New Nash Equilibrium Based on Generic Risk Element Transmission Theory

2012 ◽  
Vol 424-425 ◽  
pp. 410-414
Author(s):  
Gong Shu Lu ◽  
Cun Bin Li ◽  
Xian Li
Keyword(s):  
Nash Equilibrium ◽  
Triangular Distribution ◽  
Pareto Improvement ◽  
Improvement Strategy ◽  
Static Game ◽  
Prisoners Dilemma ◽  
Strategy Combination ◽  
Core Idea ◽  
Traditional Game ◽  
Risk Element

Nash equilibrium is the foundation of traditional game theory, while the benefits of game players under the Nash equilibrium are constant, so the core idea of generic risk transmission was applied to traditional static game. Accordingly a risk static game model, in which the benefits of players were subject to triangular distribution, was constructed. Then we obtained different equilibrium states under the different risk types of players. Furthermore, the classic Prisoners’ Dilemma was used to demonstrate the practice value of risk game. Through analyzing and solving the risk Prisoners’ Dilemma model which changed from the classic Prisoner's Dilemma model according to actual situation, the Pareto improvement strategy combination could be achieved. The new equilibrium result can give an appropriate explanation why there is always some prisoners conceal the corpus delicti in adventure

The Analysis of Willingness to Cooperate for Farmers to Participate in Water Management Based on Game Theory

2013 ◽  
Vol 448-453 ◽  
pp. 1002-1010
Author(s):  
Cong Liu
Keyword(s):  
Water Management ◽  
Game Theory ◽  
Dynamic Game ◽  
Collective Rationality ◽  
Game Analysis ◽  
Static Game ◽  
Free Riders ◽  
Evolution Analysis ◽  
Prisoners Dilemma ◽  
Willingness To Cooperate

To analyze the willingness to cooperate of farmers to participate in water management, we base on game theory and first carry on single static game analysis of willingness to cooperate for farmers to participate in water management, and find that farmers are into a Prisoners Dilemma in a single game, individual rationality comes into conflict with collective rationality, at this time farmers have a tendency to "free riders", so it is difficult to achieve cooperation between the farmers. Then trying to break the prisoners' dilemma, we carry on the farmers repeated dynamic game, the analysis is carried on in the context of incomplete information and limited rationality, we carry on game evolution analysis for willingness to cooperate for farmers to participate in water management. In order to guarantee the rationality of the study, we conduct a survey of willingness to cooperate of farmers to participate in water management in province of Zhejiang and finally confirm that the study is reasonable. And through the analysis of the full text, we conclude six important conclusions.

scholarly journals Endogenous Stackelberg leadership within a team. The coalition effect

2021 ◽  
Vol 49 (1) ◽  
pp. 53-79
Author(s):  
E.M. Skarzhinskaya ◽  
◽  
V.I. Tsurikov ◽  
Keyword(s):  
Nash Equilibrium ◽  
Theoretical Investigation ◽  
Pareto Improvement ◽  
Stackelberg Strategy ◽  
Team Members ◽  
Leadership Formation ◽  
Stackelberg Leadership ◽  
Diminishing Returns ◽  
Stackelberg Model ◽  
Specific Individual

The article engages in a theoretical investigation of the possibility of implementing the Stackelberg strategy within a team. It is assumed that the team gene-rates aggregate income that increases as the efforts invested by each agent intensify, subject to the law of diminishing returns. The goal of each agent in a team is to maximize his own individual gain. In order to achieve an outcome that is Paretopreferable over Nash equilibrium, two approaches may be used: identifying a leader or forming a smaller group (coalition) within the team whose members, in pursuance of increased individual gains, choose the route that maximizes coalition gains. It is shown that the advent of a coalition in a team results in Pareto-improvement in a simultaneous game. We analyse the possibility of endogenous leadership forming according to the Stackelberg model when using the mechanism of timing decisions. It is established that under autonomy of all team members, leadership formation can only be confidently predicted in specific individual cases. In a significantly more general case, all of the prerequisites for the formation of leadership are created by the presence of a single coalition interested in implementing the Stackelberg strategy.

scholarly journals On the Existence and Determining Stationary Nash Equilibria for Switching Controller Stochastic Games

2021 ◽  
Vol 14 ◽  
pp. 290-301
Author(s):  
Dmitrii Lozovanu ◽  
◽  
Stefan Pickl ◽  
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Static Game ◽  
Stationary Strategies ◽  
Switching Controller ◽  
Optimal Stationary Strategies ◽  
Stationary Nash Equilibrium

In this paper we consider the problem of the existence and determining stationary Nash equilibria for switching controller stochastic games with discounted and average payoffs. The set of states and the set of actions in the considered games are assumed to be finite. For a switching controller stochastic game with discounted payoffs we show that all stationary equilibria can be found by using an auxiliary continuous noncooperative static game in normal form in which the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players. Based on this we propose an approach for determining the optimal stationary strategies of the players. In the case of average payoffs for a switching controller stochastic game we also formulate an auxiliary noncooperative static game in normal form with quasi-monotonic payoffs and show that such a game possesses a Nash equilibrium if the corresponding switching controller stochastic game has a stationary Nash equilibrium.

