Formulation and analysis of combat problems as zero-sum bicriterion differential games

Prasad, U. R.; Ghose, Debasish

doi:10.1007/bf00939863

Cited by 12 publications

(4 citation statements)

References 16 publications

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“…Hence, by conditions (1) and (2), G −1 (y) is compactly open in X. Condition (5) implies that G satisfies all hypothesis of Theorem 3.2 in [1], then there existsx ∈ co G(x). By definition of G and A,x must be in D. It follows thatx ∈ co F (x), wich contradicts condition (4).…”

Section: Existence Of Weighted Nash Equilibriamentioning

confidence: 85%

“…There exists a family {(C α , K α )} α∈I satisfying (a) and (b) of condition (5) of Lemma 1 and the following one: For each β ∈ I, there exists α ∈ I such that for all x ∈ X \ K β ∪ D, A(x) ∩ C α = ∅ and for each…”

Section: Existence Of Pareto Equilibriamentioning

confidence: 94%

“…A number of classical problems in game theory are formulated as games with multiple non-comparable criteria (or vector payoffs) (see Prasad and Ghose [5]). The aim of this work is to study the existence of Pareto equilibria in such games.…”

Section: Introductionmentioning

confidence: 99%

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Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games

Chebbi¹

2008

Journal of Applied Analysis

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In this paper, an existence result of quasi-equilibrium problem is proved and used to establish the existence of weighted Nash equilibria for constrained multi-criteria games under a generalized quasiconvexity condition and a coercivity type condition on the payoff functions. As consequence, we prove the existence of Pareto equilibria for constrained multi-criteria games with non-compact strategy sets in topological vector spaces.

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Section: Existence Of Weighted Nash Equilibriamentioning

confidence: 85%

Section: Existence Of Pareto Equilibriamentioning

confidence: 94%

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Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games

Chebbi¹

2008

Journal of Applied Analysis

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“…For zero sum games this approach is elaborated in Zeleny (1976), Nieuwenhuis (1983) and Corley (1985), for non-zero sum games in Borm, van den Aarssen and Tijs (1988), who also provide a geometric description for small games, and in Ghose and Prasad (1989). Applications of zero-sum bicriterion games to combat games can be found in Prasad and Ghose (1988).…”

Section: Introductionmentioning

confidence: 99%

A perfectness concept for multicriteria games

Borm¹,

Megen²,

Tijs³

1999

Mathematical Methods of Operations Research (ZOR)

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A perfectness concept for multicriteria games van Megen, F.; Borm, P.E.M.; Tijs, S.H.Thie paper conaidera a refinement of equilibria for multicriteria gamea based on the perfectneae concept of Selten (1975). Eziatence of perfect equilibrium points ia ahown and aeveral characterizations are provided. Ftuthermore, contrary to the reault for equilibria for multicriteria games, an eaemple ehows that there ia no exact correapondence between perfect equilibrium points and the perfect Nash equilibria of the related trade-off games.1Department of Econometrice and CentER, 15lbnrg Univeraity, 75lbnrg, The Netherlnnds.

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Solving zero‐sum multi‐objective games with a‐priori secondary criteria

Harel

Eisenstadt-Matalon

Moshaiov

2022

Multi Criteria Decision Anal

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Solving non‐cooperative zero‐sum multi‐objective Games (zsMOGs), under undecided objective preferences results, for each of the players, in a Set of Rationalizable Strategies (SRS) to choose from. First, this paper deals with finding for each of the players a preferred subset of such rationalizable strategies based on a‐priori incorporation of partial preferences of the decision‐makers using secondary criteria. The obtained subset is termed the Set of Preferred Strategies (SPS). Here, a novel archive‐based co‐evolutionary algorithm is suggested to search for the SPS for each of the players. An academic example is suggested to demonstrate and validate the algorithm. It concerns a zsMOG that involves two adversarial planar manipulators. Based on a theorem that is proven here, a theoretic reference SRS is found for each of the players. This reference SRS is applied to find a reference SPS, which is used for validating the algorithm. Next, a comparison study is performed between the proposed archive‐based co‐evolutionary algorithm and an elite‐based version of this algorithm. The results clearly show that the archive‐based algorithm is superior to the elite‐based version, yielding results that correspond well to the theoretic sets.

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Formulation and analysis of combat problems as zero-sum bicriterion differential games

Cited by 12 publications

References 16 publications

Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games

Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games

A perfectness concept for multicriteria games

Solving zero‐sum multi‐objective games with a‐priori secondary criteria

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