Related papers: Average Weights and Power in Weighted Voting Games
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified…
In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of…
In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for…
This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…
We investigate the problem of computing the probability of winning in an election where voter attendance is uncertain. More precisely, we study the setting where, in addition to a total ordering of the candidates, each voter is associated…
The topic of the present paper is a generalized St.\ Petersburg game in which the distribution of the payoff $X$ is given by $P(X=sr^{k-1})=pq^{k-1}$, $k=1,2,\ldots$, where $p+q=1$, and $s,\,r>0$. As for main results, we first extend…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
We study a mixed population of adaptive agents with small and large memories, competing in a minority game. If the agents are sufficiently adaptive, we find that the average winnings per agent can exceed that obtainable in the corresponding…
In this paper we study rankings induced by power indices of players in simple game models of bicameral legislatures. For a bicameral legislature where bills are passed with a simple majority vote in each house we give a condition involving…
The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties of a composite function involving the Dirichlet divisor function and a generalized minimal power function.…
We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain…
In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…
We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite…
We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…
Research on peer effects in sociology has been focused for long on social influence power to investigate the social foundations for social interactions. This paper extends Xu(2011)'s large--network--based game model by allowing for…
We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement…
This paper presents a new use case for continuous crowdsourcing, where multiple players collectively control a single character in a video game. Similar approaches have already been proposed, but they suffer from certain limitations: (1)…
We study a game where one player selects a random function, and the other has to guess that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to…