Equilibrium Points In Games Research Articles

An Evolutionary Game Analysis of Stakeholders’ Decision-Making Behavior in Medical Data Sharing

In the era of big data, medical data sharing has become an inevitable requirement to improve the quality and efficiency of medical services. To advance the progress of medical data sharing and expedite the circulation of data value, it becomes crucial to examine the decision-making behavior of stakeholders involved in the medical-data-sharing process. To this end, we construct a three-way evolutionary game model applicable to the medical sharing scenario, analyzing the evolutionary trends in the selection strategies of data providers, the medical-data-sharing platform and data demanders. Furthermore, through theoretical analysis and simulation experiments, we explore the game equilibrium point of the system and analyze key factors that affect stakeholder strategy selection. The results of the experiment show that, in addition to data security, platforms and regulators should pay attention to the regulation and governance of the quality of data flows, which involves reasonable incentives–feedback–rewards and penalties. By strengthening the security technology and data governance system construction of sharing platforms, as well as promoting regulatory authorities to implement reward and punishment measures, etc., a stable state can be achieved in such systems. In addition, this article also proposes relevant management suggestions for medical data sharing in order to provide useful references for scientific decision making by stakeholders.

Optimizing Energy Management in Microgrids Based on Different Load Types in Smart Buildings

This paper presents an energy management strategy (EMS) based on the Stackelberg game theory for the microgrid community. Three agents or layers are considered in the proposed framework. The microgrid cluster (MGC) refers to the agent that coordinates the interactions between the microgrids and the utility grid. The microgrid agent manages the energy scheduling of its own consumers. The third agent represents the consumers inside the microgrids. The game equilibrium point is solved between different layers and each layer will benefit the most. First, an algorithm performs demand response in each microgrid according to load models in smart buildings and determines the load consumption for each consumer. Then, each microgrid determines its selling price to the consumers and the amount of energy required to purchase from the utility grid to achieve the maximum profit. Finally, the balance point will be obtained between microgrids by the microgrid cluster agent. Moreover, the proposed method uses various load types at different times based on real-life models. The result shows that considering these different load models with demand response increased the profit of the user agent by an average of 22%. The demand response is implemented by the time of use (TOU) model and real-time pricing (RTP) in the microgrid.

An aggregator-oriented hierarchical market mechanism for multi-type ancillary service provision based on the two-loop Stackelberg game

In order to utilize demand-side flexibility and meet system requirements, the aggregator (AGG) has become a vital role in the ancillary service market. To reflect the willingness of each market subject, a tri-layer ancillary service market framework for ancillary service market operator (ASMO), AGG, and users is proposed in this paper, which contains the interactions between different layers including ASMO and AGG, AGG and users. We develop a detailed market timeline that takes multi-type ancillary services into account. Moreover, due to the hierarchical market structure, we conduct a two-loop Stackelberg game to depict the effect of each market subject’s strategic behavior. Based on the game models of all the market subjects, the existence and uniqueness of the game equilibrium point are proved. In addition, considering the correlation between multi-type ancillary services, the clearing process is decomposed into two sub-problems and a distributed joint market clearing based on the particle swarm optimization algorithm is presented. Case study shows that the proposed method is profitable for all the market subjects, the market timeline is reasonable, and the joint clearing method is effective.

Evolutionary Game Analysis of Farmers' Conservation Tillage Behavior in Black Soil Areas Guided by Deep Learning.

To better protect the rights and interests of farmers, the evolutionary game theory and deep learning (DL) technology are used to analyze the conservation tillage behavior of farmers in black soil areas. Firstly, the basic hypotheses are put forward and an evolutionary game model is constructed. Secondly, the evolutionary game model between farmers and the government is analyzed, and dynamic equations are built. Finally, the model is deduced and studied, and a Convolutional Neural Network (CNN) with a double-sized convolution kernel is constructed to classify the land of remote sensing images. The experimental results manifest that after the dynamic evolutionary game, the net income generated by farmers adopting the conservation tillage strategy without government regulation is positive. The net income of government regulation is positive, and the game equilibrium point is (1, 0). After a dynamic evolutionary game, the game is balanced when the government does not regulate, the net income generated by farmers adopting conservation tillage strategies and the net income generated by government regulation and farmers adopting conservation tillage strategies are negative, the net income from government regulation is positive, and the game equilibrium point is (0, 1). The constructed CNN can achieve 91.32% overall accuracy for black soil classification, and the proposed scheme provides some references for the application of CNN in evolutionary games.

Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games

In this paper, we study a nonzero-sum stochastic differential game in the Markovian framework. We show the existence of a discontinuous Nash equilibrium point for this game. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.

