The Foole, the Shepherd, and the Knave

2018 ◽  
Author(s):  
Peter Vanderschraaf
Keyword(s):  
Repeated Games ◽  
Folk Theorem ◽  
Social Sanctions ◽  
Identity Concealment ◽  
Reconciliation Project ◽  
The Invisible

The Reconciliation Project, the attempt to show that justice is compatible with rational prudence, is evaluated in light of the classic challenges of Hobbes’ Foole, Plato’s Lydian Shepherd, and Hume’s Sensible Knave. Hobbes’ response to the Foole is justice-reciprocalist, emphasizing social sanctions, and is naturally interpreted in terms of folk theorem interactions of repeated games. Plato’s justice-Platonist response to the Shepherd, who has identity-concealing power, emphasizes goods allegedly inseparable from justice. A new Invisible Foole challenge is considered where an agent like the Foole who takes seriously only social sanctions acquires identity-concealment technology, and folk theorem responses are proposed for this challenge. The Invisible Foole challenge is similar to the most serious challenge, that of the Sensible Knave. The most compelling response to the Knave’s challenge combines elements of justice-reciprocalism and justice-Platonism.

Cooperative Homo economicus

2011 ◽  
Author(s):  
Samuel Bowles ◽  
Herbert Gintis
Keyword(s):  
Private Information ◽  
Repeated Games ◽  
Evolutionary Dynamics ◽  
Public Information ◽  
Folk Theorem ◽  
The Self ◽  
Correlated Equilibrium ◽  
Homo Economicus ◽  
Self Interest ◽  
Game Theoretic

This chapter examines whether recent advances in the theory of repeated games, as exemplified by the so-called folk theorem and related models, address the shortcomings of the self-interest based models in explaining human cooperation. It first provides an overview of folk theorems and their account of evolutionary dynamics before discussing the folk theorem with either imperfect public information or private information. It then considers evolutionarily irrelevant equilibrium as well as the link between social norms and the notion of correlated equilibrium. While the insight that repeated interactions provide opportunities for cooperative individuals to discipline defectors is correct, the chapter argues that none of the game-theoretic models mentioned above is successful. Except under implausible conditions, the cooperative outcomes identified by these models are neither accessible nor persistent, and are thus labeled evolutionarily irrelevant Nash equilibria.

A Few Bad Apples Spoil the Barrel: An Anti-Folk Theorem for Anonymous Repeated Games with Incomplete Information

2020 ◽  
Vol 110 (12) ◽  
pp. 3817-3835
Author(s):  
Takuo Sugaya ◽  
Alexander Wolitzky
Keyword(s):  
Incomplete Information ◽  
Repeated Games ◽  
Prisoner’S Dilemma ◽  
Folk Theorem ◽  
Smoothness Condition ◽  
Cournot Oligopoly ◽  
Random Matching ◽  
Games With Incomplete Information ◽  
Linear Demand ◽  
Number Of Firms

We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases. (JEL C72, C73, D83)

The Folk Theorem for Repeated Games with Time-Dependent Discounting

2021 ◽  
Author(s):  
Daehyun Kim ◽  
Xiaoxi Li
Keyword(s):  
Repeated Games ◽  
Folk Theorem ◽  
The Self ◽  
Time Dependent ◽  
Constructive Proof ◽  
The Public ◽  
Discount Factors ◽  
Time Inconsistent ◽  
Public Monitoring ◽  
Perfect Monitoring

This paper defines a general framework to study infinitely repeated games with time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeated games, we introduce an asymptotic condition to characterize the fact that players become more and more patient; that is, the discount factors at all stages uniformly converge to one. Two types of folk theorems are proven without the public randomization assumption: the asymptotic one, that is, the equilibrium payoff set converges to the feasible and individual rational set as players become patient, and the uniform one, that is, any payoff in the feasible and individual rational set is sustained by a single strategy profile that is an approximate subgame perfect Nash equilibrium in all games with sufficiently patient discount factors. We use two methods for the study of asymptotic folk theorem: the self-generating approach and the constructive proof. We present the constructive proof in the perfect-monitoring case and show that it can be extended to time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a nonmonotonicity result.

A PSEUDO "FOLK" THEOREM IN THE STRATEGIC PROVISION OF STOCK EXTERNALITIES

2003 ◽  
Vol 05 (04) ◽  
pp. 347-359 ◽  
Author(s):  
ZILI YANG
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Folk Theorem ◽  
Policy Implications ◽  
Small Positive Number ◽  
Dynamic Setting ◽  
Predetermined Level ◽  
Time Discount ◽  
Pareto Efficient ◽  
The Relationship

The paper discusses the relationship between the efficient provision and the Nash equilibrium of stock externalities in a dynamic setting. The following proposition has been proved: under certain conditions, the maximal gains of an agent in the economy by deviating from the Pareto optimal provision of stock externalities is less ∊, an arbitrary small positive number, when the time discount rate of the agents are sufficiently close to 0. Namely, under the same conditions, a Pareto efficient path is an ∊-Nash equilibrium where ∊ could be smaller than any predetermined level. The propositions are different from the folk theorems in repeated games because supporting of the ∊-Nash equilibrium does not require the threat of retaliations from other agents. The policy implications of the above results are also discussed here.

The Folk Theorem for Repeated Games: A Neu Condition

Econometrica ◽  
1994 ◽  
Vol 62 (4) ◽  
pp. 939 ◽  
Author(s):  
Dilip Abreu ◽  
Prajit K. Dutta ◽  
Lones Smith
Keyword(s):  
Repeated Games ◽  
Folk Theorem

scholarly journals The folk theorem for repeated games with observation costs

2008 ◽  
Vol 139 (1) ◽  
pp. 192-221 ◽  
Author(s):  
Eiichi Miyagawa ◽  
Yasuyuki Miyahara ◽  
Tadashi Sekiguchi
Keyword(s):  
Repeated Games ◽  
Folk Theorem
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