Related papers: Variance decompositions for extensive-form games

We study an elementary two-player card game where in each round players compare cards and the holder of the smallest card wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn…

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to…

Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…

We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…

We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry,…

Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the…

Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations,…

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…

Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization.…

In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect,…

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…