Bayesian Rationality and Social Epistemology

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Social Norms ◽  
Social Epistemology ◽  
Correlated Equilibrium ◽  
Epistemic Game Theory ◽  
Famous Theorem ◽  
Rational Agents ◽  
Natural Equilibrium ◽  
Bayesian Rationality

This chapter uses epistemic game theory to expand on the notion of social norms as choreographer of a correlated equilibrium, and to elucidate the socio-psychological prerequisites for the notion that social norms implement correlated equilibria. The correlated equilibrium is a much more natural equilibrium criterion than the Nash equilibrium, because of a famous theorem of Aumann (1987), who showed that Bayesian rational agents in an epistemic game G with a common subjective prior play a correlated equilibrium of G. Thus, while rationality and common priors do not imply Nash equilibrium, these assumptions do imply correlated equilibrium and social norms act not only as choreographer, but also supply the epistemic conditions for common priors.

Summary

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Social Norms ◽  
Social Theory ◽  
Human Behavior ◽  
Unified Model ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Correlated Equilibria ◽  
Indispensable Tool

This chapter summarizes the book's main points, covering game theory, the commonality of beliefs, the limits of rationality, social norms as correlated equilibria, and how reason is bounded by sociality, not irrationality. Among the conclusions are that game theory is an indispensable tool in modeling human behavior. Behavioral disciplines that reject or peripheralize game theory are theoretically handicapped. The Nash equilibrium is not the appropriate equilibrium concept for social theory. The correlated equilibrium is the appropriate equilibrium concept for a set of rational individuals having common priors. Social norms are correlated equilibria. The behavioral disciplines today have four incompatible models of human behavior. The behavioral sciences must develop a unified model of choice that eliminates these incompatibilities and that can be specialized in different ways to meet the heterogeneous needs of the various disciplines.

Game Theory

2016 ◽  
Author(s):  
Cristina Bicchieri ◽  
Giacomo Sillari
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Evolutionary Game Theory ◽  
Repeated Games ◽  
Evolutionary Game ◽  
Complete Information ◽  
Decision Makers ◽  
Correlated Equilibrium ◽  
Extensive Form

Game theory aims to understand situations in which decision-makers interact strategically. Chess is an example, as are firms competing for business, politicians competing for votes, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships, and so on. In such situations, the outcome depends on what the parties do jointly. Decision-makers may be people, organizations, animals, or even genes. In this chapter, the authors review fundamental notions of game theory and their application to philosophy of science. In particular, Section 1 looks at games of complete information through normal and extensive form representations, introduce the notion of Nash equilibrium and its refinements. Section 2 touches on epistemic foundations and correlated equilibrium, and Section 3 examines repeated games and their importance for the analysis of altruism and cooperation. Section 4 deals with evolutionary game theory.

scholarly journals Pricing in Information Orchestrators and Maximizing Stable Networks

2019 ◽  
Vol 21 (03) ◽  
pp. 1850013
Author(s):  
Bernardo C. Lustosa ◽  
Alberto L. Albertin ◽  
Fernando Moreira
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Information Exchange ◽  
Added Value ◽  
Innovation Networks ◽  
Network Stability ◽  
Financial Benefit ◽  
Equilibrium Conditions ◽  
Rational Agents ◽  
Pricing Options

In innovation networks based on information exchange, an orchestrating actor, or hub, captures information from peripheral actors, promotes innovation and then distributes it to the network in the form of added value. This paper identifies the pricing options proposed by the orchestrating hub that would result in the network’s stability and efficiency. Since all the companies in this ecosystem can be seen as rational agents, game theory is an appropriate framework for studying pricing as a mechanism to promote network stability. We analyze the equilibrium conditions in this context and conclude that the Nash equilibrium entails the network’s stability. Our findings indicate that, in order to maximize the innovation power of the network, the agents should be charged a price proportional to the financial benefit obtained by the net innovation. This study fills relevant gaps in the literature on monopolistic orchestrated innovation and the pricing structures of network connections.

