scholarly journals Analytical Method for Mechanism Design in Partially Observable Markov Games

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 321
Author(s):  
Julio B. Clempner ◽  
Alexander S. Poznyak
Keyword(s):  
Mechanism Design ◽  
Analytical Method ◽  
Nash Equilibria ◽  
Common Knowledge ◽  
Markov Games ◽  
Markov Game ◽  
Joint Strategy ◽  
Average Utility ◽  
Distribution Vector ◽  
Partially Observable

A theme that become common knowledge of the literature is the difficulty of developing a mechanism that is compatible with individual incentives that simultaneously result in efficient decisions that maximize the total reward. In this paper, we suggest an analytical method for computing a mechanism design. This problem is explored in the context of a framework, in which the players follow an average utility in a non-cooperative Markov game with incomplete state information. All of the Nash equilibria are approximated in a sequential process. We describe a method for the derivative of the player’s equilibrium that instruments the design of the mechanism. In addition, it showed the convergence and rate of convergence of the proposed method. For computing the mechanism, we consider an extension of the Markov model for which it is introduced a new variable that represents the product of the mechanism design and the joint strategy. We derive formulas to recover the variables of interest: mechanisms, strategy, and distribution vector. The mechanism design and equilibrium strategies computation differ from those in previous literature. A numerical example presents the usefulness and effectiveness of the proposed method.

Mechanism Design and the Law

2017 ◽  
Author(s):  
Werner Güth
Keyword(s):  
Mechanism Design ◽  
Institutional Design ◽  
Common Knowledge ◽  
Legal Rules ◽  
Revelation Principle ◽  
Game Theoretic ◽  
The Law ◽  
Legal Mechanism ◽  
Dominance Solvability

Mechanism design is the game theoretic jargon for institutional design and the even older tradition (in German) of ‘Ordnungspolitik’ (institutional design policy). When implementing institutions or mechanisms (or simply rules of conduct) such regulation should usually be codified by complementing the law appropriately. This article first derives and discusses legal rules as traditionally justified and implemented legally. This is then confronted with game theoretic mechanism design, relying on Dominance Solvability or the Revelation Principle. It is argued that the Revelation Principle is very useful for welfaristic or, more generally, consequentialistic explorations of what is attainable but offers no practical basis for legal mechanism design due to its unrealistic common knowledge restrictions.

Institutional Regulation of Public Provision

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Werner Güth
Keyword(s):  
Mechanism Design ◽  
Institutional Design ◽  
Common Knowledge ◽  
Procedural Fairness ◽  
Equal Treatment ◽  
Public Provision ◽  
Public Authorities ◽  
Legal Traditions ◽  
Procedural Approach ◽  
Game Theoretic

AbstractAfter demonstrating that institutional design based on the rational choice approach is hardly ever applicable, we suggest a procedural alternative and demonstrate its applicability with a focus on the supply side of public authorities, i.e., on the “productive state.” Whereas the former approach, based on unrealistic common knowledge assumptions, is consequentialistic, procedural fairness relies on appealing requirements of non-arbitrariness and equal treatment. In our view, game theoretic mechanism design is useful to explore the consequentialistic – e.g., welfaristic – potential but is, except for specific situations, not implementable. Compared to this, procedural fairness is in line with actually used procedures and legal traditions. Although game theoretic mechanism design can be informative, its unrealistic assumptions justify the procedural approach, which can be rigorously defined by intuitive fairness requirements.

ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMES

2013 ◽  
Vol 15 (04) ◽  
pp. 1340026 ◽  
Author(s):  
PRASENJIT MONDAL ◽  
SAGNIK SINHA
Keyword(s):  
Stochastic Game ◽  
Transition Probability ◽  
Pollution Tax ◽  
Markov Games ◽  
Ordered Field ◽  
Markov Game ◽  
Ordered Field Property ◽  
Single Matrix ◽  
Zero Sum ◽  
Field Property

In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix/bimatrix game under discounted as well as limiting average (undiscounted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases.

