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.

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.

Bounded Rationality in the Centipede Game

Episteme ◽  
2011 ◽  
Vol 8 (3) ◽  
pp. 262-280 ◽  
Author(s):  
Ashton T. Sperry-Taylor
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Bounded Rationality ◽  
Real Life ◽  
Backward Induction ◽  
Rational Behavior ◽  
Normative Analysis ◽  
Cognitive Limitations ◽  
Real People ◽  
Rational Players

AbstractNormative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they can apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize.

scholarly journals From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 782 ◽  
Author(s):  
Christos Papadimitriou ◽  
Georgios Piliouras
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Dynamical Systems ◽  
Nash Equilibria ◽  
Equilibrium Solution ◽  
Solution Concept ◽  
Constructive Proof ◽  
Specific Information ◽  
Potential Game ◽  
Chain Recurrence

In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of universal non-equilibrium solution concepts arising from an important theorem in the topology of dynamical systems that was unavailable to Nash. This approach starts with both a game and a learning dynamics, defined over mixed strategies. The Nash equilibria are fixpoints of the dynamics, but the system behavior is captured by an object far more general than the Nash equilibrium that is known in dynamical systems theory as chain recurrent set. Informally, once we focus on this solution concept—this notion of “the outcome of the game”—every game behaves like a potential game with the dynamics converging to these states. In other words, unlike Nash equilibria, this solution concept is algorithmic in the sense that it has a constructive proof of existence. We characterize this solution for simple benchmark games under replicator dynamics, arguably the best known evolutionary dynamics in game theory. For (weighted) potential games, the new concept coincides with the fixpoints/equilibria of the dynamics. However, in (variants of) zero-sum games with fully mixed (i.e., interior) Nash equilibria, it covers the whole state space, as the dynamics satisfy specific information theoretic constants of motion. We discuss numerous novel computational, as well as structural, combinatorial questions raised by this chain recurrence conception of games.

Distributive Justice in a Hybrid Utopia

2017 ◽  
pp. 43-64
Author(s):  
Venkat Venkatasubramanian
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Income Distribution ◽  
Distributive Justice ◽  
Equilibrium State ◽  
Free Market ◽  
Mathematical Formalism ◽  
Potential Game ◽  
Will Self

Chapter three developments the mathematical formalism that answers the four fundamental questions raised in Chapter 1. We utilize concepts and techniques from potential game theory to prove that the ideal free market will self-organize to reach an equilibrium state when an income distribution emerges naturally. We prove that this is a Nash Equilibrium.

Potential Games and Its Applications to Wireless Networks

2015 ◽  
pp. 1-27
Author(s):  
Wei Zhong ◽  
Jiaheng Wang ◽  
Meixia Tao
Keyword(s):  
Game Theory ◽  
Wireless Networks ◽  
Wireless Network ◽  
Relay Node ◽  
Potential Games ◽  
Relay Network ◽  
Potential Game ◽  
Multiple Access Channels ◽  
Joint Resource Allocation ◽  
Wireless Network Optimization

Potential games are a subclass of noncooperative games that bear some special properties and are often exploited in wireless network designs. In this chapter, we first introduce the concept of potential games and give definitions of different types of potential games. Then, we provide some important results and properties of potential games. After that, we introduce three algorithms to achieve Nash equilibrium of a potential game. Next, this chapter will show how to apply potential game theory to design efficient algorithms for wireless network optimization. One application of potential game theory is to study the power control problem in wireless networks. Another example is the multimode precoding design in multi-input multi-output multiple access channels. We also show how to apply potential games for joint resource allocation in a relay network where multiple users can conduct bidirectional communications through a relay node over multiple available channels.

scholarly journals POS0675 THE COMPARATIVE 3-YEAR RETENTION RATE OF TARGETED-SYNTHETIC AND BIOLOGIC DRUGS FOR RHEUMATOID ARTHRITIS: REAL-LIFE DATA FROM THE ITALIAN GISEA REGISTRY

2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 582.1-582
Author(s):  
E. G. Favalli ◽  
F. Iannone ◽  
E. Gremese ◽  
R. Gorla ◽  
R. Foti ◽  
...  
Keyword(s):  
Rheumatoid Arthritis ◽  
Adverse Events ◽  
Retention Rate ◽  
Large Population ◽  
Real Life ◽  
Mechanisms Of Action ◽  
Biologic Drugs ◽  
Real Life Setting ◽  
Study Population ◽  
Targeted Drug

Background:Long-term observational data on the real-life use of JAK inhibitors (JAKis) for rheumatoid arthritis (RA) and their comparison with biological drugs are still very limited. Large population-based registries have been increasingly used to investigate the performance of targeted drugs in a real-life setting.Objectives:The aim of this study is to evaluate and compare the 3-year retention rate of JAKis, TNF inhibitors (TNFis) and biologic drugs with other mechanisms of action (OMAs) in the large cohort of RA patients included in the Italian national GISEA registry.Methods:Data of all RA patients treated with targeted synthetic or biologic drugs were prospectively collected in the Italian multicentric GISEA registry. The analysis was limited to patients who started a first- or second-line targeted drug in the period after the first JAKi was marketed in Italy (1st December 2017). The 3-year retention rate was calculated by the Kaplan-Meier method and compared between different drug classes by a log-rank test. A descriptive analysis of reasons for discontinuation was performed.Results:The study population included 1027 RA patients (79.8% females, mean age [±SD] 56.9 [±13.5] years, mean disease duration 9.8 [±9] years, mean baseline SDAI 17.5 [±11.9], ACPA positive 67.4%, RF positive 62.7%) who received JAKis (baricitinib or tofacitinib, n=297), TNFis (n=365), or OMAs (n=365) as first or second targeted drug. Main baseline characteristics of study population were overall well balanced between treatment groups. Retention rate was numerically but not statistically higher (p=0.18) in patients treated with JAKis compared with TNFis or OMAs (80.6, 78.9 and 76.4% at 1 year and 73, 56.8 and 63.8% at 3 years, respectively) (Figure 1). Drug survival was significantly higher in patients receiving concomitant methotrexate (MTX) compared with monotherapy only in TNFis (66.8 vs 47.1%, p=0.04) but not in JAKis (76.1 vs 70.1%, p=0.54) and OMAs (66.1 vs 61.9%, p=0.41) group. Therapy was discontinued in a total of 211 patients because of ineffectiveness (n=107), adverse events (n=88), or compliance/other reasons (n=16). The most frequent reason for treatment withdrawal was ineffectiveness in both JAKis (n=30 out of 56) and TNFis (n=45 out of 74) groups, whereas OMAs were discontinued more frequently because of adverse events (n=41 out of 81).Conclusion:Our data confirmed in a real-life setting a favorable 3-year retention rate of all available targeted mechanisms of action for RA therapy. As expected, concomitant MTX significantly impacted persistence on therapy of TNFis only. Discontinuations of JAKis for adverse events were infrequent overall, confirming the safety profile observed in randomized clinical trials.Figure 1.Three-year retention rate by treatment groupDisclosure of Interests:None declared

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

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