scholarly journals Collective intentionality in economics: making Searle's theory of institutional facts relevant for game theory

2013 ◽  
Vol 6 (1) ◽  
pp. 1 ◽  
Author(s):  
Cyril Hédoin
Keyword(s):  
Game Theory ◽  
Social Norms ◽  
Correlated Equilibrium ◽  
Collective Intentionality ◽  
Legal Rules ◽  
Economic Theories ◽  
Institutional Facts ◽  
Team Reasoning ◽  
Game Theoretic ◽  
Common Understanding

Economic theories of team reasoning build on the assumption that agents can sometimes behave according to beliefs or preferences attributed to a group or a team. In this paper, I propose a different framework to introduce collective intentionality into game theory. I build on John Searle’s account, which makes collective intentionality constitutive of institutional facts. I show that as soon as one accepts that institutions (conventions, social norms, legal rules) are required to solve indetermination problems in a game, it is necessary to assume a form of collective intentionality that comes from what I call a common understanding of the situation among the players. This common understanding embodies the epistemic requirements for an institution to be a correlated equilibrium in a game. As a consequence, I question recent claims made by some economists according to which game-theoretic accounts of institutions do not need to assume collective intentionality.

Game Theory: Basic Concepts

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Solution Concept ◽  
Correlated Equilibrium ◽  
Suggested Strategy ◽  
Basic Concepts ◽  
Pure Strategies ◽  
Natural Solution ◽  
Classical Game

This chapter deals with the basic concepts of game theory. It presents the formulations for the extensive form, normal form, and Nash equilibrium. It concludes with a brief discussion of correlated equilibrium, a solution concept that has been neglected in classical game theory but is a more natural solution concept than the Nash equilibrium. This is because the correlated equilibrium directly addresses the central weaknesses of the Nash equilibrium concept: its lack of a mechanism for choosing among various equally plausible alternatives, for coordinating the behaviors of players who are indifferent among several pure strategies, and for providing incentives for players to follow the suggested strategy even when they may have private payoffs that would lead self-regarding agents to do otherwise.

scholarly journals PERIODIC STRATEGIES II: GENERALIZATIONS AND EXTENSIONS

2020 ◽  
Vol 23 (02) ◽  
pp. 2050005
Author(s):  
V. K. OIKONOMOU ◽  
J. JOST
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Cooperative Game Theory ◽  
Solution Concept ◽  
Epistemic Game Theory ◽  
Bayesian Games ◽  
Mathematical Properties ◽  
Games With Incomplete Information ◽  
Theory Framework

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper [V. K. Oikonomou and J. Jost, Periodic strategies: A new solution concept and an algorithm for nontrivial strategic form games, Adv. Compl. Syst. 20(5) (2017) 1750009], in contrast, the own payoff does not depend on the opponent’s action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover, we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

INTERPERSONAL COORDINATION AND EPISTEMIC SUPPORT FOR INTENTIONS WITH WE-CONTENT

2010 ◽  
Vol 26 (3) ◽  
pp. 345-367 ◽  
Author(s):  
Olivier Roy
Keyword(s):  
Game Theory ◽  
Epistemic Logic ◽  
The Other ◽  
Interpersonal Coordination ◽  
Epistemic Game Theory ◽  
Cast Doubt ◽  
Alternative Set

In this paper I study intentions of the form ‘I intend that we . . .’, that is, intentions with a we-content, and their role in interpersonal coordination. I focus on the notion of epistemic support for such intentions. Using tools from epistemic game theory and epistemic logic, I cast doubt on whether such support guarantees the other agents' conditional mediation in the achievement of such intentions, something that appears important if intentions with a we-content are to count as genuine intentions. I then formulate a stronger version of epistemic support, one that does indeed ensure the required mediation, but I then argue that it rests on excessively strong informational conditions. In view of this I provide an alternative set of conditions that are jointly sufficient for coordination in games, and I argue that these conditions constitute a plausible alternative to the proposed notion of epistemic support.

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