scholarly journals Refinements and higher-order beliefs: a unified survey

2019 ◽  
Vol 71 (1) ◽  
pp. 7-34 ◽  
Author(s):  
Atsushi Kajii ◽  
Stephen Morris
Keyword(s):  
Game Theory ◽  
Normal Form ◽  
Econ Theory ◽  
Complete Information ◽  
Higher Order ◽  
Economic Modelling ◽  
The Game Theory ◽  
Standard Normal ◽  
Payoff Uncertainty ◽  
Theory Interpretation

AbstractThis paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps in Game theory and economic modelling. Clarendon Press, Oxford, 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher-order beliefs literature” (Rubinstein in Am Econ Rev 79:385–391, 1989; Monderer and Samet in Games Econ Behav 1:170–190, 1989; Morris et al. in Econ J Econ Soc 63:145–157, 1995; Kajii and Morris in Econ J Econ Soc 65:1283–1309, 1997a) and the “payoff uncertainty approach” (Fudenberg et al. in J Econ Theory 44:354–380, 1988; Dekel and Fudenberg in J Econ Theory 52:243–267, 1990).

Game Theory and Other Modeling Approaches

2018 ◽  
Author(s):  
Frank C. Zagare ◽  
Branislav L. Slantchev
Keyword(s):  
Game Theory ◽  
International Relations ◽  
Incomplete Information ◽  
Dynamic Games ◽  
Complete Information ◽  
Third Wave ◽  
Extensive Form ◽  
Interactive Decision Making ◽  
The Game Theory ◽  
Almost All

Game theory is the science of interactive decision making. It has been used in the field of international relations (IR) for over 50 years. Almost all of the early applications of game theory in international relations drew upon the theory of zero-sum games, but the first generation of applications was also developed during the most intense period of the Cold War. The theoretical foundations for the second wave of the game theory literature in international relations were laid by a mathematician, John Nash, a co-recipient of the 1994 Nobel Prize in economics. His major achievement was to generalize the minimax solution which emerged from the first wave. The result is the now famous Nash equilibrium—the accepted measure of rational behavior in strategic form games. During the third wave, from roughly the early to mid-1980s to the mid-1990s, there was a distinct move away from static strategic form games toward dynamic games depicted in extensive form. The assumption of complete information also fell by the wayside; games of incomplete information became the norm. Technical refinements of Nash’s equilibrium concept both encouraged and facilitated these important developments. In the fourth and final wave, which can be dated, roughly, from around the middle of the 1990s, extensive form games of incomplete information appeared regularly in the strategic literature. The fourth wave is a period in which game theory was no longer considered a niche methodology, having finally emerged as a mainstream theoretical tool.

scholarly journals Exact Solution of Modified Veselov–Novikov Equation and Some Applications in the Game Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Damir Kurmanbayev
Keyword(s):  
Game Theory ◽  
Exact Solution ◽  
Exact Solutions ◽  
Geometric Interpretation ◽  
Higher Order ◽  
The Game Theory ◽  
Novikov Equation

A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.

The Research on the Designs of Optimal Contract when Carrying on Technical Transactions

2007 ◽  
Vol 10-12 ◽  
pp. 6-11
Author(s):  
Y.X. Sheng ◽  
W.G. Yang
Keyword(s):  
Game Theory ◽  
Incomplete Information ◽  
Operation Research ◽  
Complete Information ◽  
Optimal Contract ◽  
Optimal Contracts ◽  
The Game Theory

This article utilizes the game theory of the complete information condition and incomplete information condition equilibrium as well as the operation research optimization knowledge, carries on the analysis to the technical transaction of optimal contracts design question, under each kind of situation, in view of the different situation, design each kind of different optimal contracts, thus to do business, both sides both can accept them.

scholarly journals The Game Theory of Politeness in Language: A Formal Model of Polite Requests

2019 ◽  
Author(s):  
Roland Muehlenbernd ◽  
Przemyslaw Zywiczynski ◽  
Sławomir Wacewicz
Keyword(s):  
Game Theory ◽  
Social Behavior ◽  
Formal Model ◽  
Mathematical Proof ◽  
Signaling Theory ◽  
Order Theory ◽  
Higher Order ◽  
The Game Theory ◽  
Human Social Behavior ◽  
Higher Order Theory

