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

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

Game theory

game theory

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principled formulation of bounded rationality and a set of new types of mean field theory in statistical physics. It also shows that those topics are fundamentally one and the same.Comment: 17 pages, no figures, accepted for publicatio

Optimal Feedback Control Rules Sensitive to Controlled Endogenous Risk-Aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (Karp 1987; Whittle 1989, 1990; Chow 1993, amongst others). More realistic, the proposed approach deals with endoge- nous risks that are under the control of the decision-maker. It has strong implications on the policy decisions adopted by the decision-maker during the entire planning horizon.Controlled stochastic environment, rational decision-maker, adaptive control, optimal path, feedback optimal strategy, endogenous risk-aversion, dynamic active learning.Controlled stochastic environment, rational decision-maker, adaptive control, optimal path, feedback optimal strategy, endogenous risk-aversion, dynamic active learning.

Information Disclosure Under Different Modes of Regulation

In this study we assume that the governments are uncertain about the future product demand in a standard eco-dumping model. Allowing the governments to obtain information from firms, we examine governments.and .rms.incentives to share information. We show that, when the governments regulate the polluting .rms through emission standards, then, the governments and the .rms will reach an agreement concerning information sharing. The opposite holds, when the governments regulate pollution through emission taxes.

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.Algebraic Riccati equations;linear quadratic differential games;Nash equilibria