Special Issue "Epistemic Game Theory and Logic"

A special issue of Games (ISSN 2073-4336).

Deadline for manuscript submissions: closed (31 August 2016).

Special Issue Editor

Prof. Dr. Paul Weirich
E-Mail Website
Guest Editor
Department of Philosophy, University of Missouri, Columbia, MO 65211, USA
Interests: decision and game theory; logic

Special Issue Information

Dear Colleagues,

Game theory treats situations with multiple agents in which the outcome of an agent’s act depends on the acts of the other agents. The agents may be mindless organisms. Epistemic game theory treats in games in which the agents have minds. An agent reasons about the acts of other agents and, if the other agents observe the agent’s act, the other agents’ responses to the act. The agents use logic to draw conclusions about the prospects of acts they can perform. This Special Issue of Games deals with epistemic game theory and the contributions that logic makes to an agent’s practical reasoning about the strategy to adopt in a game. Although behavioral studies are relevant, the emphasis is on rational reasoning. Models of such reasoning may treat cognitively ideal agents as well as humans. Possible topics include: the player’s common knowledge of their game and their rationality; reasoning that supports the players’ doing their parts in a Nash equilibrium of the game; backwards induction, its results, and the conditions that support it; forward induction; learning in sequential games or in repetitions of games; Hintikka models and Kripke models of agents’ information; applications of modal logic’s methods to epistemic logic; interactive epistemology; Bayesian game theory and Bayesian equilibrium; and games with imperfect, incomplete, or asymmetric information.

Authors are invited to submit papers, not only on traditional topics in epistemic game theory and logic, but also on new topics in this area. An ideal length for a submission is about 8000 words.

Prof. Dr. Paul Weirich
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Games is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • epistemic game theory
  • epistemic logic
  • Bayesian game theory
  • common knowledge
  • backwards induction
  • interactive epistemology

Published Papers (10 papers)

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Editorial

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Open AccessEditorial
Epistemic Game Theory and Logic: Introduction
Games 2017, 8(2), 19; https://doi.org/10.3390/g8020019 - 31 Mar 2017
Abstract
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)

Research

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Open AccessArticle
The Welfare Cost of Signaling
Games 2017, 8(1), 11; https://doi.org/10.3390/g8010011 - 09 Feb 2017
Cited by 2
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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Open AccessArticle
Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies
Games 2017, 8(1), 3; https://doi.org/10.3390/g8010003 - 03 Jan 2017
Cited by 1
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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Open AccessArticle
Economic Harmony: An Epistemic Theory of Economic Interactions
Games 2017, 8(1), 2; https://doi.org/10.3390/g8010002 - 03 Jan 2017
Cited by 5
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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Open AccessArticle
Probabilistic Unawareness
Games 2016, 7(4), 38; https://doi.org/10.3390/g7040038 - 30 Nov 2016
Cited by 1
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
(This article belongs to the Special Issue Epistemic Game Theory and Logic)
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Open AccessArticle
Epistemically Robust Strategy Subsets
Games 2016, 7(4), 37; https://doi.org/10.3390/g7040037 - 25 Nov 2016
Cited by 1
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)
Open AccessArticle
Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals
Games 2016, 7(4), 36; https://doi.org/10.3390/g7040036 - 16 Nov 2016
Cited by 2
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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Open AccessArticle
Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium
Games 2016, 7(4), 35; https://doi.org/10.3390/g7040035 - 10 Nov 2016
Cited by 1
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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Open AccessArticle
Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions
Games 2016, 7(4), 32; https://doi.org/10.3390/g7040032 - 26 Oct 2016
Cited by 1
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)
Open AccessArticle
When Do Types Induce the Same Belief Hierarchy?
Games 2016, 7(4), 28; https://doi.org/10.3390/g7040028 - 09 Oct 2016
Cited by 3
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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