869 research outputs found
An experimental study of costly coordination
This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria nor do they alter the predictions of adjustment theories based on imitation or best response dynamics. As expected, however, increasing the effort cost lowers effort levels. Maximization of a stochastic potential function, a concept that generalizes risk dominance to continuous games, predicts this reduction in efforts. An error parameter estimated from initial two-person, minimum-effort games is used to predict behavior in other three-person coordination games
An Experimental Study of Costly Coordination
This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria, nor do they alter the predictions of dynamic adjustment theories based on imitation or best responses to others' decisions. As would be expected, however, increases in effort cost result in reduced effort levels. Average behavior in the final periods is consistent with a one-parameter stochastic generalization of the Nash equilibrium that is calculated by maximizing a "stochastic potential function." The noise parameter estimated from the initial two-person, minimum-effort games is used to predict behavior in subsequent experiments with three-person games, using both minimum and medium-effort payoff structures.coordination games, laboratory experiments, stochastic potential, logit equilibrium, bounded rationality, minimum effort game, median effort game
Penalty-regulated dynamics and robust learning procedures in games
Starting from a heuristic learning scheme for N-person games, we derive a new
class of continuous-time learning dynamics consisting of a replicator-like
drift adjusted by a penalty term that renders the boundary of the game's
strategy space repelling. These penalty-regulated dynamics are equivalent to
players keeping an exponentially discounted aggregate of their on-going payoffs
and then using a smooth best response to pick an action based on these
performance scores. Owing to this inherent duality, the proposed dynamics
satisfy a variant of the folk theorem of evolutionary game theory and they
converge to (arbitrarily precise) approximations of Nash equilibria in
potential games. Motivated by applications to traffic engineering, we exploit
this duality further to design a discrete-time, payoff-based learning algorithm
which retains these convergence properties and only requires players to observe
their in-game payoffs: moreover, the algorithm remains robust in the presence
of stochastic perturbations and observation errors, and it does not require any
synchronization between players.Comment: 33 pages, 3 figure
Riemannian game dynamics
We study a class of evolutionary game dynamics defined by balancing a gain
determined by the game's payoffs against a cost of motion that captures the
difficulty with which the population moves between states. Costs of motion are
represented by a Riemannian metric, i.e., a state-dependent inner product on
the set of population states. The replicator dynamics and the (Euclidean)
projection dynamics are the archetypal examples of the class we study. Like
these representative dynamics, all Riemannian game dynamics satisfy certain
basic desiderata, including positive correlation and global convergence in
potential games. Moreover, when the underlying Riemannian metric satisfies a
Hessian integrability condition, the resulting dynamics preserve many further
properties of the replicator and projection dynamics. We examine the close
connections between Hessian game dynamics and reinforcement learning in normal
form games, extending and elucidating a well-known link between the replicator
dynamics and exponential reinforcement learning.Comment: 47 pages, 12 figures; added figures and further simplified the
derivation of the dynamic
On the robustness of learning in games with stochastically perturbed payoff observations
Motivated by the scarcity of accurate payoff feedback in practical
applications of game theory, we examine a class of learning dynamics where
players adjust their choices based on past payoff observations that are subject
to noise and random disturbances. First, in the single-player case
(corresponding to an agent trying to adapt to an arbitrarily changing
environment), we show that the stochastic dynamics under study lead to no
regret almost surely, irrespective of the noise level in the player's
observations. In the multi-player case, we find that dominated strategies
become extinct and we show that strict Nash equilibria are stochastically
stable and attracting; conversely, if a state is stable or attracting with
positive probability, then it is a Nash equilibrium. Finally, we provide an
averaging principle for 2-player games, and we show that in zero-sum games with
an interior equilibrium, time averages converge to Nash equilibrium for any
noise level.Comment: 36 pages, 4 figure
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
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Chris Cannings: A Life in Games
Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career
The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies
This paper considers a class of models in which rank-based payoffs are sensitive to small amounts of noise in decision making. Examples include auction, price-competition, coordination, and location games. Observed laboratory behavior in these games is often responsive to asymmetric costs associated with deviations from the Nash equilibrium. These payoff asymmetry effects are incorporated in an approach that introduces noisy behavior via probabilistic choice. In equilibrium, behavior is characterized by a probability distribution that satisfies a "rational expectations" consistency condition: the beliefs that determine player's expected payoffs match the decision distributions that arise from applying a logit probabilistic choice function to those expected payoffs. We prove existence of a unique, symmetric logit (quantal response) equilibrium and derive comparative statics results. The paper provides a unified perspective on many recent laboratory studies of games in which Nash equilibrium predictions are inconsistent with both intuition and experimental evidence.logit equilibrium, quantal response equilibrium, probabilistic choice, auctions.
Acknowledgement Misspecification in Macroeconomic Theory
We explore methods for confronting model misspecification in macroeconomics. We construct dynamic equilibria in which private agents and policy makers recognize that models are approximations. We explore two generalizations of rational expectations equilibria. In one of these equilibria, decision makers use dynamic evolution equations that are imperfect statistical approximations, and in the other misspecification is impossible to detect even from infinite samples of time-series data. In the first of these equilibria, decision rules are tailored to be robust to the allowable statistical discrepancies. Using frequency domain methods, we show that robust decision makers treat model misspecification like time-series econometricians.
Of Ants and Voters:Maximum Entropy Prediction of Agent-Based Models with Recruitment
Maximum entropy predictions are made for the Kirman ant model as well as the Abrams-Strogatz model of language competition, also known as the voter model. In both cases the maximum entropy methodology provides good predictions of the limiting distribution of states, as was already the case for the Schelling model of segregation. An additional contribution, the analysis of the models reveals the key role played by relative entropy and the model in controlling the time horizon of the prediction
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