A Partial Folk Theorem for Games with Unknown Payoff Distributions

Wiseman, Thomas

doi:10.1111/j.1468-0262.2005.00589.x

Cited by 41 publications

(37 citation statements)

References 12 publications

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“…More generally, common learning is a potentially important tool in the analysis of dynamic games with incomplete information. Examples include reputation models such as Cripps, Mailath, and Samuelson (2007), where one player learns the "type" of the other, and experimentation models such as Wiseman (2005), where players learn about their joint payoffs in an attempt to coordinate on some (enforceable) target outcome. Characterizing equilibria in these games requires analyzing not only each player's beliefs about payoffs, but also higher-order beliefs about the beliefs of others.…”

Section: Summarizes These Payoffsmentioning

confidence: 99%

Common Learning

Cripps¹,

Ely²,

Mailath³

et al. 2008

Econometrica

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Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case. Copyright Copyright 2008 by The Econometric Society.

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Section: Summarizes These Payoffsmentioning

confidence: 99%

Common Learning

Cripps¹,

Ely²,

Mailath³

et al. 2008

Econometrica

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“…6 In contrast, in this paper, players have only limited information about the true state and the state is not perfectly revealed. Wiseman (2005), Fudenberg and Yamamoto (2010), Fudenberg and Yamamoto (2011a), and Wiseman (2012) study repeated games with unknown states. They all assume that the state of the world is fixed at the beginning of the game and does not change over time.…”

Section: Introductionmentioning

confidence: 99%

Stochastic games with hidden states

Yamamoto

2019

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This paper studies infinite‐horizon stochastic games in which players observe actions and noisy public information about a hidden state each period. We find a general condition under which the feasible and individually rational payoff set is invariant to the initial prior about the state when players are patient. This result ensures that players can punish or reward their opponents via continuation payoffs in a flexible way. Then we prove the folk theorem, assuming that public randomization is available. The proof is constructive and uses the idea of random blocks to design an effective punishment mechanism.

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“…In Aumann and Hart (1992), Aumann and Maschler (1995), Cripps and Thomas (2003), Pȩski (2008), Lovo (2009), Wiseman (2008), and Hörner, Lovo, and Tomala (2010), players receive private signals about the payoff functions and so can have different beliefs. (In Wiseman (2008), the players privately observe their own realized payoff each period; in the other papers the players do not observe their own realized payoffs, and the private signals are the players' initial information or "type.") 5 Belief-free equilibria and the use of indifference conditions have also been applied to repeated games with random matching (Deb (2009), Takahashi (2010).…”

Section: Modelmentioning

confidence: 99%

“…4 Gossner and Vieille (2003) and Wiseman (2005) studied symmetric-information settings. In Aumann and Hart (1992), Aumann and Maschler (1995), Cripps and Thomas (2003), Pȩski (2008), Lovo (2009), Wiseman (2008), and Hörner, Lovo, and Tomala (2010), players receive private signals about the payoff functions and so can have different beliefs.…”

Section: Modelmentioning

confidence: 99%

“…While the study of uncertain monitoring structures is new, there is a substantial literature on repeated games with unknown payoff functions and perfectly observed actions, notably Forges (1984), Sorin (1984Sorin ( , 1985, Hart (1985), Aumann and Maschler (1995), Cripps and Thomas (2003), Gossner and Vieille (2003), Pȩski (2008), Wiseman (2005Wiseman ( , 2008, Lovo (2009), andTomala (2010). 4 Our work makes two extensions to this literature-first to the case of unknown payoff functions and imperfectly observed actions but a known monitoring technology, and from there to the case where the monitoring structure is itself unknown.…”

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confidence: 99%

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Repeated Games Where the Payoffs and Monitoring Structure Are Unknown

Fudenberg

Yamamoto

2010

Econometrica

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This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define perfect type-contingently public ex post equilibria (PTXE), which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.

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A Partial Folk Theorem for Games with Unknown Payoff Distributions

Cited by 41 publications

References 12 publications

Common Learning

Common Learning

Stochastic games with hidden states

Repeated Games Where the Payoffs and Monitoring Structure Are Unknown

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