Incomplete-profile potential games

Zhang, Xiao; Hao, Yaqi; Cheng, Daizhan

doi:10.1016/j.jfranklin.2017.11.009

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…PROOF. From the equivalent equations (28) and the free variables shown by (29), it follows that the set of η pqr (1 ≤ p ≤ q ≤ r ≤ k) is a group of bases of the solution space X 3 . By the construction of ζ uvw pqr , it is straightforward to see that each ζ uvw pqr is orthogonal to X 3 .…”

Section: Symmetric Games and Testing Conditionsmentioning

confidence: 99%

On Matrix Method of Symmetric Games

Wang¹,

Liu²,

Li³

et al. 2022

Preprint

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This paper provides a new version of matrix semi-tensor product method based on adjacent transpositions to test symmetric games. The advantage of using adjacent transpositions lies in the great simplification of analysis of symmetric games. By using the new method, new necessary and sufficient conditions for symmetric games are proposed, and a group of bases of a symmetric game space can be easily calculated. Moreover, the testing equations with the minimum number can be concretely determined. Finally, two examples are displayed to show the effectiveness of the proposed method.

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Section: Symmetric Games and Testing Conditionsmentioning

confidence: 99%

On Matrix Method of Symmetric Games

Wang¹,

Liu²,

Li³

et al. 2022

Preprint

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“…In this case the Nash e equilibria and optimal strategies are state-depending. This kind of games has been discussed in [68]. Furthermore, the PG under restricted profile is also discussed, and the method for verifying potential and finding potential function for incomplete profile games is obtained in [48].…”

Section: Incomplete Profile Gamesmentioning

confidence: 99%

A Comprehensive Survey on STP Approach to Finite Games

Cheng¹,

Wu²,

Zhao³

et al. 2021

Preprint

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Nowadays the semi-tensor product (STP) approach to finite games has become a promising new direction. This paper provides a comprehensive survey on this prosperous field. After a brief introduction for STP and finite (networked) games, a description for the principle and fundamental technique of STP approach to finite games is presented. Then several problems and recent results about theory and applications of finite games via STP are presented. A brief comment about the potential use of STP to artificial intelligence is also proposed.

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“…In many cases, the strategies of players in a game may be limited by some actual situation, such as natural conditions, customs, rules and regulations, laws and so on. Due to these factors, a new kind of game, called the IPNFGs is introduced [4]. In an IPNFG, each player has certain suitable strategies to choose, however, some profiles which are against the rules may be infeasible.…”

Section: Introductionmentioning

confidence: 99%

“…[4] Consider a normal form game G = (N , S, C) and assume that the feasible set is a proper subset of S. Then G =(N , S, C, )is called an IPNFG, whose dynamics are…”

mentioning

confidence: 99%

Weighted Potential Incomplete-Profile Games

Pan

Zhao

2020

IEEE Access

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In this paper the weighted potential incomplete-profile games are studied. First a potential equation with algebraic form is established to check whether an incomplete-profile normal form game (IPNFG) is a weighted potential game with weight w > 0 or not, based on which, the potential function can be constructed. Then the weighted potential subspace and the non-strategic subspace and some properties of weighted potential incomplete-profile games are obtained. Finally, an example is given to illustrate our theoretical results. INDEX TERMS Incomplete-profile games, weighted potential subspace, non-strategic subspace, semitensor product of matrices.

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Incomplete-profile potential games

Cited by 14 publications

References 22 publications

On Matrix Method of Symmetric Games

On Matrix Method of Symmetric Games

A Comprehensive Survey on STP Approach to Finite Games

Weighted Potential Incomplete-Profile Games

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