scholarly journals Non-Determinism and Nash Equilibria for Sequential Game over Partial Order

2005 ◽  
Vol DMTCS Proceedings vol. AF,... (Proceedings) ◽  
Author(s):  
Stéphane Le Roux
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Ordered Set ◽  
Backward Induction ◽  
Proof Assistant ◽  
Perfect Equilibrium ◽  
Sequential Games ◽  
International Audience ◽  
Traditional Game ◽  
Deterministic Strategy

International audience In sequential games of traditional game theory, backward induction guarantees existence of Nash equilibrium by yielding a sub-game perfect equilibrium. But if payoffs range over a partially ordered set instead of the reals, then the backward induction predicate does no longer imply the Nash equilibrium predicate. Non-determinism is a solution: a suitable non-deterministic backward induction function returns a non-deterministic strategy profile which is a non-deterministic Nash equilibrium. The main notions and results in this article are constructive, conceptually simple and formalised in the proof assistant Coq.

Research of Railway Capacity Strengthening Scheme Decision Method Based on Game Theory

2014 ◽  
Vol 505-506 ◽  
pp. 571-576
Author(s):  
Xiang Xu ◽  
Xing Chen Zhang ◽  
Bin Xu
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Optimization Model ◽  
Complete Information ◽  
Evaluation Index ◽  
Capacity Strengthening ◽  
Static Game ◽  
Decision Method ◽  
Railway Capacity

Firstly, established the optimization model based on complete information static game theory, which see evaluation index as the participants of a game, capacity strengthening strategies as the strategies of participants, and the strategies contained in the Nash equilibrium of the game as the first step optimization results. Then structure an algorithm to secondary selection, which makes there is only one strategy in the final result. At last given a case study combined with Baoshen railway capacity strengthening scheme decision. The result indicated that the model has good applicability, and can reduce the subjective error effectively.

Equilibrium Strategies of Contract Choice Game between Supply Chains with Uncertain Demand

2013 ◽  
Vol 655-657 ◽  
pp. 2348-2351
Author(s):  
Bai Xun Li ◽  
Qi Wei ◽  
Min Zhou
Keyword(s):  
Nash Equilibrium ◽  
Supply Chains ◽  
Equilibrium Structure ◽  
Uncertain Demand ◽  
Newsvendor Model ◽  
Competition Intensity ◽  
Quantity Discount ◽  
Equilibrium Strategies ◽  
Contract Choice ◽  
Prisoners Dilemma

Applying competing newsvendor model, we studied the contract choice games between supply chains, each consisting of one manufacturer and one retailer. We investigated the effect of the competition intensity on the equilibrium strategies of contract choice games. It can be found that, counter to the earlier literature, in the context of competing supply chains, the choices of quantity-discount contracts are the Nash equilibrium structure for both manufacturers, however, the manufacturers will get into classic prisoners’ dilemma if the degree of competition intensity is high.

Gaming Analysis among Different Participants in the Construction of Biomass Energy Forest Base

2012 ◽  
Vol 512-515 ◽  
pp. 416-420
Author(s):  
Feng Lian Sun ◽  
Wei Wei Wang ◽  
Zhong Ji Wang
Keyword(s):  
Nash Equilibrium ◽  
Construction Cost ◽  
Additional Benefit ◽  
Optimal Combination ◽  
Biomass Energy ◽  
Pareto Improvement ◽  
The Government ◽  
Energy Forest

Through the analysis on the relations of the three main participants of the government, the enterprise and the farmers, the thesis has established the gaming model between the enterprise and the forest farmers and found that only when the additional benefit they each obtain is larger than the construction cost for the development they paid, optimal combination of Nash equilibrium can be accepted by enterprises and forest farmers and Pareto improvement will be possibly formed， the smooth development of energy forest construction can be ensured.

Universalizing and the we: endogenous game theoretic deontology

2020 ◽  
pp. 1-16
Author(s):  
Paul Studtmann ◽  
Shyam Gouri Suresh
Keyword(s):  
Nash Equilibrium ◽  
Prisoner's Dilemma ◽  
Autonomous Agents ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Pareto Improvement ◽  
Moral Framework ◽  
Interacting Agents ◽  
Game Theoretic

Abstract The Nash counterfactual considers the question: what would happen were I to change my behaviour assuming no one else does. By contrast, the Kantian counterfactual considers the question: what would happen were everyone to deviate from some behaviour. We present a model that endogenizes the decision to engage in this type of Kantian reasoning. Autonomous agents using this moral framework receive psychic payoffs equivalent to the cooperate-cooperate payoff in Prisoner’s Dilemma regardless of the other player’s action. Moreover, if both interacting agents play Prisoner’s Dilemma using this moral framework, their material outcomes are a Pareto improvement over the Nash equilibrium.

scholarly journals Reactive Strategies: An Inch of Memory, a Mile of Equilibria

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 42
Author(s):  
Artem Baklanov
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Folk Theorem ◽  
Pareto Improvement ◽  
Symmetric Equilibrium ◽  
Equilibrium Payoff ◽  
Incremental Change ◽  
Symmetric Games ◽  
Stage Game

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash Equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

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