not known beyond n = 4. In this…

Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be…

Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…

Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…

The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…

Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum…

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…

We study the structure of the underlying network of connections in the Minority Game. There is not an explicit interaction among the agents, but they interact via global magnitudes of the model and mainly through their strategies. We define…

In this paper we present results and analyses of a class of games in which heterogeneous agents are rewarded for being in a minority group. Each agent possesses a number of fixed strategies each of which are predictors of the next minority…

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,…

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an…

We introduce a new class of games, called social contribution games (SCGs), where each player's individual cost is equal to the cost he induces on society because of his presence. Our results reveal that SCGs constitute useful abstractions…

The Jump-Jump game, as a simple yet challenging casual game, provides an ideal testing environment for studying LLM decision-making capabilities. The game requires players to precisely control jumping force based on current position and…