scholarly journals Learning Convex Partitions and Computing Game-theoretic Equilibria from Best-response Queries

2021 ◽  
Vol 9 (1) ◽  
pp. 1-36
Author(s):  
Paul W. Goldberg ◽  
Francisco J. Marmolejo-Cossío
Keyword(s):  
Best Response ◽  
Convex Partitions ◽  
Game Theoretic

Collective influence maximization for multiple competing products with an awareness-to-influence model

2021 ◽  
Vol 14 (7) ◽  
pp. 1124-1136
Author(s):  
Dimitris Tsaras ◽  
George Trimponias ◽  
Lefteris Ntaflos ◽  
Dimitris Papadias
Keyword(s):  
Diffusion Processes ◽  
Influence Maximization ◽  
Second Phase ◽  
Social Graph ◽  
Practical Applications ◽  
Influence Model ◽  
Best Response ◽  
The Social ◽  
Game Theoretic ◽  
Collective Influence

Influence maximization (IM) is a fundamental task in social network analysis. Typically, IM aims at selecting a set of seeds for the network that influences the maximum number of individuals. Motivated by practical applications, in this paper we focus on an IM variant, where the owner of multiple competing products wishes to select seeds for each product so that the collective influence across all products is maximized. To capture the competing diffusion processes, we introduce an Awareness-to-Influence (AtI) model. In the first phase, awareness about each product propagates in the social graph unhindered by other competing products. In the second phase, a user adopts the most preferred product among those encountered in the awareness phase. To compute the seed sets, we propose GCW, a game-theoretic framework that views the various products as agents, which compete for influence in the social graph and selfishly select their individual strategy. We show that AtI exhibits monotonicity and submodularity; importantly, GCW is a monotone utility game. This allows us to develop an efficient best-response algorithm, with quality guarantees on the collective utility. Our experimental results suggest that our methods are effective, efficient, and scale well to large social networks.

scholarly journals LEARNING TO PLAY BEST RESPONSE IN DUOPOLY GAMES

2004 ◽  
Vol 06 (03) ◽  
pp. 443-459 ◽  
Author(s):  
JAN WENZELBURGER
Keyword(s):  
Demand Function ◽  
Optimal Strategies ◽  
Market Demand ◽  
Response Behavior ◽  
Estimation Errors ◽  
Demand Functions ◽  
Best Response ◽  
Game Theoretic ◽  
Payoff Functions ◽  
Duopoly Market

We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response behavior of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, a firm is able to play best response in the usual game theoretic sense.

A Game Theoretic Method for Resource Allocation in Scientific Cloud

2016 ◽  
Vol 6 (1) ◽  
pp. 15-41 ◽  
Author(s):  
Amin Nezarat ◽  
Gh Dastghaibifard
Keyword(s):  
Resource Allocation ◽  
Cooperative Game Theory ◽  
Cloud Services ◽  
Nash Equilibrium Point ◽  
New Methods ◽  
Best Response ◽  
Game Theoretic ◽  
Cloud Environments ◽  
Np Complete ◽  
Maximum Utilization

Due to the widespread use of cloud services, the need for proper and dynamic distribution will redouble the resources. One of the most complex problems in cloud environments is resource allocation such that on one hand the resource provider should obtain maximum utilization and on the other hand users want to lease best resources based on his time and budget constraints. Many studies which presented new methods for solving this NP-complete problem have used heuristic algorithm. Based on economic aspects of cloud environments, using market oriented model for solving allocation problem can decrease the complexity and converge it to the best solution in minimum time. In this paper a method has been proposed based on auction theory that it has used a non-cooperative game theory mechanism in an incomplete information environment. This game try to select best bidder for selling resource to it. At the end of the paper, the proposed algorithm was experienced in cloudsim and the simulated results showed that the authors' suggested model converge to the best response at Nash equilibrium point.

scholarly journals A unifying framework for iterative approximate best-response algorithms for distributed constraint optimization problems

2011 ◽  
Vol 26 (4) ◽  
pp. 411-444 ◽  
Author(s):  
Archie C. Chapman ◽  
Alex Rogers ◽  
Nicholas R. Jennings ◽  
David S. Leslie
Keyword(s):  
Computer Science ◽  
Optimization Problems ◽  
Potential Games ◽  
Science Literature ◽  
Stochastic Algorithm ◽  
Constraint Optimization ◽  
Distributed Constraint Optimization ◽  
Best Response ◽  
Game Theoretic ◽  
Constraint Optimization Problems

