Editorial

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Open AccessEditorial

Epistemic Game Theory and Logic: Introduction

by Paul Weirich

Games 2017, 8(2), 19; https://0-doi-org.brum.beds.ac.uk/10.3390/g8020019 - 31 Mar 2017

Cited by 1 | Viewed by 6820

Epistemic game theory and the systems of logic that support it are crucial for understanding rational behavior in interactive situations in which the outcome for an agent depends, not just on her own behavior, but also on the behavior of those with whom [...] Read more.

Epistemic game theory and the systems of logic that support it are crucial for understanding rational behavior in interactive situations in which the outcome for an agent depends, not just on her own behavior, but also on the behavior of those with whom she is interacting. Scholars in many fields study such interactive situations, that is, games of strategy. [...] Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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The Welfare Cost of Signaling

by Fan Yang and Ronald M. Harstad

Games 2017, 8(1), 11; https://0-doi-org.brum.beds.ac.uk/10.3390/g8010011 - 09 Feb 2017

Cited by 2 | Viewed by 6110

Abstract

Might the resource costliness of making signals credible be low or negligible? Using a job market as an example, we build a signaling model to determine the extent to which a transfer from an applicant might replace a resource cost as an equilibrium [...] Read more.

Might the resource costliness of making signals credible be low or negligible? Using a job market as an example, we build a signaling model to determine the extent to which a transfer from an applicant might replace a resource cost as an equilibrium method of achieving signal credibility. Should a ﬁrm’s announcement of hiring for an open position be believed, the ﬁrm has an incentive to use a properly-calibrated fee to implement a separating equilibrium. The result is robust to institutional changes, outside options, many ﬁrms or many applicants and applicant risk aversion, though a sufﬁciently risk-averse applicant who is sufﬁciently likely to be a high type may lead to a preference for a pooling equilibrium. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies

by Ashton T. Sperry-Taylor

Games 2017, 8(1), 3; https://0-doi-org.brum.beds.ac.uk/10.3390/g8010003 - 03 Jan 2017

Cited by 1 | Viewed by 7978

Abstract

Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of [...] Read more.

Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of belief-revision policies are beliefs, not strategies and acts. Thus, the rationality of belief-revision policies is subject to Bayesian epistemology. The components of any belief-revision policy are credences constrained by the probability axioms, by conditionalization, and by the principles of indifference and of regularity. The principle of indifference states that an agent updates his credences proportionally to the evidence, and no more. The principle of regularity states that an agent assigns contingent propositions a positive (but uncertain) credence. The result is rational constraints on real people’s credences that account for their uncertainty. Nonetheless, there is the open problem of non-evidential components that affect people’s credence distributions, despite the rational constraint on those credences. One non-evidential component is people’s temperaments, which affect people’s evaluation of evidence. The result is there might not be a proper recommendation of a strategy profile for a game (in terms of a solution concept), despite agents’ beliefs and corresponding acts being rational. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Economic Harmony: An Epistemic Theory of Economic Interactions

by Ramzi Suleiman

Games 2017, 8(1), 2; https://0-doi-org.brum.beds.ac.uk/10.3390/g8010002 - 03 Jan 2017

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Abstract

We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We [...] Read more.

We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We show that the aforementioned minor epistemic modification of the concept of utility is quite powerful in generating plausible and successful predictions of experimental results, obtained in the standard ultimatum game, and the sequential common pool resource dilemma (CPR) game. Notably, the cooperation and fairness observed in the studied games are accounted for without adding an other-regarding component in the players’ utility functions. For the standard ultimatum game, the theory predicts a division of φ and 1 − φ, for the proposer and responder, respectively, where φ is the famous Golden Ratio (≈0.618), most known for its aesthetically pleasing properties. We discuss possible extensions of the proposed theory to repeated and evolutionary ultimatum games. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Probabilistic Unawareness

by Mikaël Cozic

Games 2016, 7(4), 38; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040038 - 30 Nov 2016

Cited by 4 | Viewed by 5819

Abstract

The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the [...] Read more.

The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands—modal and probabilistic—of doxastic logic. Full article

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Epistemically Robust Strategy Subsets

by Geir B. Asheim, Mark Voorneveld and Jörgen W. Weibull

Games 2016, 7(4), 37; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040037 - 25 Nov 2016

Cited by 1 | Viewed by 6369

Abstract

We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is [...] Read more.

We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set

Y_{i}

contains all player types that believe with sufficient probability that the others are of types in

Y_{- i}

and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals

by Cyril Hédoin

Games 2016, 7(4), 36; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040036 - 16 Nov 2016

Cited by 5 | Viewed by 5901

Abstract

This paper develops a game-theoretic and epistemic account of a peculiar mode of practical reasoning that sustains focal points but also more general forms of rule-following behavior which I call community-based reasoning (CBR). It emphasizes the importance of counterfactuals in strategic interactions. In [...] Read more.

This paper develops a game-theoretic and epistemic account of a peculiar mode of practical reasoning that sustains focal points but also more general forms of rule-following behavior which I call community-based reasoning (CBR). It emphasizes the importance of counterfactuals in strategic interactions. In particular, the existence of rules does not reduce to observable behavioral patterns but also encompasses a range of counterfactual beliefs and behaviors. This feature was already at the core of Wittgenstein’s philosophical account of rule-following. On this basis, I consider the possibility that CBR may provide a rational basis for cooperation in the prisoner’s dilemma. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium

by Giacomo Bonanno

Games 2016, 7(4), 35; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040035 - 10 Nov 2016

Cited by 1 | Viewed by 7593

Abstract

In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In [...] Read more.

In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno, 2016), the notion of PBE was used to provide a characterization of SE in terms of a strengthening of the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of “conservative” belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions

by Jing Chen and Silvio Micali

Games 2016, 7(4), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040032 - 26 Oct 2016

Cited by 3 | Viewed by 5486

Abstract

In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the [...] Read more.

In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the “best informed player” would be sure to obtain if he/she were to sell the goods to his/her opponents via take-it-or-leave-it offers. Our mechanism is probabilistic and of an extensive form. It relies on a new solution concept, for analyzing extensive-form games of incomplete information, which assumes only mutual belief of rationality. Moreover, our mechanism enjoys several novel properties with respect to privacy, computation and collusion. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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When Do Types Induce the Same Belief Hierarchy?

by Andrés Perea and Willemien Kets

Games 2016, 7(4), 28; https://0-doi-org.brum.beds.ac.uk/10.3390/g7040028 - 09 Oct 2016

Cited by 4 | Viewed by 5970

Abstract

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if [...] Read more.

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy. Full article

(This article belongs to the Special Issue Epistemic Game Theory and Logic)

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