Related papers: Expected characteristic in Tunnels & Trolls charac…
Suppose we have $n$ dice, each with $s$ faces (assume $s\geq n$). On the first turn, roll all of them, and remove from play those that rolled an $n$. Roll all of the remaining dice. In general, if at a certain turn you are left with $k$…
The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in…
A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical…
We consider (random) strategic interactions in a large population consisting of a variety of players. A rational player chooses actions that maximize certain utility functions, while a behavioral player chooses actions based on preferences…
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes.…
We investigate how to efficiently predict play personas based on playtraces. Play personas can be computed by calculating the action agreement ratio between a player and a generative model of playing behavior, a so-called procedural…
Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such…
The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…
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…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
Given a (possibly infinite) subset $A$ of the natural numbers, we ask how many times a fair six-sided die must be rolled until the rolled numbers add up to an element of $A$. Using a one-dimensional dynamic programming recursion together…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
We analyze what happens to the average duration of a game of Chutes and Ladders as the probability of rolling $\delta \in \{ 1,2,3,4,5,6\}$ approaches 100%. We utilize Markov models, and Monte Carlo simulations in Python. We also introduce…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
Dice control involves "setting" the dice and then throwing them carefully, in the hope of influencing the outcomes and gaining an advantage at craps. How does one test for this ability? To specify the alternative hypothesis, we need a…
We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T),…
Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…
We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of…
We model the formation of networks as a game where players aspire to maximize their own centrality by increasing the number of other players to which they are path-wise connected, while simultaneously incurring a cost for each added…