AbstractDistributed constraint optimization problems (DCOPs) are important in many areas of computer science and optimization. In a DCOP, each variable is controlled by one of many autonomous agents, who together have the joint goal of maximizing a global objective function. A wide variety of techniques have been explored to solve such problems, and here we focus on one of the main families, namely iterative approximate best-response algorithms used as local search algorithms for DCOPs. We define these algorithms as those in which, at each iteration, agents communicate only the states of the variables under their control to their neighbours on the constraint graph, and that reason about their next state based on the messages received from their neighbours. These algorithms include the distributed stochastic algorithm and stochastic coordination algorithms, the maximum-gain messaging algorithms, the families of fictitious play and adaptive play algorithms, and algorithms that use regret-based heuristics. This family of algorithms is commonly employed in real-world systems, as they can be used in domains where communication is difficult or costly, where it is appropriate to trade timeliness off against optimality, or where hardware limitations render complete or more computationally intensive algorithms unusable. However, until now, no overarching framework has existed for analyzing this broad family of algorithms, resulting in similar and overlapping work being published independently in several different literatures. The main contribution of this paper, then, is the development of a unified analytical framework for studying such algorithms. This framework is built on our insight that when formulated as non-cooperative games, DCOPs form a subset of the class of potential games. This result allows us to prove convergence properties of iterative approximate best-response algorithms developed in the computer science literature using game-theoretic methods (which also shows that such algorithms can also be applied to the more general problem of finding Nash equilibria in potential games), and, conversely, also allows us to show that many game-theoretic algorithms can be used to solve DCOPs. By so doing, our framework can assist system designers by making the pros and cons of, and the synergies between, the various iterative approximate best-response DCOP algorithm components clear.

scholarly journals Airline Booking Limit Competition Game Under Differentiated Fare Structure

2017 ◽  
Vol 33 (3) ◽  
pp. 615-622 ◽  
Author(s):  
Joonkyum Lee ◽  
Bumsoo Kim
Keyword(s):  
Nash Equilibrium ◽  
Airline Industry ◽  
Relative Magnitude ◽  
Theoretic Approach ◽  
Pure Nash Equilibrium ◽  
Initial Allocation ◽  
Best Response ◽  
Booking Limits ◽  
Game Theoretic ◽  
Game Theoretic Approach

We address a two-firm booking limit competition game in the airline industry. We assume aggregate common demand, and differentiated ticket fare and capacity, to make this study more realistic. A game theoretic approach is used to analyze the competition game. The optimal booking limits and the best response functions are derived. We show the existence of a pure Nash equilibrium and provide the closed-form equilibrium solution. The location of the Nash equilibrium depends on the relative magnitude of the ratios of the full and discount fares. We also show that the sum of the booking limits of the two firms remains the same regardless of the initial allocation proportion of the demand.

scholarly journals Crime, punishment, and evolution in an adversarial game

2015 ◽  
Vol 27 (3) ◽  
pp. 317-337 ◽  
Author(s):  
MICHAEL MCBRIDE ◽  
RYAN KENDALL ◽  
MARIA R. D'ORSOGNA ◽  
MARTIN B. SHORT
Keyword(s):  
Multiple Equilibrium ◽  
Response Dynamics ◽  
Alternative Strategies ◽  
Cooperative Equilibrium ◽  
Equilibrium Refinements ◽  
Best Response Dynamics ◽  
Best Response ◽  
Response Dynamic ◽  
Game Theoretic ◽  
Best Response Dynamic

We examine the game theoretic properties of a model of crime first introduced by Short et al. (2010 Phys. Rev. E82, 066114) as the SBD Adversarial Game. We identify the rationalizable strategies and one-shot equilibria under multiple equilibrium refinements. We further show that SBD's main result about the effectiveness of defecting-punishers (“Informants”) in driving the system to evolve to the cooperative equilibrium under an imitation dynamic generalizes to a best response dynamic, though only under certain parameter regimes. The nature of this strategy's role, however, differs significantly between the two dynamics: in the SBD imitation dynamic, Informants are sufficient but not necessary to achieve the cooperative equilibrium, while under the best response dynamic, Informants are necessary but not sufficient for convergence to cooperation. Since a policy of simply converting citizens to Informants will not guarantee success under best response dynamics, we identify alternative strategies that may help the system reach cooperation in this case, e.g., the use of moderate but not too severe punishments on criminals.

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