Potential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Nash Equilibrium ◽  
Special Class ◽  
Potential Games ◽  
Action Spaces

This chapter introduces a special class of N-player games, the so-called potential games, for which the Nash equilibrium is guaranteed to exist and is generally easy to find. It begins by considering a game with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies from the action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N), respectively. The notation is given for the outcome of the game for the player Pᵢ and all players wanting to minimize their own outcomes. The chapter goes on to discuss identical interests games, minimum vs. Nash equilibrium in potential games, bimatrix potential games, characterization of potential games, and potential games with interval action spaces. It concludes with practice exercises and their corresponding solutions, along with an additional exercise.

A Bayesian Optimization Approach to Compute Nash Equilibrium of Potential Games Using Bandit Feedback

2019 ◽  
Author(s):  
Anup Aprem ◽  
Stephen Roberts
Keyword(s):  
Nash Equilibrium ◽  
Potential Games ◽  
Bayesian Optimization ◽  
Real Interval ◽  
Optimization Approach ◽  
Multi Agent Systems ◽  
Dynamic Potential ◽  
Discrete Action ◽  
Novel Algorithms ◽  
Action Spaces

Abstract Computing a Nash equilibrium for strategic multi-agent systems is challenging for black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential games. We use a Bayesian optimization framework to obtain novel algorithms to solve finite (discrete action spaces) and infinite (real interval action spaces) potential games, utilizing the structure of potential games. Numerical results illustrate the efficiency of the approach in computing a Nash equilibrium of static potential games and linear Nash equilibrium of dynamic potential games.

scholarly journals Refinements of Nash equilibrium in potential games

2014 ◽  
Vol 9 (3) ◽  
pp. 555-582 ◽  
Author(s):  
Oriol Carbonell-Nicolau ◽  
Richard P. McLean
Keyword(s):  
Nash Equilibrium ◽  
Potential Games

scholarly journals Multiple Activities in Networks

2018 ◽  
Vol 10 (3) ◽  
pp. 34-85 ◽  
Author(s):  
Ying-Ju Chen ◽  
Yves Zenou, ◽  
Junjie Zhou
Keyword(s):  
Nash Equilibrium ◽  
Network Model ◽  
Network Structure ◽  
Comparative Statics ◽  
Network Density ◽  
Full Characterization ◽  
The One

We consider a network model where individuals exert efforts in two types of activities that are interdependent. These activities can be either substitutes or complements. We provide a full characterization of the Nash equilibrium of this game for any network structure. We show, in particular, that quadratic games with linear best-reply functions aggregate nicely to multiple activities because equilibrium efforts obey similar formulas to that of the one-activity case. We then derive some comparative-statics results showing how own productivity affects equilibrium efforts and how network density impacts equilibrium outcomes. (JEL C72, D11, D85, Z13)

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 From paths to stars

1991 ◽  
Vol 14 (2) ◽  
pp. 345-348
Author(s):  
A. F. Alameddine
Keyword(s):  
Structural Characterization ◽  
Special Class ◽  
Fibonacci Numbers ◽  
Similar Question ◽  
Number Of Cycles

The number of cycles in the complementT′of a treeTis known to increase with the diameter of the tree. A similar question is raised and settled for the number of complete subgraphs inT′for a special class of trees via Fibonacci numbers. A structural characterization of extremal trees is also presented.

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