Ambiguous Bayesian Games

In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.

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“…Thus, by formula (32) and Theorem 5, since 0 < ≤ 1 and − 1 2 × (1 − ) × ≥ 0, for any ( , − ) ∈ {( , − )}, we can obtain…”

Section: Rules For Dominance Relations With Ambiguous Informationmentioning

confidence: 89%

“…Thus, our model handles imprecise probability of payoffs, but in this paper we have no concern with the imprecise probabilities over the types of players. Zhang et al . have extended Bayesian games to games with ambiguous probabilities of the player's types, but they did not deal with ambiguous payoffs as we do in this paper.…”

Section: Related Workmentioning

confidence: 99%

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Luo

Jiang

2017

Int. J. Intell. Syst.

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“…To achieve this goal, we need identify further axioms to derive the ambiguity degree as well as construct a representation theorem based on the axioms proposed. Another tempting avenue is to apply our decision model into game theory as (Zhang et al 2014) did. Finally, although our method can model the general human behaviour in decision making under ambiguity as shown by solving some well-known paradoxes in the research field of decision-making, it is still worth discussing the construction of a parameterised model based on our ambiguity aversion model to describe the individual's behaviour for real world application.…”

Section: Discussionmentioning

confidence: 99%

An Ambiguity Aversion Model for Decision Making under Ambiguity

Luo

Jiang

2017

AAAI

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In real life, decisions are often made under ambiguity, where it is difficult to estimate accurately the probability of each single possible consequence of a choice. However, this problem has not been solved well in existing work for the following two reasons. (i) Some of them cannot cover the Ellsberg paradox and the Machina Paradox. Thus, the choices that they predict could be inconsistent with empirical observations. (ii) Some of them rely on parameter tuning without offering explanations for the reasonability of setting such bounds of parameters. Thus, the prediction of such a model in new decision making problems is doubtful. To the end, this paper proposes a new decision making model based on D-S theory and the emotion of ambiguity aversion. Some insightful properties of our model and the validating on two famous paradoxes show that our model indeed is a better alternative for decision making under ambiguity.

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“…Sometimes it is likely that one player just has a probability distribution over some sets of the types of the other players. To this end, Zhang et al 58 extend the model of Bayesian games to the one with ambiguous types of players. They also discuss how to solve this kind of game and some properties of a solution.…”

Section: Related Workmentioning

confidence: 99%

A decision support framework for security resource allocation under ambiguity

Liu

McAreavey

et al. 2020

Int J Intell Syst

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There has been increasing interest in using Stackelberg game (known as a security game) to allocate limited security resources against different attacker types with a specific probability distribution. However, real problems of this kind often face ambiguous information, such as imprecise, unreliable and absent payoffs, and ambiguous assignments of these payoffs. To this end, based on decision theory and the Dempster-Shafer theory of evidence, this paper proposes a novel framework that can handle these common types of ambiguity. More specifically, this paper deploys the underlying principles of existing rules from decision theory, as a way to characterise different attitudes to ambiguity, during the transformation of ambiguous payoffs into point-valued payoffs. Hence, our framework holds some good properties: (i) it subsumes traditional security games without ambiguous payoffs, (ii) a uniform margin of error will not affect the results and (iii) the influence

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Ambiguous Bayesian Games

Cited by 8 publications

References 32 publications

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

An Ambiguity Aversion Model for Decision Making under Ambiguity

A decision support framework for security resource allocation under ambiguity

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