Knightian games and robustness to ambiguity

Stauber, Ronald

doi:10.1016/j.jet.2010.08.008

Cited by 21 publications

(14 citation statements)

References 20 publications

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“…There is also a literature on incomplete information games with ambiguous beliefs about states of the world. Such Bayesian games with ambiguous beliefs are analyzed for example in Kajii and Ui (2005), Bose et al (2006), Bose and Daripa (2009) and Stauber (2011). In the present paper, the environment of the game is common knowledge and thus there is never any ambiguity about any states of the world -the only ambiguity present is in regards to the actions chosen by a player's opponents.…”

Section: Introductionmentioning

confidence: 91%

Trembles in extensive games with ambiguity averse players

Aryal

Stauber

2014

Econ Theory

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We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility as characterized in Gilboa and Schmeidler (1989), our definitions capture the intuition that players may consider the possibility of slight mistakes, analogous to the intuition leading to trembling-hand perfect equilibrium as introduced in Selten (1975). We prove existence for two of our equilibrium notions, and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to distinct behavioral implications, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.

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Section: Introductionmentioning

confidence: 91%

Trembles in extensive games with ambiguity averse players

Aryal

Stauber

2014

Econ Theory

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“…In [3] it is shown that the limit property holds for equilibria under ambiguous beliefs correspondences; key for this result is the sequential convergence assumption imposed on the sequence of beliefs correspondences. The sensitivity of equilibrium to ambiguity is also discussed by [22] in a different context. In fact, an equilibrium notion for ambiguous games which relies on the Beweley unanimity rule is therein defined.…”

Section: Related Literature On Ambiguous Gamesmentioning

confidence: 99%

“…. , σ n ), conditions (17) and (21) imply that (10) holds, while, conditions (18) and (22) imply that (11) holds, for every player i.…”

Section: The Limit Theoremmentioning

confidence: 99%

On the stability of equilibria in incomplete information games under ambiguity

Marco

Romaniello

2013

ams

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In this paper, we look at the (Kajii and Ui) mixed equilibrium notion, which has been recognized by previous literature as a natural solution concept for incomplete information games in which players have multiple priors on the space of payoff relevant states. We investigate the problem of stability of mixed equilibria with respect to perturbations on the sets of multiple priors. We find out that the (Painlevé-Kuratowski) convergence of posteriors ensures that stability holds; whereas, convergence of priors is not enough to obtain stability since it does not always implies convergence of posteriors when we consider updating rules (for multiple priors) based on the classical Bayesian approach.

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“…searchers, who typically only require that small perturbations of beliefs lead to ε-best responses and ε-equilibria for every nearby perturbation (see Stauber (2006Stauber ( , 2011 or Barelli (2009)). In our case, we require that ε-variations of beliefs may only lead to higher-order O (ε 2 ) variations of equilibrium strategies and expected payoffs.…”

Section: Introductionmentioning

confidence: 99%

Robustness of equilibrium in the Kyle model of informed speculation

Boulatov¹,

Bernhardt

2015

Ann Finance

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We analyze a static Kyle (1983) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a finite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the first variation in any agent's expected payoff with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker's beliefs about the informed speculator's trading strategy do not reduce his expected payoffs. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms.) We also establish that if a non-linear equilibrium exists, then it is not robust. JEL Classification Numbers: G12, G14, C62.

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Knightian games and robustness to ambiguity

Cited by 21 publications

References 20 publications

Trembles in extensive games with ambiguity averse players

Trembles in extensive games with ambiguity averse players

On the stability of equilibria in incomplete information games under ambiguity

Robustness of equilibrium in the Kyle model of informed speculation

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