Linguistic Politeness (LP) is a fascinating domain of language, as it directly interfaces with human social behavior. Here, we show how game theory, as a higher-order theory of behavior, can provide the tools to understand and model LP phenomena. We show this for the specific case of requests, where the magnitude of request and the resultant Rate of Imposition are subsumed under a more powerful explanatory principle: alignment of interests. We put forward the Politeness Equilibrium Principle (PEP), whereby the more disalignment there is between the interests of Speaker and Hearer, the more LP Speaker needs to offset the imbalance. In the second part of our paper, we flesh out our ideas by means of a formal model inspired by evolutionary signaling theory, and provide a mathematical proof showing that the model follows the PEP. We see this work as an important first step in the direction of reconciling theories of language with signaling theory, by incorporating language into more general models of communication.

scholarly journals Conceptual & economic modelling on whistleblowing decision-making phenomena

2015 ◽  
Vol 12 (3) ◽  
pp. 534-540
Author(s):  
Shewangu Dzomira
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Conceptual Model ◽  
Economic Model ◽  
Unethical Behavior ◽  
Economic Modelling ◽  
Mixed Strategies ◽  
The Game Theory ◽  
Mixed Equilibrium ◽  
High Chance

The whistleblower is always in a dilemma situation whenever making a decision on whether to blow or not blow the whistle after observing unethical behavior or wrongdoing. This paper provides conceptual model and an economic model for whistleblowing decision making phenomena through mixed strategies of the game theory. The instinctual issue of whistleblowing game’s mixed equilibrium would be that the probabilities rest on the opponent’s payoffs and not on the player’s own payoffs. Even if blowing the whistle is not really definite, a satisfactorily high chance of disinterring the wrongdoing ought to discourage commission of unethical behavior.

Reputation and Gossip in Game Theory

2019 ◽  
pp. 213-229
Author(s):  
Charles Roddie
Keyword(s):  
Game Theory ◽  
Strategic Behavior ◽  
Third Party ◽  
The Past ◽  
Past Behavior ◽  
Future Behavior ◽  
The Game Theory ◽  
Shed Light

When interacting with others, it is often important for you to know what they have done in similar situations in the past: to know their reputation. One reason is that their past behavior may be a guide to their future behavior. A second reason is that their past behavior may have qualified them for reward and cooperation, or for punishment and revenge. The fact that you respond positively or negatively to the reputation of others then generates incentives for them to maintain good reputations. This article surveys the game theory literature which analyses the mechanisms and incentives involved in reputation. It also discusses how experiments have shed light on strategic behavior involved in maintaining reputations, and the adequacy of unreliable and third party information (gossip) for maintaining incentives for cooperation.

scholarly journals The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1443
Author(s):  
Zhiyuan Dong ◽  
Ai-Guo Wu
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Quantum Game ◽  
Final State ◽  
The Game Theory ◽  
Initial States ◽  
Quantum Strategy ◽  
Selection Of

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.

scholarly journals Multi-Robot Searching using Game-Theory Based Approach

10.5772/6232 ◽  
2008 ◽  
Vol 5 (4) ◽  
pp. 44 ◽  
Author(s):  
Yan Meng
Keyword(s):  
Game Theory ◽  
Dynamic Programming ◽  
Utility Function ◽  
Real Time ◽  
Dynamic Environment ◽  
Equilibrium Solutions ◽  
Strategy Equilibrium ◽  
The Game Theory ◽  
Target Searching ◽  
Multi Robot

This paper proposes a game-theory based approach in a multi–target searching using a multi-robot system in a dynamic environment. It is assumed that a rough priori probability map of the targets' distribution within the environment is given. To consider the interaction between the robots, a dynamic-programming equation is proposed to estimate the utility function for each robot. Based on this utility function, a cooperative nonzero-sum game is generated, where both pure Nash Equilibrium and mixed-strategy Equilibrium solutions are presented to achieve an optimal overall robot behaviors. A special consideration has been taken to improve the real-time performance of the game-theory based approach. Several mechanisms, such as event-driven discretization, one-step dynamic programming, and decision buffer, have been proposed to reduce the computational complexity. The main advantage of the algorithm lies in its real-time capabilities whilst being efficient and robust to dynamic environments.

scholarly journals Cooperative n-person Prisoner's Dilemma on a Network

2021 ◽  
Vol 14 ◽  
pp. 122-126
Author(s):  
Aleksandra L. Grinikh ◽  
◽  
Leon A. Petrosyan ◽  
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Pairwise Interaction ◽  
Network Interaction ◽  
The Game Theory

In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the in uence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.

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