scholarly journals DISCRETE CONCAVITY FOR POTENTIAL GAMES

2008 ◽  
Vol 10 (01) ◽  
pp. 137-143 ◽  
Author(s):  
TAKASHI UI
Keyword(s):  
Nash Equilibrium ◽  
Potential Function ◽  
Discrete Analogue ◽  
Potential Games ◽  
Discrete Concavity

This paper proposes a discrete analogue of concavity appropriate for potential games with discrete strategy sets. It guarantees that every Nash equilibrium maximizes a potential function.

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

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.

Study of potential games using Ising interaction

2021 ◽  
Author(s):  
U. Tejasvi ◽  
R. D. Eithiraj ◽  
S. Balakrishnan
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Large Population ◽  
Real Life ◽  
Potential Games ◽  
Potential Game ◽  
Countable Number ◽  
Symmetric Games ◽  
Close Observation ◽  
Hamiltonian Analysis

Problems can be handled properly in game theory as long as a countable number of players are considered, whereas, in real life, we have a large number of players. Hence, games at the thermodynamic limit are analyzed in general. There is a one-to-one correspondence between classical games and the modeled Hamiltonian at a particular equilibrium condition, usually the Nash equilibrium. Such a correspondence is arrived for symmetric games, namely the Prisoner’s Dilemma using the Ising Hamiltonian. In this work, we have shown that another class of games known as potential games can be analyzed with the Ising Hamiltonian. Analysis of this work brings out very close observation with real-world scenarios. In other words, the model of a potential game studied using Ising Hamiltonian predicts behavioral aspects of a large population precisely.

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.

Uniqueness of Nash equilibrium in continuous two-player weighted potential games

2018 ◽  
Vol 459 (2) ◽  
pp. 1208-1221 ◽  
Author(s):  
Francesco Caruso ◽  
Maria Carmela Ceparano ◽  
Jacqueline Morgan
Keyword(s):  
Nash Equilibrium ◽  
Potential Games ◽  
Uniqueness Of Nash Equilibrium

scholarly journals Optimization via game theoretic control

2020 ◽  
Vol 7 (7) ◽  
pp. 1120-1122
Author(s):  
Daizhan Cheng ◽  
Zequn Liu
Keyword(s):  
Nash Equilibrium ◽  
Potential Function ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Promising Method ◽  
Potential Game ◽  
Networked System ◽  
Game Theoretic ◽  
Solve Optimization Problem

Summary Using game theoretic control to solve optimization problem is a recently developed promising method. The key technique is to convert a networked system into a potential game, with a pre-assigned criterion as the potential function. An algorithm is designed for updating strategies to reach a Nash equilibrium (i.e. optimal solution).

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