On the Strategic Equivalence of Linear Dynamic and Repeated Games

2015 ◽  
Vol 17 (03) ◽  
pp. 1550006
Author(s):  
Joachim Hubmer
Keyword(s):  
Repeated Games ◽  
Dynamic Game ◽  
Repeated Game ◽  
Transition Function ◽  
The State ◽  
State Variables ◽  
Equivalent Representation ◽  
Deterministic Dynamic ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that is linear in the state, there exists a strategically equivalent representation as a repeated game. A dynamic game is said to be linear in the state if it holds for both the state transition function as well as for the one-period payoff function that (i) they are additively separable in action profiles and states and (ii) the state variables enter linearly. Strategic equivalence refers to the observation that the two sets of subgame perfect equilibria coincide, up to a natural projection of dynamic game strategy profiles on the much smaller set of repeated game histories. Furthermore, it is shown that the strategic equivalence result still holds for certain stochastic elements in the transition function if one allows for additional signals in the repeated game or in the presence of a public correlating device.

scholarly journals Dynamic games with (almost) perfect information

2020 ◽  
Vol 15 (2) ◽  
pp. 811-859
Author(s):  
Wei He ◽  
Yeneng Sun
Keyword(s):  
Dynamic Games ◽  
Pure Strategy ◽  
Infinite Horizon ◽  
Complete Information ◽  
Perfect Information ◽  
State Variables ◽  
Deterministic Dynamic ◽  
Upper Hemicontinuity ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

This paper aims to solve two fundamental problems on finite‐ or infinite‐horizon dynamic games with complete information. Under some mild conditions, we prove the existence of subgame‐perfect equilibria and the upper hemicontinuity of equilibrium payoffs in general dynamic games with simultaneous moves (i.e., almost perfect information), which go beyond previous works in the sense that stagewise public randomization and the continuity requirement on the state variables are not needed. For alternating move (i.e., perfect‐information) dynamic games with uncertainty, we show the existence of pure‐strategy subgame‐perfect equilibria as well as the upper hemicontinuity of equilibrium payoffs, extending the earlier results on perfect‐information deterministic dynamic games.

Finite Horizon Game for Voluntary Provision of a Discrete Public Good

2015 ◽  
Vol 17 (03) ◽  
pp. 1550005
Author(s):  
Shizuka Nishikawa
Keyword(s):  
Public Good ◽  
Dynamic Game ◽  
Symmetric Case ◽  
The Public ◽  
Cost Structures ◽  
Asymmetric Costs ◽  
Discrete Public Good ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Made In

This paper analyzes a dynamic game for the provision of a discrete public good that will be provided only when a certain number of contributions are made. In each period players are randomly ordered and each player decides whether to contribute or not to the provision of the public good. If not enough contributions are made to provide the public good, the game goes to the next period and continue until the public good is either provided or the game ends at the final period. The paper first assumes symmetric players and shows that the exact period in which the public good will be provided is determined under subgame-perfect equilibria and that for some cost structures there will be a delay in provision of the public good. Counterintuitively, in some cases the public good is provided earlier at higher costs than at lower costs. The paper then introduces a partial public good, which requires fewer contributions to be provided but has a smaller value. We show that for some costs, introducing the partial public good eliminates the possibility of providing any kind of public good. For other cost structures, introducing the partial public good may improve social welfare. At last, asymmetric costs are introduced. The results are similar to the symmetric case.

scholarly journals Equilibrium payoffs in two-player discounted OLG games

2021 ◽  
Author(s):  
Chihiro Morooka
Keyword(s):  
Repeated Games ◽  
Overlapping Generations ◽  
Mixed Strategies ◽  
Feasible Set ◽  
Stage Game ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Perfect Monitoring

AbstractThis paper studies payoffs in subgame perfect equilibria of two-player discounted overlapping generations games with perfect monitoring. Assuming that mixed strategies are observable and a public randomization device is available, it is shown that sufficiently patient players can obtain any payoffs in the interior of the smallest rectangle containing the feasible and strictly individually rational payoffs of the stage game, when we first choose the rate of discount and then choose the players’ lifespan. Unlike repeated games without overlapping generations, obtaining payoffs outside the feasible set of the stage game does not require unequal discounting.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

scholarly journals Search for a moving target in a competitive environment

2021 ◽  
Author(s):  
Benoit Duvocelle ◽  
János Flesch ◽  
Hui Min Shi ◽  
Dries Vermeulen
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Competitive Environment ◽  
Moving Target ◽  
Time Varying ◽  
Greedy Strategy ◽  
Time Dynamic ◽  
Dynamic Search ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWe consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

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