scholarly journals Reactive Strategies: An Inch of Memory, a Mile of Equilibria

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 42
Author(s):  
Artem Baklanov
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Folk Theorem ◽  
Pareto Improvement ◽  
Symmetric Equilibrium ◽  
Equilibrium Payoff ◽  
Incremental Change ◽  
Symmetric Games ◽  
Stage Game

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash Equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring

2002 ◽  
Vol 2 (1) ◽  
Author(s):  
George J. Mailath ◽  
Steven A. Matthews ◽  
Tadashi Sekiguchi
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Finitely Repeated Games ◽  
Game Equilibrium ◽  
Public Signals ◽  
Stage Game ◽  
Public Monitoring ◽  
Public Signal ◽  
Action Profile

We present three examples of finitely repeated games with public monitoring that have sequential equilibria in private strategies, i.e., strategies that depend on own past actions as well as public signals. Such private sequential equilibria can have features quite unlike those of the more familiar perfect public equilibria: (i) making a public signal less informative can create Pareto superior equilibrium outcomes; (ii) the equilibrium final-period action profile need not be a stage game equilibrium; and (iii) even if the stage game has a unique correlated (and hence Nash) equilibrium, the first-period action profile need not be a stage game equilibrium.

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.

scholarly journals Strong and Safe Nash Equilibrium in Some Repeated 3-Player Games

2019 ◽  
Vol 65 (3) ◽  
pp. 271-295 ◽  
Author(s):  
Tadeusz Kufel ◽  
Sławomir Plaskacz ◽  
Joanna Zwierzchowska
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Equilibrium Payoff ◽  
Equilibrium Strategies ◽  
Strong Nash Equilibrium ◽  
Player Game ◽  
Stage Game

The paper examines an infinitely repeated 3-player extension of the Prisoner’s Dilemma game. We consider a 3-player game in the normal form with incomplete information, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage, players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players’ payoffs do not exceed the nondeviating player payoff more than by a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale’s good strategies described in Smale’s paper (1980), where the repeated Prisoner’s Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.

scholarly journals A complete folk theorem for finitely repeated games

2020 ◽  
Vol 49 (4) ◽  
pp. 1129-1142
Author(s):  
Ghislain-Herman Demeze-Jouatsa
Keyword(s):  
Repeated Games ◽  
Pure Strategy ◽  
Complete Information ◽  
Repeated Game ◽  
Complete Characterization ◽  
Folk Theorem ◽  
Equilibrium Payoff ◽  
Perfect Monitoring ◽  
Special Case

AbstractThis paper analyzes the set of pure strategy subgame perfect Nash equilibria of any finitely repeated game with complete information and perfect monitoring. The main result is a complete characterization of the limit set, as the time horizon increases, of the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely repeated game. This model includes the special case of observable mixed strategies.

scholarly journals The Folk Theorem in Repeated Games With Anonymous Random Matching

Econometrica ◽  
2020 ◽  
Vol 88 (3) ◽  
pp. 917-964 ◽  
Author(s):  
Joyee Deb ◽  
Takuo Sugaya ◽  
Alexander Wolitzky
Keyword(s):  
Repeated Games ◽  
Cheap Talk ◽  
Folk Theorem ◽  
Random Matching ◽  
Record Keeping ◽  
Communication Devices ◽  
Stage Game

We prove the folk theorem for discounted repeated games with anonymous random matching. We allow non‐uniform matching, include asymmetric payoffs, and place no restrictions on the stage game other than full dimensionality. No record‐keeping or communication devices—including cheap talk communication and public randomization—are necessary.

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.

Classes of Potential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Resource Allocation ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Potential Games ◽  
Congestion Games ◽  
Fictitious Play ◽  
Resource Allocation Problem ◽  
Distributed Resource Allocation ◽  
Symmetric Games ◽  
The Cost

This chapter discusses several classes of potential games that are common in the literature and how to derive the Nash equilibrium for such games. It first considers identical interests games and dummy games before turning to decoupled games and bilateral symmetric games. It then describes congestion games, in which all players are equal, in the sense that the cost associated with each resource only depends on the total number of players using that resource and not on which players use it. It also presents other potential games, including the Sudoku puzzle, and goes on to analyze the distributed resource allocation problem, the computation of Nash equilibria for potential games, and fictitious play. It concludes with practice exercises and their corresponding solutions, along with additional exercises.

scholarly journals Nash versus coarse correlation

2020 ◽  
Vol 23 (4) ◽  
pp. 1178-1204 ◽  
Author(s):  
Konstantinos Georgalos ◽  
Indrajit Ray ◽  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Individual Choice ◽  
Pure Nash Equilibrium ◽  
Expected Payoff ◽  
Equilibrium Payoff ◽  
Payoff Dominance ◽  
Dominated Strategies ◽  
Person Game ◽  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

Model of Intrusion Detection Based on the Game Theory

2013 ◽  
Vol 347-350 ◽  
pp. 3971-3974 ◽  
Author(s):  
Heng Xiao ◽  
Cao Fang Long
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Network Security ◽  
Intrusion Detection ◽  
Working Group ◽  
Ad Hoc ◽  
Game Model ◽  
The Game Theory ◽  
Network Application ◽  
Stage Game

With the development of network application, network security is facing greater pressure. Based on the characteristics of intrusion detection in the wireless network of the Ad hoc working group, the article introduces the game theory, proposes a game model of network security, concluds the Nash equilibrium in the stage game, repeats game, the pareto Nash equilibrium, more attack both income and payment, so that they get the best choice.

Sign in / Sign up

Export Citation Format

Share Document