Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

Wiszniewska-Matyszkiel, Agnieszka

doi:10.1007/s10957-013-0317-5

Cited by 20 publications

(7 citation statements)

References 38 publications

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“…The general theory of dynamic games with a continuum of players is still being developed by, e.g., Wiszniewska-Matyszkiel [20] for games with a common global state variable, Lasry and Lions [30] for stochastic mean field games where each player is associated with a private state variable and Wiszniewska-Matyszkiel [31] for games with both common global and private state variables.…”

Section: Discussionmentioning

confidence: 99%

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Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

Wiszniewska-Matyszkiel

2016

J Optim Theory Appl

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In this paper, a new concept of equilibrium in dynamic games with incomplete or distorted information is introduced. In the games considered, players have incomplete information about crucial aspects of the game and formulate beliefs about the probabilities of various future scenarios. The concept of belief distorted Nash equilibrium combines optimization based on given beliefs and self-verification of those beliefs. Existence and equivalence theorems are proven, and this concept is compared to existing ones. Theoretical results are illustrated using several examples: extracting a common renewable resource, a large minority game, and a repeated Prisoner's Dilemma.Keywords Distorted information · Dynamic games · Nash equilibrium · Belief distorted Nash equilibrium (BDNE ) · Self-verification of beliefs

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Section: Discussionmentioning

confidence: 99%

“…The Proof of Proposition 4.2 uses a standard technique for solving the Bellman equation, while the proof of Proposition 4.1 applies a decomposition method from Wiszniewska-Matyszkiel [20].…”

Section: A Common Ecosystemmentioning

confidence: 99%

Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

Wiszniewska-Matyszkiel

2016

J Optim Theory Appl

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“…Existence results and properties of equilibria for such games are proven, among others, in Wiszniewska-Matyszkiel (2002) for open loop information structure. However, by Wiszniewska-Matyszkiel (2014a), in discrete time dynamic games with a continuum of players the existence of an open loop Nash equilibrium is equivalent to existence of a closed loop Nash equilibrium.…”

Section: Corollary 7 In Games With a Continuum Of Players With Payoffmentioning

confidence: 97%

“…The general theory of dynamic games with a continuum of players is still being developed: there are the author's papers Wiszniewska-Matyszkiel (2002) and Wiszniewska-Matyszkiel (2003) and a new branch of mean-field games started by Weintraub et al (2005) and Lasry and Lions (2007). There are also interesting applications of such games in various economic problems.…”

Section: Proposition 13 If Both R I Are Small Enough Then: (A) the Pmentioning

confidence: 99%

Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

Wiszniewska-Matyszkiel¹

2015

Ann Oper Res

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In this paper the concept of belief distorted Nash equilibrium (BDNE) is introduced. It is a new concept of equilibrium for games in which players have incomplete, ambiguous or distorted information about the game they play, especially in a dynamic context. The distortion of information of a player concerns the fact how the other players and/or an external system changing in response to players' decisions, are going to react to his/her current decision. The concept of BDNE encompasses a broader concept of pre-BDNE, which reflects the fact that players best respond to their beliefs, and self-verification of those beliefs. The relations between BDNE and Nash or subjective equilibria are examined, as well as the existence and properties of BDNE. Examples are presented, including models of a common ecosystem, repeated Cournot oligopoly, a repeated Minority Game or local public good with congestion effect and a repeated Prisoner's Dilemma.

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“…In an openloop formation, the simplest solution, the game's repeated nature is ignored and time is the only information an agent takes into account at each stage. Excluding private and global state variables (which are used to track game history in closed-loop formations) from the inclusions used to compute optimal agent strategies makes open-loop formations more tractable [89]. Game stages can be combined into a single static game and the entire trajectory chosen at once to satisfy equilibria.…”

Section: Feedback Nash Equilibriummentioning

confidence: 99%

Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts

Bergerson

2021

Preprint

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Multi-agent inverse reinforcement learning (MIRL) can be used to learn reward functions from agents in social environments. To model realistic social dynamics and outcomes, MIRL methods must account for suboptimal human reasoning and behavior. Traditional formalisms of game theory provide computationally tractable behavioral models, but assume agents have unrealistic cognitive capabilities. The objective of this research is to identify and compare mechanisms used in MIRL methods to a) handle the presence of noise, biases and heuristics in agent decision making and b) model realistic equilibrium solution concepts based on suboptimal behavior. MIRL research was systematically reviewed to identify solution attempts for these challenges. The methods and results of these studies were analyzed and compared based on factors including performance accuracy, efficiency, and descriptive quality. We found that the primary methods for handling noise, biases and heuristics in MIRL were extensions of Maximum Entropy (MaxEnt) IRL to multi-agent settings. We also found that traditional Nash equilibrium (NE) solution concepts were ill-suited to model human behavior, and more success could be found with generalization of the NE. These solutions include the correlated equilibrium, logistic stochastic best response equilibrium and entropy regularized mean field NE. Methods which use recursive reasoning or updating also perform well, including the feedback NE and archive multi-agent adversarial IRL. Success in modeling specific biases and heuristics in single-agent IRL and promising results using a Theory of Mind approach in MIRL imply that modeling specific biases and heuristics in MIRL may be useful. Flexibility and unbiased inference in the identified alternative solution concepts suggest that a solution concept which has both recursive and generalized characteristics may perform well at modeling realistic social interactions.

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Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

Cited by 20 publications

References 38 publications

Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts

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