WHEN IS A STRATEGY IN GAMES?

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Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. But what is strategy? What is logic of strategy? In recent years, the dominance of game theory can be witnessed in all this. However, there are many serious problems with the concept of strategy in game theory. Not to mention the classical game theory, which aimed at the highest mathematical abstraction, it is rare to find serious attempts to capture the essence of strategic reasoning even in more recent trends in game theory, such as evolutionary or epistemic game theory. It is good news that logicians and game theorists are becoming more enthusiastic about their collaborations. Starting with the active interaction between epistemic logic and game theory, new research fields such as game logic or strategy logic have appeared. I shall argue, however, there is an unbridgeable gap between the concept of strategy in game theory and that in real games. As an antidote, I propose to analyze the concept of strategy in Baduk (Weichi, Go). For, in this ancient Asian board game, which has become famous by the recent success of AlphaGo, we can get lessons for both theoretical and practical reasoning. Admittedly, the previous discussions of strategy in Baduk literature are not thorough enough to secure a rigorous definition of strategy. However, there is one important clue: What is salient in usual approaches to strategic reasoning in Baduk is that strategy is always discussed together with tactics. Ultimately, I aim at a concept of strategy, according to which (1) it is not necessarily the case that a strategy is found in any game, (2) there has to be an intriguing interaction between a strategy and tactics, (3) it is inconsistency-robust. I shall present an analysis of a historical game record as an example that satisfies all these desiderata. Insofar as this preliminary attempt deserves more careful examination, it would be interesting to raise questions such as "Does AlphaGo have Any Strategy?" or "Could There Be a Strategy in a Mirror Game?". By discussing these questions, I will be able to hint at some implications to some crucial concepts, such as backward induction or common knowledge, in game theory Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. But what is strategy? What is logic of strategy? In recent years, the dominance of game theory can be witnessed in all this. However, there are many serious problems with the concept of strategy in game theory. Not to mention the classical game theory, which aimed at the highest mathematical abstraction, it is rare to find serious attempts to capture the essence of strategic reasoning even in more recent trends in game theory, such as evolutionary or epistemic game theory. It is good news that logicians and game theorists are becoming more enthusiastic about their collaborations. Starting with the active interaction between epistemic logic and game theory, new research fields such as game logic or strategy logic have appeared. I shall argue, however, there is an unbridgeable gap between the concept of strategy in game theory and that in real games. As an antidote, I propose to analyze the concept of strategy in Baduk (Weichi, Go). For, in this ancient Asian board game, which has become famous by the recent success of AlphaGo, we can get lessons for both theoretical and practical reasoning. Admittedly, the previous discussions of strategy in Baduk literature are not thorough enough to secure a rigorous definition of strategy. However, there is one important clue: What is salient in usual approaches to strategic reasoning in Baduk is that strategy is always discussed together with tactics. Ultimately, I aim at a concept of strategy, according to which (1) it is not necessarily the case that a strategy is found in any game, (2) there has to be an intriguing interaction between a strategy and tactics, (3) it is inconsistency-robust. I shall present an analysis of a historical game record as an example that satisfies all these desiderata. Insofar as this preliminary attempt deserves more careful examination, it would be interesting to raise questions such as "Does AlphaGo have Any Strategy?" or "Could There Be a Strategy in a Mirror Game?". By discussing these questions, I will be able to hint at some implications to some crucial concepts, such as backward induction or common knowledge, in game theory.
Publisher
COLL PUBLICATIONS
Issue Date
2018-08
Language
English
Article Type
Article
Citation

JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS, v.5, no.5, pp.1169 - 1203

ISSN
2055-3706
URI
http://hdl.handle.net/10203/246942
Appears in Collection
HSS-Journal Papers(저널논문)
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