scholarly journals ERRATUM: "RATIONAL DYNAMICS AND EPISTEMIC LOGIC IN GAMES"

2007 ◽  
Vol 09 (02) ◽  
pp. 377-409 ◽  
Author(s):  
JOHAN VAN BENTHEM
Keyword(s):  
Backward Induction ◽  
Recursive Algorithms ◽  
Strategic Games ◽  
Solution Sets ◽  
Solution Algorithms ◽  
Mutual Knowledge ◽  
Dominated Strategies ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Extensive Games

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

RATIONAL DYNAMICS AND EPISTEMIC LOGIC IN GAMES

2007 ◽  
Vol 09 (01) ◽  
pp. 13-45 ◽  
Author(s):  
JOHAN VAN BENTHEM
Keyword(s):  
Backward Induction ◽  
Recursive Algorithms ◽  
Strategic Games ◽  
Solution Sets ◽  
Solution Algorithms ◽  
Mutual Knowledge ◽  
Dominated Strategies ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Extensive Games

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

PLAUSIBILITY ORDERINGS IN DYNAMIC GAMES

2014 ◽  
Vol 30 (3) ◽  
pp. 331-364 ◽  
Author(s):  
Andrés Perea
Keyword(s):  
Belief Revision ◽  
Dynamic Games ◽  
Backward Induction ◽  
Common Belief ◽  
Revision Theory ◽  
Forward Induction ◽  
Strong Belief ◽  
Game Theoretic ◽  
Plausibility Ordering

In this paper we explore game-theoretic reasoning in dynamic games within the framework of belief revision theory. More precisely, we focus on the forward induction concept of ‘common strong belief in rationality’ (Battigalli and Siniscalchi (2002) and the backward induction concept of ‘common belief in future rationality’ (Baltag et al. 2009; Perea 2014). For both concepts we investigate whether the entire collection of selected belief revision policies for a player can be characterized by a unique plausibility ordering. We find that this is indeed possible for ‘common strong belief in rationality’, whereas this may be impossible in some games for ‘common belief in future rationality’.

scholarly journals Progress in Behavioral Game Theory

1997 ◽  
Vol 11 (4) ◽  
pp. 167-188 ◽  
Author(s):  
Colin F Camerer
Keyword(s):  
Game Theory ◽  
Social Values ◽  
Future Research ◽  
Backward Induction ◽  
Behavioral Game Theory ◽  
Dominated Strategies ◽  
Behavioral Game ◽  
Experimental Findings

Behavioral game theory aims to predict how people actually behave by incorporating psychological elements and learning into game theory. With this goal in mind, experimental findings can be organized into three categories: players have systematic 'reciprocated social values,' like desires for fairness and revenge. Phenomena discovered in studies of individual judgments and choices, like 'framing' and overconfidence, are also evident in games. Strategic principles, like irrelevance of strategy labels and timing of moves, iterated elimination of dominated strategies, and backward induction, are violated. Future research should incorporate these findings, along with learning and 'pregame theory,' into formal game theory.

scholarly journals Efficient Computation of Semivalues for Game-Theoretic Network Centrality

2018 ◽  
Vol 63 ◽  
pp. 145-189 ◽  
Author(s):  
Mateusz K. Tarkowski ◽  
Piotr L. Szczepański ◽  
Tomasz P. Michalak ◽  
Paul Harrenstein ◽  
Michael Wooldridge
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Centrality Measures ◽  
Efficient Computation ◽  
Solution Concepts ◽  
Banzhaf Index ◽  
The Shapley Value ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Network Centralities

Some game-theoretic solution concepts such as the Shapley value and the Banzhaf index have recently gained popularity as measures of node centrality in networks. While this direction of research is promising, the computational problems that surround it are challenging and have largely been left open. To date there are only a few positive results in the literature, which show that some game-theoretic extensions of degree-, closeness- and betweenness-centrality measures are computable in polynomial time, i.e., without the need to enumerate the exponential number of all possible coalitions. In this article, we show that these results can be extended to a much larger class of centrality measures that are based on a family of solution concepts known as semivalues. The family of semivalues includes, among others, the Shapley value and the Banzhaf index. To this end, we present a generic framework for defining game-theoretic network centralities and prove that all centrality measures that can be expressed in this framework are computable in polynomial time. Using our framework, we present a number of new and polynomial-time computable game-theoretic centrality measures.

Optimal eco-labeling strategy with imperfectly informed consumers

2019 ◽  
Vol 119 (6) ◽  
pp. 1166-1188 ◽  
Author(s):  
Tijun Fan ◽  
Yang Song ◽  
Huan Cao ◽  
Haiyang Xia
Keyword(s):  
Social Welfare ◽  
Environmental Quality ◽  
Design Methodology ◽  
Quality Criteria ◽  
Backward Induction ◽  
Content Type ◽  
Subgame Perfect Nash Equilibrium ◽  
Equilibrium Strategies ◽  
The Social ◽  
Game Theoretic

Purpose The purpose of this paper is to find the optimal environmental quality criteria for a strategic eco-labeling authority with three objectives (i.e. maximizing the aggregate environmental quality, maximizing the industry profit and maximizing the social welfare). Particularly, the authors investigate how the existence of imperfectly informed consumers affects labeling criteria determination and competition among firms. Design/methodology/approach A game-theoretic modeling approach was adopted in this paper. A three-stage sequential game was modeled and backward induction was used to solve for a subgame perfect Nash equilibrium. To investigate the impacts of the existence of imperfectly informed consumers, the equilibrium, if all consumers are perfectly informed of the eco-label, was studied as a benchmark. Findings A more strict eco-labeling criterion improves revenues for both the labeled and unlabeled firms. It is interesting to find that the eco-labeling criteria to maximize industry profits are stricter than the criteria to maximize social welfare. Moreover, when the fraction of imperfectly informed consumers increases, the eco-labeling criteria to maximize aggregate environmental quality or industry profits will be more strict, while the criteria to maximize the social welfare will be looser. Originality/value The authors analyze the equilibrium strategies for firms against the eco-labeling criteria certified by authority with different objectives. The obtained optimal labeling strategies could provide insightful guidelines for the certifying authority to select the best suitable labeling criteria to achieve its goals.

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