scholarly journals A Procedural Characterization of Solution Concepts in Games

2014 ◽  
Vol 49 ◽  
pp. 143-170 ◽  
Author(s):  
J. Y. Halpern ◽  
Y. Moses
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Sequential Equilibrium ◽  
Solution Concepts ◽  
Knowledge Based ◽  
Precise Sense ◽  
Uniform Definition ◽  
Game Theoretic ◽  
Theoretic Solution

We show how game-theoretic solution concepts such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of a knowledge-based program with counterfactual semantics. In a precise sense, this program can be viewed as providing a procedural characterization of rationality.

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.

The Heuristic Use of Game Theory: Insights for Conflict Resolution

2007 ◽  
Vol 3 (2) ◽  
Author(s):  
Ben D. Mor
Keyword(s):  
Game Theory ◽  
Conflict Resolution ◽  
Bargaining Game ◽  
Solution Concepts ◽  
Negotiated Settlement ◽  
Protracted Conflict ◽  
History Of ◽  
Game Theoretic ◽  
Three Stages ◽  
Theoretic Solution

This article illustrates the heuristic use of game theory by applying it to the analysis of conflict resolution. To this end, we will proceed in three stages. First, we will define a generic bargaining game, which confronts two states that share a history of protracted conflict. Second, we will then introduce a gradual and controlled change in the preferences of the two states for the outcomes that are generated by the bargaining game. Third, for the game series that will be produced, we will apply alternative game-theoretic solution concepts and examine the expected implications of different information conditions. That is, we will establish by means of the theory what the states are expected to do in response to the induced change in their own preferences, in those of the opponent—and in their perception of each other. By modifying these parameters, we will be able to analyze the obstacles that are expected to arise in the peacemaking process and the conditions that are required to attain and stabilize a negotiated settlement.

scholarly journals Algorithms for Closed Under Rational Behavior (CURB) Sets

2010 ◽  
Vol 38 ◽  
pp. 513-534 ◽  
Author(s):  
M. Benisch ◽  
G. B. Davis ◽  
T. Sandholm
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Solution Concept ◽  
Rational Behavior ◽  
Strategy Space ◽  
Normal Form Games ◽  
Polynomial Time Algorithms ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Best Responses

We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a player’s best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a game’s smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.

scholarly journals Team Production and Esteem: A Dual Selves Model with Belief-Dependent Preferences

Games ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 33
Author(s):  
Matthias Greiff
Keyword(s):  
Game Theory ◽  
Incomplete Information ◽  
Affective Responses ◽  
Team Production ◽  
Solution Concepts ◽  
Game Theoretic ◽  
Psychological Game Theory ◽  
Expression Of Emotions ◽  
Theoretic Solution ◽  
High Effort

We propose a dual selves model to integrate affective responses and belief-dependent emotions into game theory. We apply our model to team production and model a worker as being composed of a rational self, who chooses effort, and an emotional self, who expresses esteem. Similar to psychological game theory, utilities depend on beliefs, but only indirectly. More concretely, emotions affect utilities, and the expression of emotions depends on updated beliefs. Modeling affective responses as actions chosen by the emotional self allows us to apply standard game-theoretic solution concepts. The model reveals that with incomplete information about abilities, workers only choose high effort if esteem is expressed based on interpersonal comparisons and if the preference for esteem is a status preference.

scholarly journals An Introduction to Applicable Game Theory

1997 ◽  
Vol 11 (1) ◽  
pp. 127-149 ◽  
Author(s):  
Robert Gibbons
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Private Information ◽  
Dynamic Games ◽  
Complete Information ◽  
Main Theme ◽  
Sequential Equilibrium ◽  
Solution Concepts ◽  
Bayesian Nash Equilibrium ◽  
Games With Incomplete Information

This paper offers an introduction to game theory for applied economists. The author gives simple definitions and intuitive examples of four kinds of games and their corresponding solution concepts: Nash equilibrium in static games of complete information; subgame-perfect Nash equilibrium in dynamic games of complete information; Bayesian Nash equilibrium in static games with incomplete (or 'private') information; and perfect Bayesian (or sequential) equilibrium in dynamic games with incomplete information. The main theme of the paper is that there are important differences among the games but important similarities among the solution concepts.

scholarly journals GAMES, game theory and artificial intelligence

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
John T. Hanley
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Game Theory ◽  
Decision Making ◽  
Design Methodology ◽  
Solution Concepts ◽  
Content Type ◽  
Game Theoretic ◽  
The Subject ◽  
Theoretic Solution

PurposeThe purpose of this paper is to illustrate how game theoretic solution concepts inform what classes of problems will be amenable to artificial intelligence and machine learning (AI/ML), and how to evolve the interaction between human and artificial intelligence.Design/methodology/approachThe approach addresses the development of operational gaming to support planning and decision making. It then provides a succinct summary of game theory for those designing and using games, with an emphasis on information conditions and solution concepts. It addresses how experimentation demonstrates where human decisions differ from game theoretic solution concepts and how games have been used to develop AI/ML. It concludes by suggesting what classes of problems will be amenable to AI/ML, and which will not. It goes on to propose a method for evolving human/artificial intelligence.FindingsGame theoretic solution concepts inform classes of problems where AI/ML 'solutions' will be suspect. The complexity of the subject requires a campaign of learning.Originality/valueThough games have been essential to the development of AI/ML, practitioners have yet to employ game theory to understand its limitations.

scholarly journals The State of Solving Large Incomplete-Information Games, and Application to Poker

AI Magazine ◽  
2010 ◽  
Vol 31 (4) ◽  
pp. 13 ◽  
Author(s):  
Tuomas Sandholm
Keyword(s):  
Incomplete Information ◽  
The State ◽  
Solution Concepts ◽  
Security Applications ◽  
Incomplete Information Games ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Information Games

Game-theoretic solution concepts prescribe how rational parties should act, but to become operational the concepts need to be accompanied by algorithms. I will review the state of solving incomplete-information games. They encompass many practical problems such as auctions, negotiations, and security applications. I will discuss them in the context of how they have transformed computer poker. In short, game-theoretic reasoning now scales to many large problems, outperforms the alternatives on those problems, and in some games beats the best humans.

Sign in / Sign up

Export Citation Format

Share Document