scholarly journals Subgame Consistent Cooperative Behavior in an Extensive form Game with Chance Moves

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1061
Author(s):  
Denis Kuzyutin ◽  
Nadezhda Smirnova
Keyword(s):  
Cooperative Behavior ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Time Consistency ◽  
Extensive Form ◽  
Subgame Consistency ◽  
Cooperative Agreement ◽  
Cooperative Strategies ◽  
Cooperation Mechanism ◽  
Person Game

We design a mechanism of the players’ sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players’ attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player’s optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism.

The analysis of evolutionary prisoner’s dilemma game based on weighting effect

2021 ◽  
pp. 2150066
Author(s):  
Xinting Hu ◽  
Mengyun Wu
Keyword(s):  
Prisoner's Dilemma ◽  
Weighting Function ◽  
Random Network ◽  
Cooperative Behavior ◽  
Equilibrium Points ◽  
Prisoner’S Dilemma ◽  
The Real ◽  
Scale Free ◽  
Cooperative Strategies ◽  
Average Payoff

In this paper, an improved evolutionary prisoner’s dilemma (PD) game model is proposed by considering the weighting effect. Taking into account individual’s perceived payoff (benefits), the evolutionary tendency of the cooperators and three equilibrium points of the proposed model are obtained. We then numerically investigate how different exterior and interior factors influence on individuals’ cooperative behavior and their payoff both in the ER random network and the BA scale-free network. Our results reveal that the heterogeneous network structure is conducive to cooperation. In addition, the existence of leader nodes is an important driving force for promoting individuals’ cooperation. By further analyzing the rationality coefficient which appears in the weighting function, we obtain that a greater of irrationality could lead more people to take cooperative strategies. Finally, two indicators which are used to measure the real average payoff and perceived average payoff are defined. The results show that the real average payoff and perceived average payoff are larger in the heterogeneity network than that in homogeneous network.

Quantifying Commitment in Nash Equilibria

2019 ◽  
Vol 21 (02) ◽  
pp. 1940011
Author(s):  
Thomas A. Weber
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Canonical Extension ◽  
Perfect Equilibrium ◽  
Form Game ◽  
Normal Form Game ◽  
The Given

To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.

Cooperative Strategies and Genome Cybernetics in Formation of Complex Bacterial Patterns

1994 ◽  
Vol 367 ◽  
Author(s):  
Eshel Ben-Jacob ◽  
Ofer Shochet ◽  
Inon Cohen ◽  
Adam Tenenbaum ◽  
Andras CzirÓk ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Degrees Of Freedom ◽  
Cooperative Behavior ◽  
Building Blocks ◽  
Growth Conditions ◽  
Living Systems ◽  
Cooperative Strategies ◽  
Additional Level ◽  
Bacterial Patterns ◽  
The Individual

AbstractWe present a study of interfacial pattern formation during growth of bacterial colonies. Growth of bacterial colonies bears similarities but presents an inherent additional level of complexity in comparison with non-living systems. In the former case, the building blocks themselves are living systems, each with its own autonomous self-interest and internal degrees of freedom. The bacteria have developed sophisticated communication channels, which they utilize when growth conditions are tough. Here we present a non-local communicating walkers model to study the effect of local bacterium-bacterium interaction and communication via chemotaxis signaling. We demonstrate how communication enables the colony to develop complex patterns in response to adverse growth conditions. This self-organization of the colony, which can be achieved only via cooperative behavior of the bacteria, may be viewed as the outcome of an interplay between the micro-level (the individual bacterium) and the macro-level (the colony). Some qualitative features of the complex morphologies can be accounted for by invoking ideas from pattern formation in non-living systems together with a simplified model of chemotactic “feedback”.

COOPERATIVE STRATEGIES IN FORMATION OF COMPLEX BACTERIAL PATTERNS

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 849-868 ◽  
Author(s):  
ESHEL BEN-JACOB ◽  
OFER SHOCHET ◽  
INON COHEN ◽  
ADAM TENENBAUM ◽  
ANDRAS CZIRÓK ◽  
...  
Keyword(s):  
Environmental Conditions ◽  
Cooperative Behavior ◽  
Growth Conditions ◽  
Bacterial Strains ◽  
Cooperative Strategies ◽  
Continuous Approach ◽  
Complex Patterns ◽  
Bacterial Patterns ◽  
The Individual ◽  
Generic Strategies

In nature, bacterial colonies often must cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication channels on all levels. The result is that a profusion of complex patterns are formed during growth of various bacterial strains and for different environmental conditions. Some qualitative features of the complex morphologies may be accounted for by invoking ideas from pattern formation in non-living systems together with a simplified model of chemotactic “feedback”. We present a non-local communicating walkers model to study the effect of local bacterium-bacterium interaction and communication via chemotaxis signaling. The model is an hybridization of the continuous approach (to handle chemicals’ diffusion) and the atomistic approach (each “atom” or “walker” represents 104–105 bacteria). Using the model we demonstrate how communication enables the colony to develop complex patterns in response to adverse growth conditions. Efficient response of the colony requires self-organization on all levels, which can be achieved only via cooperative behavior of the bacteria. It can be viewed as the action of an interplay between the micro-level (the individual bacterium) and the macro-level (the colony) in the determination of the emerging pattern. We show that seemingly unrelated patterns can result from the employment of the same generic strategies.

scholarly journals Environmental Regulation of  Firms that Experience Dynamic  Inconsistency

2021 ◽  
Author(s):  
◽  
James Zuccollo
Keyword(s):  
Environmental Regulation ◽  
Optimal Taxation ◽  
Dynamic Game ◽  
Time Consistency ◽  
Behavioural Economics ◽  
Time Inconsistency ◽  
Tax Rate ◽  
Taxation Policy ◽  
Course Of Action ◽  
Consistency Problem

<p>The recent push for environmental regulation has invigorated the discussion of mechanism design and optimal taxation policy. Recent decades have also seen growing interest in behavioural economics and empirically based theory. In this thesis we take a step towards combining the two by asking how a regulator may correct an externality in situations where they have a time consistency problem. Time inconsistency is one of the notable developments of behavioural economics. It posits that an agent’s decisions do not remain consistent over time, which causes a utility loss if the agent cannot commit themselves to a particular course of action and stick to it. The solution to inconsistency problems is to precommit to a course of action and prevent future deviations from it. However, finding a mechanism to enable such precommitment is often problematic. A regulator who maximises welfare can have a time consistency problem because welfare will depend on the decisions of firm and households who may themselves be inconsistent. That inconsistency then propagates to the regulator’s decision and reduces the level of welfare that the regulator can reach. Alternatively, the regulator’s time consistency problem can be caused by non-stationarity in their time preferences. To reach the firstbest outcome the regulator must not only eliminate the environmental externality: they must also overcome their own time inconsistency problem. This thesis draws from the literature on strategic delegation to construct a taxation game in which the regulator can achieve the first best taxation regime without the need for external precommitment devices. We study a dynamic game where the regulator chooses a tax rate and the regulated monopolist chooses their price. We show that the Markov-perfect equilibrium price path of this game will replicate the first best plan. Our results holds for time inconsistency caused by both jump states and quasihyperbolic discounting.</p>

scholarly journals Environmental Regulation of  Firms that Experience Dynamic  Inconsistency

2021 ◽  
Author(s):  
◽  
James Zuccollo
Keyword(s):  
Environmental Regulation ◽  
Optimal Taxation ◽  
Dynamic Game ◽  
Time Consistency ◽  
Behavioural Economics ◽  
Time Inconsistency ◽  
Tax Rate ◽  
Taxation Policy ◽  
Course Of Action ◽  
Consistency Problem

<p>The recent push for environmental regulation has invigorated the discussion of mechanism design and optimal taxation policy. Recent decades have also seen growing interest in behavioural economics and empirically based theory. In this thesis we take a step towards combining the two by asking how a regulator may correct an externality in situations where they have a time consistency problem. Time inconsistency is one of the notable developments of behavioural economics. It posits that an agent’s decisions do not remain consistent over time, which causes a utility loss if the agent cannot commit themselves to a particular course of action and stick to it. The solution to inconsistency problems is to precommit to a course of action and prevent future deviations from it. However, finding a mechanism to enable such precommitment is often problematic. A regulator who maximises welfare can have a time consistency problem because welfare will depend on the decisions of firm and households who may themselves be inconsistent. That inconsistency then propagates to the regulator’s decision and reduces the level of welfare that the regulator can reach. Alternatively, the regulator’s time consistency problem can be caused by non-stationarity in their time preferences. To reach the firstbest outcome the regulator must not only eliminate the environmental externality: they must also overcome their own time inconsistency problem. This thesis draws from the literature on strategic delegation to construct a taxation game in which the regulator can achieve the first best taxation regime without the need for external precommitment devices. We study a dynamic game where the regulator chooses a tax rate and the regulated monopolist chooses their price. We show that the Markov-perfect equilibrium price path of this game will replicate the first best plan. Our results holds for time inconsistency caused by both jump states and quasihyperbolic discounting.</p>

scholarly journals Research on Cooperative Behavior of Green Technology Innovation in Construction Enterprises Based on Evolutionary Game

Buildings ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 19
Author(s):  
Qing’e Wang ◽  
Wei Lai ◽  
Mengmeng Ding ◽  
Qi Qiu
Keyword(s):  
Income Distribution ◽  
Technology Innovation ◽  
Cooperative Behavior ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Green Technology ◽  
Construction Enterprises ◽  
Cooperative Evolution ◽  
Cooperative Strategies ◽  
Punishment Mechanism

The dynamic evolution game model is built by using evolutionary game theory, and the evolutionarily stable strategy is analyzed by matlab2018b software in this paper. The cooperation willingness, sharing level, income distribution, and punishment mechanism are comprehensively considered in this model, and numerical simulations of the influence of various influencing factors on the cooperation strategy selection of green technology innovation for construction enterprises are carried out. Then, countermeasures and suggestions are put forward. The results of evolutionary game analysis show that the cooperation willingness, sharing level, income distribution, and punishment mechanism have a significant impact on the cooperative evolution direction of green technology innovation for construction enterprises, separately. Stronger cooperation willingness or higher relative value of positive spillover, or reasonable income distribution can promote partners to adopt active cooperative strategies, while appropriately increasing punishment intensity can prevent opportunistic behaviors and improve the probability of success of cooperative innovation.

scholarly journals Will Increasing Government Subsidies Promote Open Innovation? A Simulation Analysis of China’s Wind Power Industry

2021 ◽  
Vol 13 (23) ◽  
pp. 13497
Author(s):  
Wei Gao ◽  
Daojuan Wang
Keyword(s):  
Open Innovation ◽  
Simulation Analysis ◽  
Innovation Policy ◽  
Cooperative Behavior ◽  
Empirical Studies ◽  
Dynamic Game ◽  
Absorption Capacity ◽  
Influential Factors ◽  
Positive Role ◽  
Mediating Role

Keeping open innovation both stable and sustainable can be difficult when it involves cooperation between large enterprises. Some empirical studies suggest that subsidy policies can play a positive role. This study addresses two key questions that follow from this observation: first, if the intensity of a subsidy policy is increased, can it play a greater role in strengthening the stability of cooperation between firms? Second, what other factors play a mediating role in this effect? Utilizing a dynamic game model, this paper analyses influential factors such as absorptive capacity, frequency of engagement and technical value on cooperative stability, and investigates the role of innovation policy in the process of cooperation through a random number-driven simulation. The findings indicate that only when the absorption capacity and technological value of both partners meet a certain threshold is the probability of positive cooperative behavior improved. Otherwise, increased subsidies tend to foster negative cooperative behavior instead.

scholarly journals Stochastic data transmission model with uncertainty on dropper's appearance

2020 ◽  
Vol 13 ◽  
pp. 427-440
Author(s):  
Juan Xue ◽  
◽  
Elena M. Parilina ◽  
Keyword(s):  
Cooperative Behavior ◽  
Dynamic Game ◽  
Transmission Model ◽  
Stochastic Dynamic ◽  
Limited Information ◽  
Equilibrium Concept ◽  
Infinite Time ◽  
Lack Of Information ◽  
Stochastic Data ◽  
States Of Nature

We consider a stochastic dynamic game with uncertainty about appearance of an dropper in infinite time horizon. For the lack of information about whether the dropper is present or not, two different states of nature can appear with some given probabilities at each stage. We study the non-cooperative behavior of players, and Nash equilibrium is considered as an equilibrium concept. We investigate how limited information about the dropper's appearance impacts the anti-jamming strategy.

scholarly journals Marketing Resource Allocation Strategy Optimization Based on Dynamic Game Model

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Yan Long ◽  
Hongshan Zhao
Keyword(s):  
Nonlinear Dynamics ◽  
Network Model ◽  
Data Transmission ◽  
Dynamic Game ◽  
Transmission Model ◽  
Game Model ◽  
Two Stage ◽  
Cooperative Solution ◽  
Subgame Consistency ◽  
Stage Game

Game theory has become an important tool to study the competition between oligopolistic enterprises. After combing the existing literature, it is found that there is no research combining two-stage game and nonlinear dynamics to analyze the competition between enterprises for advertising. Therefore, this paper establishes a two-stage game model to discuss the effect of the degree of firms’ advertising input on their profits. And the complexity of the system is analyzed using nonlinear dynamics. This paper analyzes and studies the dynamic game for two types of application network models: data transmission model and transportation network model. Under the time-gap ALOHA protocol, the noncooperative behavior of the insiders in the dynamic data transmission stochastic game is examined as well as the cooperative behavior. In this paper, the existence of Nash equilibrium and its solution algorithm are proved in the noncooperative case, and the “subgame consistency” of the cooperative solution (Shapley value) is discussed in the cooperative case, and the cooperative solution satisfying the subgame consistency is obtained by constructing the “allocation compensation procedure.” The cooperative solution is obtained by constructing the “allocation compensation procedure” to satisfy the subgame consistency. In this paper, we propose to classify the packets transmitted by the source nodes, and by changing the strategy of the source nodes at the states with different kinds of packets, we find that the equilibrium payment of the insider increases in the noncooperative game with the addition of the “wait” strategy. In the transportation dynamic network model, the problem of passenger flow distribution and the selection of service parameters of transportation companies are also studied, and a two-stage game theoretical model is proposed to solve the equilibrium price and optimal parameters under Wardrop’s criterion.

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