Regularized differential extragradient method for searching for an equilibrium point in two-person saddle-point games with approximate input data

A two-person saddle-point game with approximately given input data is examined. In general, the search for an equilibrium point in games of this type is unstable with respect to perturbations in the input data, and special regularization methods are required for their solution. To this end, two variants of the regularized differential extragradient method are proposed. Their convergence is analyzed, and a regularizing operator is constructed.

PAYOFF DOMINANCE AND THE STACKELBERG HEURISTIC

Payoff dominance, a criterion for choosing between equilibrium points in games, is intuitively compelling, especially in matching games and other games of common interests, but it has not been justified from standard game-theoretic rationality assumptions. A psychological explanation of it is offered in terms of a form of reasoning that we call the Stackelberg heuristic in which players assume that their strategic thinking will be anticipated by their co-player(s). Two-person games are called Stackelberg-soluble if the players' strategies that maximize against their co-players' best replies intersect in a Nash equilibrium. Proofs are given that every game of common interests is Stackelberg-soluble, that a Stackelberg solution is always a payoff-dominant outcome, and that in every game with multiple Nash equilibria a Stackelberg solution is a payoff-dominant equilibrium point. It is argued that the Stackelberg heuristic may be justified by evidentialist reasoning.

Perfect equilibrium points and lexicographic domination

This paper investigates a problem of the perfect equilibrium point in games in normal form by introducing a lexicographic domination of strategies for players, which turns out to be equivalent to a “local” domination of strategies. It is shown that a perfect equilibrium point is lexicographically undominated, and moreover that the lexicographic domination can narrow down the set of undominated equilibrium points in the ordinary sense when there are more than two players in a game.

Money, trust and equilibrium points in games in extensive form

Money, trust and equilibrium points in games in extensive form

Equilibrium Points for Games with Infinitely Many Players

Abstract : Conditions that guarantee the existence of equilibrium points for games with infinitely many players are discussed; essentially what is needed is that the payoff functions are continuous in an appropriate sense. If the continuity assumption does not hold then one shows by an example that equilibrium points may not exist. (Author)

Equilibrium points in games with vector payoffs

AbstractHistorical. The topic of games with vector payoffs is one which could be expected to attract attention on the basis of its intrinsic interest. However, the history of the particular problem treated in Dr. Shapley's paper was not of this kind and m a y have some interest of its own. During an interval when the writer of this note was engaged in operations research his group was asked t o analyze a combat situation in which movement of f o r c e s and the inhibition of such movement were critical It turned out to be feasible to represent essential aspects of this situation by a game‐like model with reasonably well defined courses of action corresponding to pure strategies for each side. However, each pair of these strategies, one for each player, generated both a time delay in the movement and losses to the moving forces not balanced by losses to the inhibiting player. That is the model was a game with vector pay off in the sense of this paper. Since the values of these delays and losses would be realized in a subsequent battle in the area approached by the movement in question, it was clear that some s o r t of exchange ratio between attrition and delay must exist. Efforts to obtain estimates of such a ratio failed completely. In fact, several rather arbitrary weightings of delay and attrition were assumed and the resulting numerical games solved for the sake of the insight they could provide, but this was a rather unsatisfactory expedient. Had the theory presented in this paper been available, it would have been possible at least to sharpen the questions asked in pursuit of the „exchange ratio,”︁ and probably to eliminate rationally considerable sets of strategy pairs a s unsuitable or a s representing extreme cases in the weighting.In any event, the theory was not a t hand and the study could not wait on its development. The problem was, however, brought to the attention of Dr. Shapley, with this paper a s a consequence.Nature of the Results. Perhaps a comment on the kind of results which are presented is in order since there is a sort of fitness to them. As was noted above, the occurrence of vector payoff represents a failure to resolve some of the questions whose answers are needed in order to construct a game model. This being the case, one should not be disappointed that the theory does not produce a clear cut, well defined solution concept. What it does produce, if the payoff vectors have K + 1 components, is a ZK parameter set of equilibrium points, in comparison with a unique solution for a numerical game similarly specified. (The fact that numerical game solutions need not be unique has its counterpart among vector game equilibrium points also, of course.) Such an „equilibrium set,”︁ however, need not cover a major part of the joint mixed strategy space, even in games with only a few pure strategies for each player. Accordingly, although finding these sets may be extremely tedious for a particular game, they may well turn out to be worth having in the sense that they limit the domain over which weighting comparisons of the payoff vector components need be made. Since Dr. Shapley's results concern both „strong”︁ and „weak”︁ equilibrium points it is pertinent to note that this distinction appears „usually”︁ to concern the boundaries of the „equilibrium sets.”︁ That is one might expect that the set of strong equilibrium points omits boundary points which are included in the weak case. It should be remarked, however, that this characterization of the distinction is not precise or universal, and instances of its failure can be produced.