The power index at infinity: Weighted voting in sequential infinite anonymous games

After we describe the waiting queue problem, we identify a partially observable 2n+1-player voting game with only one pivotal player; the player at the n-1 order. Given the simplest rule of heterogeneity presented in this paper, we show that for any infinite sequential voting game of size 2n+1, a power index of size n is a good approximation of the power index at infinity, and it is difficult to achieve. Moreover, we show that the collective utility value of a coalition for a partially observable anonymous game given an equal distribution of weights is n²+n. This formula is developed for infinite sequential anonymous games using a stochastic process that yields a utility function in terms of the probability of the sequence and voting outcome of the coalition. Evidence from Wikidata editing sequences is presented and the results are compared for 10 coalitions

La teoría de juegos y la matemática

Realizada la consulta bibliográfica se encuentra amplia aplicación e investigación en las áreas económicas en comparación con la cantidad de trabajos en otras áreas, esto llama altamente la atención debido a que la teoría de juegos puede ser aplica por ejemplo, subastas y licitaciones, mecanismos de decisión pública, y economía laboral, Aguado, Juan C. (2015) considera que las aplicaciones son muy variadas y abarcan desde el Comportamiento de los individuos hasta Iteraciones en Oligopolios, de igual manera Monsalve, S., Arévalo J. (2005) consideran que las aplicaciones de la teoría de juegos van más allá del área económica, siendo posible su aplicación en el estudio del comportamiento estratégico de los individuos en diferentes ambientes, influencia de las expectativas, toma de decisiones distribución de la información, tensión entre equilibrio y eficiencia, diseño de contratos, etc.El objetivo de este artículo es presentar los conceptos básicos de la teoría de juegos y como esta apoya a la matemática. Guzmán, M de. (1984) Opina que “el sabor a juego puede impregnar de tal modo el trabajo, que lo haga mucho más motivado, estimulante, incluso agradable y, para algunos, aún apasionante”, el empleo de juegos podría ayudar a disminuir el temor de los jóvenes hacia la matemática sin olvidar lo que el mismo Guzman, M de. (1984) dice: “la matemática no es sólo diversión, sino ciencia e instrumento de exploración de su realidad propia mental y externa y así ha de plantearse”. “Teoría de Juegos y Emprendimiento” trabajo realizado por Moreira, Rodas y Contreras en la Universidad de Guayaquil y “Pensamiento Estratégico, Teoría de Juegos y Comportamiento Humano” trabajo realizado por Herrero y Pinedo en el 2005 son algunos de los antecedentes encontrados

A Generalized Training Approach for Multiagent Learning

This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime wherein Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, $\alpha$-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and applies readily to general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and $\alpha$-Rank. We demonstrate the competitive performance of $\alpha$-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where $\alpha$-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain

Approximation methods for infinite bayesian stackelberg games: Modeling distributional payoff uncertainty.

ABSTRACT Game theory is fast becoming a vital tool for reasoning about complex real-world security problems, including critical infrastructure protection. The game models for these applications are constructed using expert analysis and historical data to estimate the values of key parameters, including the preferences and capabilities of terrorists. In many cases, it would be natural to represent uncertainty over these parameters using continuous distributions (such as uniform intervals or Gaussians). However, existing solution algorithms are limited to considering a small, finite number of possible attacker types with different payoffs. We introduce a general model of infinite Bayesian Stackelberg security games that allows payoffs to be represented using continuous payoff distributions. We then develop several techniques for finding approximate solutions for this class of games, and show empirically that our methods offer dramatic improvements over the current state of the art, providing new ways to improve the robustness of security game models

Approximation methods for infinite bayesian stackelberg games: Modeling distributional payoff uncertainty.

ABSTRACT Game theory is fast becoming a vital tool for reasoning about complex real-world security problems, including critical infrastructure protection. The game models for these applications are constructed using expert analysis and historical data to estimate the values of key parameters, including the preferences and capabilities of terrorists. In many cases, it would be natural to represent uncertainty over these parameters using continuous distributions (such as uniform intervals or Gaussians). However, existing solution algorithms are limited to considering a small, finite number of possible attacker types with different payoffs. We introduce a general model of infinite Bayesian Stackelberg security games that allows payoffs to be represented using continuous payoff distributions. We then develop several techniques for finding approximate solutions for this class of games, and show empirically that our methods offer dramatic improvements over the current state of the art, providing new ways to improve the robustness of security game models

Addressing stability issues in mediated complex contract negotiations for constraint-based, non-monotonic utility spaces

Negotiating contracts with multiple interdependent issues may yield non- monotonic, highly uncorrelated preference spaces for the participating agents. These scenarios are specially challenging because the complexity of the agents’ utility functions makes traditional negotiation mechanisms not applicable. There is a number of recent research lines addressing complex negotiations in uncorrelated utility spaces. However, most of them focus on overcoming the problems imposed by the complexity of the scenario, without analyzing the potential consequences of the strategic behavior of the negotiating agents in the models they propose. Analyzing the dynamics of the negotiation process when agents with different strategies interact is necessary to apply these models to real, competitive environments. Specially problematic are high price of anarchy situations, which imply that individual rationality drives the agents towards strategies which yield low individual and social welfares. In scenarios involving highly uncorrelated utility spaces, “low social welfare” usually means that the negotiations fail, and therefore high price of anarchy situations should be avoided in the negotiation mechanisms. In our previous work, we proposed an auction-based negotiation model designed for negotiations about complex contracts when highly uncorrelated, constraint-based utility spaces are involved. This paper performs a strategy analysis of this model, revealing that the approach raises stability concerns, leading to situations with a high (or even infinite) price of anarchy. In addition, a set of techniques to solve this problem are proposed, and an experimental evaluation is performed to validate the adequacy of the proposed approaches to improve the strategic stability of the negotiation process. Finally, incentive-compatibility of the model is studied.Spain. Ministerio de Educación y Ciencia (grant TIN2008-06739-C04-04