Synthesis of Mechanisms Including Circuit Defects, Branch Defects and Input-Crank Rotatability

1992 ◽  
Author(s):  
Jyun-Cheng Cheng ◽  
Dilip Kohli
Keyword(s):  
Mechanism Design ◽  
Analytical Method ◽  
Input Output ◽  
Design Variables ◽  
Synthesis Of Mechanisms ◽  
Circuit Defects ◽  
Novel Concept ◽  
Output Equation

Abstract In this paper, an analytical method is developed for synthesizing linkages (with a quadratic input-output equation) which are free from circuit and branch defects and, in addition, may be required to have fully rotatable cranks. A novel concept called the range defect of the input link is introduced. It is shown that the range defect results in a circuit defect. Further, all circuit defects except those introduced as a result of range defects can be eliminated by eliminating branch defects. The circuit defect introduced by the range defect is eliminated by first eliminating the range defect and then eliminating the branch defect. Inequalities are developed as a function of mechanism design variables which represent the existence of range defects and therefore a possible circuit defect. The circuit defect identifiers are then developed and used in the synthesis of function generating planar four-bar and spatial RSSR linkages. The method developed is general and is applicable to any mechanism with a quadratic input-output equation such as RSSP, spherical 4-bar and 4R3P linkages.

Partially Observable Semi-Markov Games with Discounted Payoff

2006 ◽  
Vol 24 (5) ◽  
pp. 1035-1059 ◽  
Author(s):  
Mrinal K. Ghosh ◽  
Anindya Goswami
Keyword(s):  
Markov Games ◽  
Partially Observable

A Policy Improvement Algorithm for Solving a Mixture Class of Perfect Information and AR-AT Semi-Markov Games

2020 ◽  
Vol 22 (02) ◽  
pp. 2040008
Author(s):  
P. Mondal ◽  
S. K. Neogy ◽  
A. Gupta ◽  
D. Ghorui
Keyword(s):  
Perfect Information ◽  
Policy Improvement ◽  
Markov Games ◽  
Markov Game ◽  
Improvement Algorithm ◽  
Finite State ◽  
Markov Decision ◽  
Mixture Class ◽  
Zero Sum ◽  
Action Spaces

Zero-sum two-person discounted semi-Markov games with finite state and action spaces are studied where a collection of states having Perfect Information (PI) property is mixed with another collection of states having Additive Reward–Additive Transition and Action Independent Transition Time (AR-AT-AITT) property. For such a PI/AR-AT-AITT mixture class of games, we prove the existence of an optimal pure stationary strategy for each player. We develop a policy improvement algorithm for solving discounted semi-Markov decision processes (one player version of semi-Markov games) and using it we obtain a policy-improvement type algorithm for computing an optimal strategy pair of a PI/AR-AT-AITT mixture semi-Markov game. Finally, we extend our results when the states having PI property are replaced by a subclass of Switching Control (SC) states.

Mechanism Design of a Two DOF Heavy Positioner and Turns-Over Structure

2012 ◽  
Vol 271-272 ◽  
pp. 1017-1021
Author(s):  
Yan Hua Tang ◽  
Yong Sheng Zhao
Keyword(s):  
Mechanism Design ◽  
Analytical Method ◽  
Simulation Analysis ◽  
Auxiliary Equipment ◽  
Water Chamber ◽  
Adams Simulation

In order to solve the machining translocation of the nuclear water chamber sealing head, a new Two DOF Heavy Positioner structure is proposed as the auxiliary equipment of processing nuclear water chamber sealing head. The article briefly describes the components of the 2 DOF heavy positioner, analyses the motion of the Turns-over Structure with analytical method and calculates variation of the swinging position of the screw , overturning speed and acceleration with Matlab as a platform，and verifies the correctness and credibility of the results by ADAMS simulation analysis.

Constrained Markov Games: Nash Equilibria

2000 ◽  
pp. 213-221 ◽  
Author(s):  
Eitan Altman ◽  
Adam Shwartz
Keyword(s):  
Nash Equilibria ◽  
Markov Games
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