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.

Quadratic-monomial generated domains from mixed signed, directed graphs

2019 ◽  
Vol 29 (02) ◽  
pp. 279-308
Author(s):  
Michael A. Burr ◽  
Drew J. Lipman
Keyword(s):  
Directed Graphs ◽  
Complete Characterization ◽  
Combinatorial Structure ◽  
Signed Directed Graph ◽  
Odd Cycle ◽  
Combinatorial Classification ◽  
Special Case ◽  
Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

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.

scholarly journals A CHARACTERIZATION OF SELF-ADJOINT OPERATORS DETERMINED BY THE WEAK FORMULATION OF SECOND-ORDER SINGULAR DIFFERENTIAL EXPRESSIONS

2009 ◽  
Vol 51 (2) ◽  
pp. 385-404 ◽  
Author(s):  
MOHAMED EL-GEBEILY ◽  
DONAL O'REGAN
Keyword(s):  
Complete Characterization ◽  
Second Order ◽  
Inner Product ◽  
Type I ◽  
Weak Formulation ◽  
Friedrichs Extension ◽  
Sesquilinear Form ◽  
Adjoint Operators ◽  
Special Case

AbstractIn this paper we describe a special class of self-adjoint operators associated with the singular self-adjoint second-order differential expression ℓ. This class is defined by the requirement that the sesquilinear form q(u, v) obtained from ℓ by integration by parts once agrees with the inner product 〈ℓu, v〉. We call this class Type I operators. The Friedrichs Extension is a special case of these operators. A complete characterization of these operators is given, for the various values of the deficiency index, in terms of their domains and the boundary conditions they satisfy (separated or coupled).

The complexity of resolution refinements

2007 ◽  
Vol 72 (4) ◽  
pp. 1336-1352 ◽  
Author(s):  
Joshua Buresh-Oppenheim ◽  
Toniann Pitassi
Keyword(s):  
Theorem Proving ◽  
Complete Characterization ◽  
Exponential Separation ◽  
Semantic Resolution ◽  
Special Case

AbstractResolution is the most widely studied approach to propositional theorem proving. In developing efficient resolution-based algorithms, dozens of variants and refinements of resolution have been studied from both the empirical and analytic sides. The most prominent of these refinements are: DP (ordered), DLL (tree), semantic, negative, linear and regular resolution. In this paper, we characterize and study these six refinements of resolution. We give a nearly complete characterization of the relative complexities of all six refinements. While many of the important separations and simulations were already known, many new ones are presented in this paper; in particular, we give the first separation of semantic resolution from general resolution. As a special case, we obtain the first exponential separation of negative resolution from general resolution. We also attempt to present a unifying framework for studying all of these refinements.

A NOTE ON REPEATED GAMES WITH VANISHING ACTIONS

2005 ◽  
Vol 07 (01) ◽  
pp. 107-115 ◽  
Author(s):  
REINOUD JOOSTEN
Keyword(s):  
Repeated Games ◽  
Relative Frequency ◽  
Time Horizon ◽  
Convex Combination ◽  
Pure Strategy ◽  
Repeated Game ◽  
Entire Time ◽  
Long Run ◽  
Average Rewards ◽  
Threat Point

A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k ∈ {1,2} at least once in every rk ∈ ℕ consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon. A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r1, r2 and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play. We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m × n-games provided r1 > m ≥ 2, r2 > n ≥ 2.

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.

scholarly journals Repeated Game Analysis of a CSMA/CA Network under a Backoff Attack

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5393 ◽  
Author(s):  
Juan Parras ◽  
Santiago Zazo
Keyword(s):  
Repeated Games ◽  
Distributed Algorithm ◽  
Equilibrium Points ◽  
Repeated Game ◽  
Folk Theorem ◽  
Medium Access ◽  
Game Analysis ◽  
Static Game ◽  
Carrier Sense ◽  
Correlated Equilibria

We study a CSMA/CA (Carrier Sense Medium Access with Collision Avoidance) wireless network where some stations deviate from the defined contention mechanism. By using Bianchi’s model, we study how this deviation impacts the network throughput and show that the fairness of the network is seriously affected, as the stations that deviate achieve a larger share of the resources than the rest of stations. Previously, we modeled this situation using a static game and now, we use repeated games, which, by means of the Folk theorem, allow all players to have better outcomes. We provide analytical solutions to this game for the two player case using subgame perfect and correlated equilibria concepts. We also propose a distributed algorithm based on communicating candidate equilibrium points for learning the equilibria of this game for an arbitrary number of players. We validate approach using numerical simulations, which allows comparing the solutions we propose and discussing the advantages of using each of the methods we propose.

Reputation and the Flow of Information in Repeated Games

Econometrica ◽  
2020 ◽  
Vol 88 (4) ◽  
pp. 1697-1723
Author(s):  
Eduardo Faingold
Keyword(s):  
High Frequency ◽  
Repeated Games ◽  
Complete Information ◽  
Equilibrium Payoff ◽  
Monitoring Technology ◽  
Long Run ◽  
Short Run ◽  
Reputation Effects ◽  
Public Monitoring ◽  
Flow Of Information

Equilibrium payoff bounds from reputation effects are derived for repeated games with imperfect public monitoring in which a long‐run player interacts frequently with a population of short‐run players and the monitoring technology scales with the length of the period of interaction. The bounds depend on the monitoring technology through the flow of information, a measure of signal informativeness per unit of time based on relative entropy. Examples are shown where, under complete information, the set of equilibrium payoffs of the long‐run player converges, as the period length tends to zero, to the set of static equilibrium payoffs, whereas when the game is perturbed by a small ex ante probability on commitment types, reputation effects remain powerful in the high‐frequency limit.

EXTENT AND GROWTH EFFECTS OF INFORMALITY IN TURKEY: EVIDENCE FROM A FIRM-LEVEL SURVEY

2017 ◽  
Vol 62 (05) ◽  
pp. 1017-1037 ◽  
Author(s):  
KEREM CANTEKIN ◽  
CEYHUN ELGIN
Keyword(s):  
Complete Information ◽  
Complete Characterization ◽  
Firm Characteristics ◽  
Firm Level ◽  
Cross Sectional ◽  
Growth Effects ◽  
Turkish Economy ◽  
Level Data ◽  
Shed Light

In this paper, we provide a measure for both the prevalence and growth effects of informality in Turkey using firm-level data from the Turkish Economy. The survey is conducted in April–May 2013 covering 1000 representative firms interviewing owners/head managers of the firms. Based on the information given by these owners and managers, the survey makes a complete characterization of several firm characteristics, provides complete information on the extent of informality as well as its effects on various economic outcomes of these firms. The cross-sectional econometric analysis we conduct using the survey data shows that there is an inverted-U relationship between a specific measure of informality and growth expectations of firms. These results shed light on our understanding of the specific channels through which informality affects firms’ growth not only in Turkey but in other emerging markets as well.

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