Special Issue "Logic and Game Theory"

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

Deadline for manuscript submissions: closed (1 May 2018)

Special Issue Editors

Guest Editor
Prof. Michael Wooldridge

Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
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Interests: intersection of logic; computational complexity; and game theory
Guest Editor
Dr. Julian Gutierrez

Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
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Interests: logic; games and concurrency
Guest Editor
Dr. Paul Harrenstein

Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
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Guest Editor
Dr. Giuseppe Perelli

Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
Website | E-Mail

Special Issue Information

Dear Colleagues,

Logicians and game theorists have long found that ideas from each other's fields can usefully inform their own. From the perspective of logic, game theory provides a natural framework with which to capture key logical concepts. From the perspective of game theory, logic provides a natural and powerful tool with which to make explicit the many and subtle assumptions, such as common knowledge of rationality, which underpin game theoretic solution concepts. In computer science, the paradigm of rational verification aims to which properties hold of concurrent systems under the assumption that system components are in game theoretic equilibrium.

This Special Issue will profile the state-of-the-art in logic and game theory, showcasing key problems and directions. Published articles will have both a logic and game theoretic component, and will appeal to a broad audience.

Keywords

  • logic and game theory
  • knowledge representation and game theory
  • reasoning about equilibria
  • rational verification
  • rational synthesis
  • equilibrium checking
  • concurrency and game theory
  • concurrent games

Published Papers (3 papers)

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Research

Open AccessArticle An Automated Method for Building Cognitive Models for Turn-Based Games from a Strategy Logic
Games 2018, 9(3), 44; https://doi.org/10.3390/g9030044
Received: 18 May 2018 / Revised: 2 July 2018 / Accepted: 4 July 2018 / Published: 6 July 2018
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Abstract
Whereas game theorists and logicians use formal methods to investigate ideal strategic behavior, many cognitive scientists use computational cognitive models of the human mind to predict and simulate human behavior. In this paper, we aim to bring these fields closer together by creating [...] Read more.
Whereas game theorists and logicians use formal methods to investigate ideal strategic behavior, many cognitive scientists use computational cognitive models of the human mind to predict and simulate human behavior. In this paper, we aim to bring these fields closer together by creating a generic translation system which, starting from a strategy for a turn-based game represented in formal logic, automatically generates a computational model in the Primitive Information Processing Elements (PRIMs) cognitive architecture, which has been validated on various experiments in cognitive psychology. The PRIMs models can be run and fitted to participants’ data in terms of decisions, response times, and answers to questions. As a proof of concept, we run computational modeling experiments on the basis of a game-theoretic experiment about the turn-based game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We run such models starting from logical representations of several strategies, such as backward induction and extensive-form rationalizability, as well as different player types according to stance towards risk and level of theory of mind. Hereby, response times and decisions for such centipede-like games are generated, which in turn leads to concrete predictions for future experiments with human participants. Such precise predictions about different aspects, including reaction times, eye movements and active brain areas, cannot be derived on the basis of a strategy logic by itself: the computational cognitive models play a vital role and our generic translation system makes their construction more efficient and systematic than before. Full article
(This article belongs to the Special Issue Logic and Game Theory)
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Open AccessArticle Buying Optimal Payoffs in Bi-Matrix Games
Games 2018, 9(3), 40; https://doi.org/10.3390/g9030040
Received: 23 May 2018 / Revised: 20 June 2018 / Accepted: 22 June 2018 / Published: 26 June 2018
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Abstract
We consider non-zero sum bi-matrix games where one player presumes the role of a leader in the Stackelberg model, while the other player is her follower. We show that the leader can improve her reward if she can incentivise her follower by paying [...] Read more.
We consider non-zero sum bi-matrix games where one player presumes the role of a leader in the Stackelberg model, while the other player is her follower. We show that the leader can improve her reward if she can incentivise her follower by paying some of her own utility to the follower for assigning a particular strategy profile. Besides assuming that the follower is rational in that he tries to maximise his own payoff, we assume that he is also friendly towards his leader in that he chooses, ex aequo, the strategy suggested by her—at least as long as it does not affect his expected payoff. Assuming this friendliness is, however, disputable: one could also assume that, ex aequo, the follower acts adversarially towards his leader. We discuss these different follower behavioural models and their implications. We argue that the friendliness leads to an obligation for the leader to choose, ex aequo, an assignment that provides the highest follower return, resulting in ‘friendly incentive equilibria’. For the antagonistic assumption, the stability requirements for a strategy profile should be strengthened, comparable to the secure Nash equilibria. In general, no optimal incentive equilibrium for this condition exists, and therefore we introduce ε-optimal incentive equilibria for this case. We show that the construction of all of these incentive equilibria (and all the related leader equilibria) is tractable. Full article
(This article belongs to the Special Issue Logic and Game Theory)
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Open AccessArticle An Abstraction-Refinement Methodologyfor Reasoning about Network Games
Games 2018, 9(3), 39; https://doi.org/10.3390/g9030039
Received: 2 May 2018 / Revised: 14 June 2018 / Accepted: 17 June 2018 / Published: 22 June 2018
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Abstract
Network games (NGs) are played on directed graphs and are extensively used in network design and analysis. Search problems for NGs include finding special strategy profiles such as a Nash equilibrium and a globally-optimal solution. The networks modeled by NGs may be huge. [...] Read more.
Network games (NGs) are played on directed graphs and are extensively used in network design and analysis. Search problems for NGs include finding special strategy profiles such as a Nash equilibrium and a globally-optimal solution. The networks modeled by NGs may be huge. In formal verification, abstraction has proven to be an extremely effective technique for reasoning about systems with big and even infinite state spaces. We describe an abstraction-refinement methodology for reasoning about NGs. Our methodology is based on an abstraction function that maps the state space of an NG to a much smaller state space. We search for a global optimum and a Nash equilibrium by reasoning on an under- and an over-approximation defined on top of this smaller state space. When the approximations are too coarse to find such profiles, we refine the abstraction function. We extend the abstraction-refinement methodology to labeled networks, where the objectives of the players are regular languages. Our experimental results demonstrate the effectiveness of the methodology. Full article
(This article belongs to the Special Issue Logic and Game Theory)
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