scholarly journals Optimal Channel Design: A Game Theoretical Analysis

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 675 ◽  
Author(s):  
MHR. Khouzani ◽  
Pasquale Malacaria
Keyword(s):  
Convex Programming ◽  
Design Problem ◽  
Information Leakage ◽  
Optimal Strategies ◽  
Theoretical Framework ◽  
Convex Programming Problem ◽  
Channel Design ◽  
Inference Problem ◽  
Equilibrium Strategies ◽  
Nash Equilibrium Strategies

This paper studies the problem of optimal channel design. For a given input probability distribution and for hard and soft design constraints, the aim here is to design a (probabilistic) channel whose output leaks minimally from its input. To analyse this problem, general notions of entropy and information leakage are introduced. It can be shown that, for all notions of leakage here defined, the optimal channel design problem can be solved using convex programming with zero duality gap. Subsequently, the optimal channel design problem is studied in a game-theoretical framework: games allow for analysis of optimal strategies of both the defender and the adversary. It is shown that all channel design problems can be studied in this game-theoretical framework, and that the defender’s Bayes–Nash equilibrium strategies are equivalent to the solutions of the convex programming problem. Moreover, the adversary’s equilibrium strategies correspond to a robust inference problem.

An Introduction to Uncertain Futures

2018 ◽  
Author(s):  
Jens Beckert ◽  
Richard Bronk
Keyword(s):  
Optimal Strategies ◽  
Theoretical Framework ◽  
Objective Probability ◽  
Political Debate ◽  
Probability Functions ◽  
Market Economies ◽  
Socially Constructed ◽  
The Future ◽  
Radical Uncertainty ◽  
Calculative Practices

This chapter provides a theoretical framework for considering how imaginaries and narratives interact with calculative devices to structure expectations and beliefs in the economy. It analyses the nature of uncertainty in innovative market economies and examines how economic actors use imaginaries, narratives, models, and calculative practices to coordinate and legitimize action, determine value, and establish sufficient conviction to act despite the uncertainty they face. Placing the themes of the volume in the context of broader trends in economics and sociology, the chapter argues that, in conditions of widespread radical uncertainty, there is no uniquely rational set of expectations, and there are no optimal strategies or objective probability functions; instead, expectations are often structured by contingent narratives or socially constructed imaginaries. Moreover, since expectations are not anchored in a pre-existing future reality but have an important role in creating the future, they become legitimate objects of political debate and crucial instruments of power in markets and societies.

scholarly journals A Faithful Mechanism for Incremental Multi-Agent Agreement Problems with Self-Interested and Privacy-Preserving Agents

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Farzaneh Farhadi ◽  
Nicholas R. Jennings
Keyword(s):  
Information Leakage ◽  
Optimal Strategies ◽  
Privacy Preserving ◽  
Limited Attention ◽  
Limited Information ◽  
Multi Agent Systems ◽  
Negotiation Strategies ◽  
Multi Agent ◽  
Theoretical And Numerical Analysis ◽  
Negotiation Mechanism

AbstractDistributed multi-agent agreement problems (MAPs) are central to many multi-agent systems. However, to date, the issues associated with encounters between self-interested and privacy-preserving agents have received limited attention. Given this, we develop the first distributed negotiation mechanism that enables self-interested agents to reach a socially desirable agreement with limited information leakage. The agents’ optimal negotiation strategies in this mechanism are investigated. Specifically, we propose a reinforcement learning-based approach to train agents to learn their optimal strategies in the proposed mechanism. Also, a heuristic algorithm is designed to find close-to-optimal negotiation strategies with reduced computational costs. We demonstrate the effectiveness and strength of our proposed mechanism through both game theoretical and numerical analysis. We prove theoretically that the proposed mechanism is budget balanced and motivates the agents to participate and follow the rules faithfully. The experimental results confirm that the proposed mechanism significantly outperforms the current state of the art, by increasing the social-welfare and decreasing the privacy leakage.

NASH EQUILIBRIUM STRATEGIES REVISITED IN SOFTWARE RELEASE GAMES

2020 ◽  
pp. 1-21
Author(s):  
Yasuhiro Saito ◽  
Tadashi Dohi
Keyword(s):  
Nash Equilibrium ◽  
Optimization Theory ◽  
Applied Probability ◽  
Equilibrium Strategies ◽  
Release Policy ◽  
Software Release ◽  
Nash Equilibrium Strategies ◽  
Person Game

A software release game was formulated by Zeephongsekul and Chiera [Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470–481] and was reconsidered by Dohi et al. [Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325–346] in a framework of two-person nonzero-sum games. In this paper, we further point out the faults in the above literature and revisit the Nash equilibrium strategies in the software release games from the viewpoints of both silent and noisy type of games. It is shown that the Nash equilibrium strategies in the silent and noisy of software release games exist under some parametric conditions.

scholarly journals Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables

2018 ◽  
Vol 20 (01) ◽  
pp. 1750030 ◽  
Author(s):  
Atsuhiro Satoh ◽  
Yasuhito Tanaka
Keyword(s):  
Nash Equilibrium ◽  
Objective Function ◽  
The Other ◽  
Minimax Strategy ◽  
Equilibrium Strategies ◽  
Minimax Strategies ◽  
Nash Equilibrium Strategies ◽  
Special Case ◽  
Maximin Strategy

We examine maximin and minimax strategies for players in a two-players game with two strategic variables, [Formula: see text] and [Formula: see text]. We consider two patterns of game; one is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s, and the other is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the [Formula: see text]-game, and the maximin strategy and the minimax strategy in the [Formula: see text]-game are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the [Formula: see text]-game nor the [Formula: see text]-game. But, in a special case, where the objective function of Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the [Formula: see text]-game and the [Formula: see text]-game.

scholarly journals Equilibrium and Optimization in a Double-Ended Queueing System with Dynamic Control

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Yuejiao Wang ◽  
Zaiming Liu
Keyword(s):  
Queueing System ◽  
Service System ◽  
Dynamic Control ◽  
Optimal Strategies ◽  
Control Policy ◽  
Arrival Rate ◽  
Social Benefit ◽  
Equilibrium Strategies ◽  
Taxi Service ◽  
The Relationship

In this paper, we consider a double-ended queueing system which is a passenger-taxi service system. In our model, we also consider the dynamic taxi control policy which means that the manager adjusts the arrival rate of taxis according to the taxi stand congestion. Under three different information levels, we study the equilibrium strategies as well as socially optimal strategies for arriving passengers by a reward-cost structure. Furthermore, we present several numerical experiments to analyze the relationship between the equilibrium and socially optimal strategies and demonstrate the effect of different information levels as well as several parameters on social benefit.

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