Continuous fictitious play in zero-sum games

Robinson (1951) showed that the learning process of Discrete Fictitious Play converges from any initial condition to the set of Nash equilibria in two-player zero-sum games. In several earlier works, Brown (1949, 1951) makes some heuristic arguments for a similar convergence result for the case of Continuous Fictitious Play (CFP). The standard reference for a formal proof is Harris (1998); his argument requires several technical lemmas, and moreover, involves the advanced machinery of Lyapunov functions. In this note we present a simple alternative proof. In particular, we show that Brown''s convergence result follows easily from a result obtained by Monderer et al. (1997).mathematical economics;

Linkage and Multilevel Governance

Economic models of emissions trading implicitly assume a simple unitary governance structure, where a single regulator designs and enforces an emissions trading program. The Kyoto Protocol, however, employs a multilevel governance structure in which international, regional, national, sub-national, and even private actors have significant roles in designing and enforcing the trading program. Under this structure, international trading of credits requires complex linking of disparate regional, national, and subnational trading program. This paper describes the multilevel governance model employed in the Kyoto Protocol and then analyzes some of the problems this complexity creates for the project of creating an international market in environmental benefit credits to realize technology transfer benefits. This paper shows that multilevel governance creates costs that can interfere with technology transfer and free trade in credits. It concludes that rules sufficiently stringent to encourage technology transfer in the face of significant additionality problems will likely burden free trade in credits. Unfortunately, rules sufficiently relaxed to make international transactions simple and problem free will lack integrity and spawn non-additional credits greatly limiting the Kyoto Protocol\u27s potential as a technology transfer mechanism. The paper suggests that these governance complexities counsel against automatic embrace of linkage

Extended Iterative Scheme for QCD: the Four-Gluon Vertex

We study the self-consistency problem of the generalized Feynman rule (nonperturbatively modified vertex of zeroth perturbative order) for the 4-gluon vertex function in the framework of an extended perturbation scheme accounting for non-analytic coupling dependence through the Lambda scale. Tensorial structure is restricted to a minimal dynamically closed basis set. The self-consistency conditions are obtained at one loop, in Landau gauge, and at the lowest approximation level (r=1) of interest for QCD. At this level, they are found to be linear in the nonperturbative 4-gluon coefficients, but strongly overdetermined due to the lack of manifest Bose symmetry in the relevant Dyson-Schwinger equation. The observed near decoupling from the 2-and-3-point conditions permits least-squares quasisolutions for given 2-and-3-point input within an effective one-parameter freedom. We present such solutions for N_F=2 massless quarks and for the pure gluon theory, adapted to the 2-and-3-point coefficients determined previously.Comment: 46 pages, 11 figure

Singularities at rims in three-dimensional fluid flow

Asymptotic solutions are presented for Stokes flow near circular rims in three-dimensional geometries. Using nonstandard toroidal coordinates, asymptotic analytical expressions are derived for different corner angles. In comparison to the two-dimensional case, an extra critical corner angle value is derived, below which the swirling behaviour of a particle is absent. Illustrations of the motion of a particle near a rim in a three-dimensional fluid flow are given for different corner angles

A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes

Alternating offers bargaining with loss aversion

The Rubinstein alternating offers bargaining game is reconsidered under the assumption that each player is loss averse and the associated reference point is equal to the highest turned down offer of the opponent in the past. This makes the payoffs and therefore potential equilibrium strategies dependent on the history of play. A subgame perfect equilibrium is constructed, in which the strategies depend on the history of play throughthe current reference points. It is shown that this equilibrium is unique under some assumptions that it shares with the equilibrium in the classical model: immediate acceptance of equilibrium offers, indifference between acceptance and rejection of such offers, and strategies depending only on the current reference points. It is also shown that in this equilibrium loss aversion is a disadvantage. Moreover, a relation with asymmetric Nashbargaining is established, where a player’s bargaining power is negatively related to own loss aversion and positively to the opponent’s loss aversion.mathematical economics;

Deep Reinforcement Learning based Optimal Control of Hot Water Systems

Energy consumption for hot water production is a major draw in high efficiency buildings. Optimizing this has typically been approached from a thermodynamics perspective, decoupled from occupant influence. Furthermore, optimization usually presupposes existence of a detailed dynamics model for the hot water system. These assumptions lead to suboptimal energy efficiency in the real world. In this paper, we present a novel reinforcement learning based methodology which optimizes hot water production. The proposed methodology is completely generalizable, and does not require an offline step or human domain knowledge to build a model for the hot water vessel or the heating element. Occupant preferences too are learnt on the fly. The proposed system is applied to a set of 32 houses in the Netherlands where it reduces energy consumption for hot water production by roughly 20% with no loss of occupant comfort. Extrapolating, this translates to absolute savings of roughly 200 kWh for a single household on an annual basis. This performance can be replicated to any domestic hot water system and optimization objective, given that the fairly minimal requirements on sensor data are met. With millions of hot water systems operational worldwide, the proposed framework has the potential to reduce energy consumption in existing and new systems on a multi Gigawatt-hour scale in the years to come

Distributed generation: definition, benefits and issues

This paper starts from the observation that there is a renewed interest in small-scale electricity generation. The authors start with a survey of existing small-scale generation technologies and then move on with a discussion of the major benefits and issues of small-scale electricity generation. Different technologies are evaluated in terms of their possible contribution to the listed benefits and issues. Small-scale generation is also commonly called distributed generation, embedded generation or decentralised generation. In a final section, an attempt is made to define the latter concepts more precisely. It appears that there is no consensus on a precise definition as the concept encompasses many technologies and applications.Distributed generation, embedded generation, electricity