Distribution-Valued Solution Concepts

Under its conventional positive interpretation, game theory predicts that the mixed strategy pro?le of players in a noncooperative game will satisfy some setvalued solution concept. Relative probabilities of pro?les in that set are unspeci?ed, and all pro?les not satisfying it are implicitly assigned probability zero. However the axioms underlying Bayesian rationality say that we should reason about player behavior using a probability density over all mixed strategy pro?les, not using a subset of all such pro?les. Such a density over pro?les can be viewed as a solution concept that is distribution-valued rather than set-valued. A distribution-valued concept provides a best single prediction for any noncooperative game, i.e., a universal re?nement. In addition, regulators can use a distribution-valued solution concept to make Bayes optimal choices of a mechanism, as required by Savage's axioms. In particular, they can do this in strategic situations where conventional mechanism design cannot provide advice. We illustrate all of this on a Cournot duopoly game.Quantal Response Equilibrium, Bayesian Statistics, Entropic prior, Maximum entropy JEL Codes: C02, C11, C70, C72

A theory of unstructured bargaining using distribution-valued solution concepts

In experiments it is typically found that many joint utility outcomes arise in any given unstructured bargaining game. This suggests using a positive unstructured bargaining concept that maps a bargaining game to a probability distribution over outcomes rather than to a single outcome. We show how to "translate" Nash's bargaining axioms to apply to such distributional bargaining concepts. We then prove that a subset of those axioms forces the distribution over outcomes to be a power-law. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However in general these modes of the joint utility distribution are not Bayes-optimal predictions for the joint uitlity, nor are the bargains corresponding to those outcomes the most likely bargains. We then show how an external regulator can use distributional solution concepts to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System.JEL Codes:

Analyzing Policy Risk and Accounting for Strategy: Auctions in the National Airspace System

We examine the potential for simple auction mechanisms to efficiently allocate arrival and departure slots during Ground Delay Programs (GDPs). The analysis is conducted using a new approach to predicting strategic behavior called Predictive Game Theory (PGT). The difference between PGT and the familiar Equilibrium Concept Approach (ECA) is that PGT models produce distribution-valued solut tion concepts rather than set-valued ones. The advantages of PGT over ECA in policy analysis and design are that PGT allows for decision-theoretic prediction and policy evaluation. Furthermore, PGT allows for a comprehensive account of risk, including two types of risk, systematic and modeling, that cannot be considered with the ECA. The results show that the second price auction dominates the first price auction in many decision-relevant categories, including higher expected efficiency, lower variance in efficiency, lower probability of significant efficiency loss and higher probability of significant efficiency gain. These findings are despite the fact that there is no a priori reason to expect the second price auction to be more efficient because none of the conventional reasons for preferring second price over first price auctions, i.e. dominant strategy implementability, apply to the GDP slot auction setting.auction, ground delay program, entropy, predictive game theory, strategic risk

How to Use Decision Theory to Choose Among Mechanisms

We extend a recently introduced approach to the positive problem of game theory, Predictive Game Theory (PGT Wolpert (2008). In PGT, modeling a game results in a probability distribution over possible behavior profiles. This contrasts with the conventional approach where modeling a game results in an equilibrium set of possible behavior profiles. We analyze three PGT models. Two of these are based on the well-known quantal response and epsilon equilibrium concepts, while the third is entirely new to the economics literature. We use a Cournot game to demonstrate how to use our extension of PGT, concentrating on model combination, modeler uncertainty, and mechanism design. In particular, we emphasize how PGT allows a modeler to perform prediction and mechanism design in a manner that is fully consistent with decision theory. We do this even in situations where conventional approaches yield multiple equilibria, an ability that is necessary for a fully decision theoretic mechanism design. Where possible, PGT results are compared against equilibrium set analogs.

Game Mining: How to Make Money from those about to Play a Game

It is known that a player in a noncooperative game can benefit by publicly re- stricting their possible moves before start of play. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that is contingent on the game's outcome. We explore what happens when external parties (who we call game miners) discover this fact and seek to profit from it by entering an outcome-contingent contract with the players. We analyze various bargaining games between miners and players for determining such an outcome- contingent contract. We establish restrictions on the strategic settings in which a game miner can profit, and bounds on the game miner's profit given various structured bargaining games. These bargaining games include playing the players against one another, as well as allowing the players to pay the miner(s) for exclu- sivity and first-mover advantage. We also establish that when all players can enter contracts with miners, to guarantee the existence of equilibria it is necessary to assume that players can randomize over the contracts they make.

Clustering of Local Group distances: publication bias or correlated measurements? I. The Large Magellanic Cloud

The distance to the Large Magellanic Cloud (LMC) represents a key local rung of the extragalactic distance ladder. Yet, the galaxy's distance modulus has long been an issue of contention, in particular in view of claims that most newly determined distance moduli cluster tightly - and with a small spread - around the "canonical" distance modulus, (m-M)_0 = 18.50 mag. We compiled 233 separate LMC distance determinations published between 1990 and 2013. Our analysis of the individual distance moduli, as well as of their two-year means and standard deviations resulting from this largest data set of LMC distance moduli available to date, focuses specifically on Cepheid and RR Lyrae variable-star tracer populations, as well as on distance estimates based on features in the observational Hertzsprung-Russell diagram. We conclude that strong publication bias is unlikely to have been the main driver of the majority of published LMC distance moduli. However, for a given distance tracer, the body of publications leading to the tightly clustered distances is based on highly non-independent tracer samples and analysis methods, hence leading to significant correlations among the LMC distances reported in subsequent articles. Based on a careful, weighted combination, in a statistical sense, of the main stellar population tracers, we recommend that a slightly adjusted canonical distance modulus of (m-M)_0 = 18.49 +- 0.09 mag be used for all practical purposes that require a general distance scale without the need for accuracies of better than a few percent.Comment: 35 pages (AASTeX preprint format), 5 postscript figures; AJ, in press. For full database of LMC distance moduli, see http://astro-expat.info/Data/pubbias.htm

Development of a Defense Meteorological Satellite Program (DMSP) F-15 Disturbance Storm-time (Dst) Index

As the DoD\u27s use of space and space assets increases, so does its need for timely and accurate predictions of space weather conditions. A good understanding of the data from satellites together with data from ground stations can help model and determine variations in the space environment. An accurate, real-time Disturbance storm-time (Dst) index would be a primary input into current and future space weather models The Dst index is a measure of geomagnetic activity used to assess the severity of magnetic storms. The index is based on the average value of the horizontal component of the Earth\u27s magnetic field measured at four ground-based observatories. Use of the Dst as an index of storm strength is possible since the strength of the surface magnetic field at low latitudes is proportional to the energy content of the ring current, which increases during magnetic storms. Since ground-based magnetometers are not Air Force owned, development of a Dst index using the magnetometer from a DMSP satellite would remove the Air Force Weather Agency\u27s reliance on outside Dst sources. This research presents a method to create a Dst-like index using the magnetometer of the DMSP F-15 satellite. The solar quiet signal was determined for this magnetometer, and the resulting Dst index was compared against the official World Data Center Dst for several magnetic storms. Statistical analysis was accomplished using the paired t-test which shows good agreement between the DMSP derived Dst and ground-based index. In all of the storms analyzed, statistical results; mean, standard deviation, confidence intervals, etc., were always an order of magnitude smaller than the presented factors for error

Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations