scholarly journals One-pile misère Nim for three or more players

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
Annela R. Kelly
Keyword(s):  
Game Theory ◽  
Binary Representation ◽  
Impartial Game ◽  
Classical Game

The analysis of the classical game of Nim relies on binary representation of numbers as shown in the books of Berlekamp and Gardener. There is considerable interest in generalizations and modifications of the game. We will consider one-pile misère Nim for more than two players. In the case of three or more players, the impartial game theory results rarely apply. In this note, we analyze the game in a variety of cases where alliances are formed among the players.

Quantum Game of Dual-channel Supply Chain under Free-riding Behavior

2021 ◽  
Vol 1 (1) ◽  
pp. 3-17
Author(s):  
Yu-Chung Chang ◽  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Quantum Entanglement ◽  
Free Riding ◽  
Selling Price ◽  
Quantum Game ◽  
Optimal Price ◽  
Dual Channel ◽  
Dual Channel Supply Chain ◽  
Classical Game

Based on the perspective of the quantum game, this paper explores when the online direct sales channel takes the free-riding behavior after the retail channel provides high-quality experience and services and how the dual-channel supply chain establishes a commodity pricing strategy. The retailer’s selling price follows a decreasing function of the free-riding behavior coefficient. while the online direct selling price does an increasing function of the free-riding behavior coefficient. Under centralized decision-making, there is no quantum entanglement, so the quantum game solution is consistent with the classical game solution. Under decentralized decision-making, the optimal price and profit of the quantum game are higher than those of the classical game when the quantum entanglement degree is greater than zero. When the quantum entanglement tends to be infinite, the optimal price of the quantum game finally remains in convergence. The quantum game theory is a more optimal decision-making method than the classical game theory.

Game Theory and the Law

2021 ◽  
pp. 55-70
Author(s):  
Marlies Ahlert
Keyword(s):  
Game Theory ◽  
Common Knowledge ◽  
Ideal Theory ◽  
Specific Information ◽  
Strategic Interactions ◽  
Bargaining Problems ◽  
Game Forms ◽  
Classical Game ◽  
Micro Foundations ◽  
Adaptation Model

Classical game theory analyses strategic interactions under extreme idealisations. It assumes cognitively unconstrained players with common knowledge concerning game forms, preferences, and rationality. Such ideal theory is highly relevant for human self-understanding as a rational being or what Selten called ‘rationology’. Yet, ideal theory is highly irrelevant for real actors who are in Selten’s sense boundedly rational. Starting from essential features of real bargaining problems, elements of Selten’s ‘micro-psychological’ and Raiffa’s ‘telescopic’ behavioural bargaining theory are introduced. From this, an outline of a workable rationality approach to bargaining emerges. It suggests relying on telescopic elements from Raiffa’s model to provide general outcome orientation and on insights from Selten’s aspiration adaptation model of individual decision making to develop process-sensitive action advice. A bird’s eye view of a prominent recent case of ‘bargaining in the shadow of the courts’ shows a surprisingly good fit of outcomes with the implications of Raiffa’s telescopic approach while remaining compatible with a Seltenian process. Though due to a lack of specific information because the micro-foundations for the telescopic theory cannot be provided, it is at least clear how further case studies and experiments might be put to work here.

Fuzzy Optimal Approaches to 2-P Cooperative Games

2016 ◽  
Vol 3 (2) ◽  
pp. 22-35
Author(s):  
Mubarak S. Al-Mutairi
Keyword(s):  
Game Theory ◽  
Favourable Outcome ◽  
Decision Makers ◽  
Fuzzy Approach ◽  
Fuzzy Information ◽  
Missing Information ◽  
Conflicting Objectives ◽  
Potential Benefits ◽  
Classical Game ◽  
Classical Game Theory

In game theory, two or more parties need to make decisions with fully or partially conflicting objectives. In situations where reaching a more favourable outcome depends upon cooperation between the two conflicting parties, some of the mental and subjective attitudes of the decision makers must be considered. While the decision to cooperate with others bears some risks due to uncertainty and loss of control, not cooperating means giving up potential benefits. In practice, decisions must be made under risk, uncertainty, and incomplete or fuzzy information. Because it is able to work well with vague, ambiguous, imprecise, noisy or missing information, the fuzzy approach is effective for modeling such multicriteria conflicting situations. The well-known game of Prisoner's Dilemma, which reflects a basic situation in which one must decide whether to cooperate or not with a competitor, is systematically solved using a fuzzy approach. The fuzzy procedure is used to incorporate some of the subjective attitudes of the decision makers that are difficult to model using classical game theory. Furthermore, it permits researchers to consider the subjective attitudes of the decision makers and make better decisions in subjective, uncertain, and risky situations.

Exponential Families and Game Dynamics

1982 ◽  
Vol 34 (2) ◽  
pp. 374-405 ◽  
Author(s):  
Ethan Akin
Keyword(s):  
Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Exponential Families ◽  
Von Neumann ◽  
Rational Player ◽  
Large Populations ◽  
Pure Strategies ◽  
Classical Game ◽  
Classical Game Theory

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.

scholarly journals Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

2019 ◽  
Vol 9 (13) ◽  
pp. 2635 ◽  
Author(s):  
Konstantinos Giannakis ◽  
Georgia Theocharopoulou ◽  
Christos Papalitsas ◽  
Sofia Fanarioti ◽  
Theodore Andronikos
Keyword(s):  
Game Theory ◽  
Finite Automata ◽  
State Machines ◽  
Conditional Strategy ◽  
Abstract Machines ◽  
Quantum Finite Automata ◽  
Quantum Version ◽  
Important Field ◽  
Classical Game ◽  
Classical Game Theory

Classical game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the prisoner’s dilemma (PD), have attracted a lot of attention. This game variant can be considered as a specific type of game where the player’s actions and strategies are formed using notions from quantum computation. Similarly, state machines, and specifically finite automata, have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine well-known conditional strategies that have been studied within the framework of the classical repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with a probability of 1, achieving some interesting results. We also study the quantum version of PD under the Eisert–Wilkens–Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

Classical, Modern, and New Game Theory / Klassische, Moderne und Neue Spieltheorie

2002 ◽  
Vol 222 (5) ◽  
Author(s):  
Manfred J. Holler
Keyword(s):  
Game Theory ◽  
Economic Behavior ◽  
Decision Makers ◽  
Main Theme ◽  
Second Stage ◽  
Third Stage ◽  
History Of ◽  
Payoff Functions ◽  
Successful Behavior ◽  
Classical Game

SummaryThis paper is a brief history of game theory with its main theme being the nature of the decision makers assumed in the various stages of its historical development. It demonstrates that changes in the “image of man” nourished the developments of what many believe to be progress in game theory. The first stage, classical game theory, is defined by John von Neumann’s and Oskar Morgenstern’s pioneering book “Game Theory and Economic Behavior” which introduced the concept of individual rational players and focuses on conflicting interests. The second stage, modern game theory, is defined by the Nash player who is not only rational but, at least implicitly, assumes that all players are rational to such a degree that players can coordinate their strategies so that a Nash equilibrium prevails. The third stage, new game theory, is defined by the Harsanyi player who is rational but knows very little about the other players, e.g., their payoff functions or the way they form beliefs about other players’ payoff functions or beliefs. The Harsanyi player either plays a highly sophisticated epistemic game on the forming of beliefs or rests content with himself by imitating the observed successful behavior of other agents.

HOW CAN QUESTIONS BE INFORMATIVE BEFORE THEY ARE ANSWERED? STRATEGIC INFORMATION IN INTERROGATIVE GAMES

Episteme ◽  
2012 ◽  
Vol 9 (2) ◽  
pp. 189-204 ◽  
Author(s):  
Emmanuel J. Genot ◽  
Justine Jacot
Keyword(s):  
Game Theory ◽  
The State ◽  
Information Structures ◽  
Strategic Information ◽  
State Of Nature ◽  
Gricean Pragmatics ◽  
Asking Questions ◽  
Classical Game ◽  
Special Case ◽  
Classical Game Theory

AbstractWe examine a special case of inquiry games and give an account of the informational import of asking questions. We focus on yes-or-no questions, which always carry information about the questioner's strategy, but never about the state of Nature, and show how strategic information reduces uncertainty through inferences about other players' goals and strategies. This uncertainty cannot always be captured by information structures of classical game theory. We conclude by discussing the connection with Gricean pragmatics and contextual constraints on interpretation.

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