273 research outputs found
A Numerical Algorithm to find Soft-Constrained Nash Equilibria in Scalar LQ-Games
Get PDFIn this paper we provide a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game.The algorithm is based on the calculation of the eigenstructure of a certain matrix.The analysis follows the lines of the approach taken by Engwerda in [7] to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations
Calculation of an approximate solution of the infinite time-varying LQ-problem
Get PDFLinear Programming;Algorithm;Optimal Control;operations research
The (in)finite horizon open-loop Nash LQ game: An application to EMU
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141595.pdf (Publisher’s version ) (Closed access)In this paper, we study macroeconomic stabilization in the Economic and Monetary Union(EMU) using a dynamic games approach. In modeling this problem, it turns out that theplayers include the time derivative of the state variable of the game in their performancecriterion. As far as the authors know, this kind of problem has not before been dealt withrigorously in dynamic games theoretic literature. Therefore, we first consider a generalizationof the linear‐quadratic differential game, in which we allow for cross terms in theperformance criteria. Following the analysis of Engwerda [10,12], we present formulas tocalculate open‐loop Nash equilibria for both the finite‐planning horizon and the infinite‐planninghorizon. Particular attention is paid to computational aspects. In the second part ofthis paper, we use the obtained theoretical results to study macroeconomic stabilization inthe Economic and Monetary Union (EMU).23 p
Policymakers' Coalitions and Stabilization Policies in the EMU
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67076.pdf (Publisher’s version ) (Closed access)A highly integrated area like the EMU features a large amount of interactions between the participating countries. In this context the interactions of monetary and fiscal policies are a crucial issue. This paper focuses on how coalitions among policymakers are formed and discusses their effects on the stabilization of output and price. We emphasize the role played by the institutional design of “cooperation forums” (as, e.g., the ECOFIN). If the coalition formation game is played without communication among the policymakers, full cooperation is an unlikely outcome. On the other hand, if policymakers can communicate, full cooperation becomes a possible equilibrium, while the complete non-cooperative solution is, in general, not a stable equilibrium. This supports the view that institutions for discussions can play a crucial role in achieving international cooperation even when these institutions are not endowed with enforcement powers
Stabilization of an Uncertain Simple Fishery Management Game
Get PDFThis note analyzes in a fishery management problem the effects of relaxing one of the usual assumptions in the literature of dynamic games. Specifically, the assumption that players restrict to strategies that stabilize the system. Previous works in the literature have shown that feedback Nash equilibria can exist in which a player can improve unilaterally by choosing a feedback control for which the closed-loop system is unstable. This paper considers in some more detail the implication this setting has in the framework of a simple fishery management. It is shown that if the fishermen are not short-sighted in their valuation of future profits, the considered approach implies a division of them into two groups. One group going for maximal profits and the other group taking care of the imposed stability constraint. To see how noise might impact these results we additionally consider a framework where fishermen take into account the possibility that the fish growth might be corrupted by external factors. We consider a deterministic approach of dealing with noise in this set-up. The model predicts that the more people are involved in the group taking care of the stabilization constraint, the less active they get. Furthermore it predicts that the natural reaction of any of these persons is to increase his activities if he expects more noise. But that this activity is reduced, and partly replaced by more active control policies by group members, if the size of the group increases. Activity of fishermen going for maximal profits is not affected by noise expectations
Robust open-loop Nash equilibria in the noncooperative LQ game revisited
Get PDFThis paper reconsiders existence of worst-case Nash equilibria in noncooperative multi-player differential games, this, within an open-loop information structure. We show that these equilibria can be obtained by determining the open-loop Nash equilibria of an associated differential game with an additional initial state constraint. For the special case of linear-quadratic differential games, we derive both necessary and sufficient conditions for solvability of the finite planning horizon problem. In particular, we demonstrate that, unlike in the standard linear-quadratic differential game setting, uniqueness of equilibria may fail to hold. A both necessary and sufficient condition under which there is a unique equilibrium is provided. A sufficient existence condition for a unique equilibrium is derived in terms of a Riccati differential equation. Consequences for control policies are demonstrated in a simple debt stabilization game
New proposals for the validation of trace-driven simulations
Get PDFsimulation;simulation models;operations research
Performance of Delta-hedging strategies in interval models - A robustness study
Get PDFhedging;volatility;option pricing
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