Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games

Nayyar, Ashutosh; Gupta, Abhishek; Langbort, Cédric; Başar, Tamer

doi:10.1109/tac.2013.2283743

Cited by 82 publications

(126 citation statements)

References 18 publications

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“…Main Results. Following the approach introduced in [15], we now construct a new game G2 with two virtual players, where at every time step t ∈ {1, . .…”

Section: Evolution Of Conditional Beliefsmentioning

confidence: 99%

“…One of the crucial assumptions we made in the game formulation is the strategy independence of beliefs in Assumption 2. As discussed in our companion paper [15], this assumption plays a crucial role in computing the Markov perfect Nash equilibrium of game G2 using a backward induction dynamic programming. In this section, we briefly describe the reason why this assumption is important.…”

Section: Effects On Expected Costsmentioning

confidence: 99%

“…However, by comparison, such general frameworks for games of asymmetric information are scant (for exceptions, see [11][12][13][14]). This paper, in addition to its earlier finite-game version [15], provides such a framework. …”

mentioning

confidence: 99%

“…In this work, we extend the framework and results of [15] to infinite games, particularly those with linear state and observation equations and Gaussian random variables. For quadratic cost functions of the players satisfying certain assumptions, we show that a unique common information based Markov perfect equilibrium exists.…”

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confidence: 99%

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Common Information Based Markov Perfect Equilibria for Linear-Gaussian Games with Asymmetric Information

Gupta

Nayyar

Langbort³

et al. 2014

SIAM J. Control Optim.

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Abstract. We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic information about the state process and the other controller's past actions and observations. This leads to a dynamic game of asymmetric information among the controllers. Building on our earlier work on finite games with asymmetric information, we devise an algorithm to compute a Nash equilibrium by using the common information among the controllers. We call such equilibria common information based Markov perfect equilibria of the game, which can be viewed as a refinement of Nash equilibrium in games with asymmetric information. If the players' cost functions are quadratic, then we show that under certain conditions a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. We also show through an example that there could be other Nash equilibria in a game of asymmetric information, not corresponding to common information based Markov perfect equilibria.1. Introduction. A game models a scenario where multiple strategic controllers (or players) optimize their objective functionals, which depend not only on the self actions but also on the actions of other controllers. In stochastic static games, players observe the realization of some random state of nature, possibly through separate noisy channels, and use such observations to independently determine their actions so that the expected values of their individual cost (or utility) functions are optimized. In a stochastic dynamic game, on the other hand, the players act at multiple time steps, based on observation or measurement of some dynamic process which itself is driven by past actions as well as random quantities, which could again be called random states of nature. What information each player acquires at each stage of the game determines what is called the information structure of the underlying game. If all the players acquire the same information at each time step, then the dynamic game is said to be a game of symmetric information. However, in many real scenarios, the players do not have access to the same information about the underlying state processes and other players' observations and past actions. Such games are known as games with asymmetric information. For example, several problems in economic interactions [1][2][3], attacks on cyber-physical systems [4], auctions, cryptography, etc. can be modeled as games of asymmetric information among strategic players.Games with symmetric and/or perfect information have been well studied in the literature; see, for example, [5][6][7][8][9]. In these games, the players have the same beliefs on the states of the game, future observations and future expected costs or payoffs. However, in games with asymmetric information, the players need not have the same beliefs on th...

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“…Main Results. Following the approach introduced in [15], we now construct a new game G2 with two virtual players, where at every time step t ∈ {1, . .…”

Section: Evolution Of Conditional Beliefsmentioning

confidence: 99%

Section: Effects On Expected Costsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Common Information Based Markov Perfect Equilibria for Linear-Gaussian Games with Asymmetric Information

Gupta

Nayyar

Langbort³

et al. 2014

SIAM J. Control Optim.

Self Cite

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“…Recently, [6] generalized the results to the case when players observe signals rather than actions, and showed that the value of the stochastic game existed if one of the players was fully informed and controlled the transition of the state. A more general case when the players have common information but neither one can have full knowledge of the other one's full information is discussed in [7]- [9], which is out of the scope of this paper.…”

Section: Introductionmentioning

confidence: 99%

LP formulation of asymmetric zero-sum stochastic games

Shamma

2014

53rd IEEE Conference on Decision and Control

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Decentralized control for discrete‐time mean‐field systems with multiple controllers of delayed information

Qi,

Liu,

Zhang

et al. 2023

Asian Journal of Control

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In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete‐time mean field system. Different from previous works, multiple controllers with different information sets are involved in the mean field system dynamics. The coupling of different controllers makes it quite difficult in finding the optimal control strategy. Fortunately, by applying the Pontryagin's maximum principle, the corresponding decentralized control problem of the finite horizon is investigated. The contributions of this paper can be concluded as follows: For the first time, based on the solution of a group of mean‐field forward and backward stochastic difference equations (MF‐FBSDEs), the necessary and sufficient solvability conditions are derived for the asymmetric information LQ control for the mean field system with multiple controllers. Furthermore, by the use of an innovative orthogonal decomposition approach, the optimal decentralized control strategy is derived, which is based on the solution to a non‐symmetric Riccati‐type equation.

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Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games

Cited by 82 publications

References 18 publications

Common Information Based Markov Perfect Equilibria for Linear-Gaussian Games with Asymmetric Information

Common Information Based Markov Perfect Equilibria for Linear-Gaussian Games with Asymmetric Information

LP formulation of asymmetric zero-sum stochastic games

Decentralized control for discrete‐time mean‐field systems with multiple controllers of delayed information

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