Pseudo-Gradient Dynamics with Cognitive Predictions in Noncooperative Dynamical Systems

Yan, Yuyue; Hayakawa, Tomohisa

doi:10.1109/cdc51059.2022.9993306

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…To deal with the uncertainties in the private information of the agents, we investigate stability conditions for a Nash equilibrium for arbitrary sensitivity parameters, arbitrary cognitive levels of the agents, and arbitrary knowledge network of the payoff functions. Different from preliminary version [32], this paper generalizes the results to the case where the agents are allowed to adopt Level-k thinking with k > 3. In addition, we present the applications of the results in homogeneous and differentiated oligopoly markets.…”

Section: Introductionmentioning

confidence: 85%

“…Except for this manner, it is possible to use other types of recursive reasoning such as [31] for characterizing proactive decision-making with Level-k thinking in noncooperative system if the agents are hesitating in how much proactive they should be. APPENDIX 1) Derivation of (31), (32): The derivation of ( 31) is a direct consequence of ( 17), (19) along with…”

Section: Discussionmentioning

confidence: 99%

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Incorporation of Likely Future Actions of Agents into Pseudo-Gradient Dynamics of Noncooperative Games

Yan,

Hayakawa

2024

IEEE Trans. Automat. Contr.

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In this paper, we connect cognitive hierarchy theory with the pseudo-gradient dynamics in noncooperative systems to extend the pseudo-gradient dynamics with some prediction behaviors under Level-k thinking. In this framework, each agent believes that he is the most sophisticated person in the noncooperative system and makes the proactive decision according to some strategic reasoning of the other agents' likely actions. Depending on a knowledge network of payoff functions, the modified pseudogradient dynamics are presented under the assumption that the agents may be able to reason the other agents' best-response states and use these predicted states in the pseudo-gradient dynamics. Some sufficient conditions are provided to guarantee stability of a Nash equilibrium with uncertain sensitivity parameters or uncertain knowledge network. The transition of the agents' target state while increasing the cognitive levels for a two-agent noncooperative system with quadratic payoff functions is characterized. We present the utility of our approach for homogeneous and differentiated oligopoly markets. Our result indicates that to ensure asymptotic stability of the differentiated oligopoly markets with Cournot competition under pseudo-gradient dynamics, a larger market with more firms requires more differentiated products.

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Section: Introductionmentioning

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Incorporation of Likely Future Actions of Agents into Pseudo-Gradient Dynamics of Noncooperative Games

Yan,

Hayakawa

2024

IEEE Trans. Automat. Contr.

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Pareto-Improving Incentive Mechanism for Noncooperative Dynamical Systems Under Sustainable Budget Constraint

Yan,

Hayakawa

2024

IEEE Trans. Automat. Contr.

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A Pareto-improving incentive mechanism to improve the weighted social welfare and achieve continual Pareto improvement for a pseudo-gradient-based noncooperative dynamical system is developed. In the proposed approach, the system manager remodels agents' dynamical decision making by collecting taxes from some agents and giving some of the collected taxes to other agents as subsidies with a sustainable budget constraint. Sufficient conditions are derived under which agents' state converges towards the socially maximum state associated with a weighted social welfare function depending on the priority ratio of the agents and the initial state. We present several illustrative numerical examples to illustrate the efficacy of our results and reveal the fact that the potentialization of the payoff structure has a very strong relation to generating Pareto-improving system trajectories.

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Pseudo-Gradient Dynamics with Cognitive Predictions in Noncooperative Dynamical Systems

Cited by 2 publications

References 16 publications

Incorporation of Likely Future Actions of Agents into Pseudo-Gradient Dynamics of Noncooperative Games

Incorporation of Likely Future Actions of Agents into Pseudo-Gradient Dynamics of Noncooperative Games

Pareto-Improving Incentive Mechanism for Noncooperative Dynamical Systems Under Sustainable Budget Constraint

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