non cooperative games
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2022 ◽  
Vol 355 ◽  
pp. 02041
Author(s):  
Ruiqi Zhang ◽  
Yuting Cao ◽  
Yuzhang Li

This paper introduced Helbing’s social force model, modified it with game theory. Then how individuals in the space behave in dynamic non-cooperative games was described, different macro grouping characteristics were obtained. Individual behaviours at the micro level were simulated. Setting different parameters and conditions of the model, the macro effects of individual behaviours were observed. The overall behaviour of the system was studied. It could be used to guide the allocation of public resources.


2021 ◽  
Author(s):  
Julian Gutierrez ◽  
Lewis Hammond ◽  
Anthony W. Lin ◽  
Muhammad Najib ◽  
Michael Wooldridge

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).


2021 ◽  
Author(s):  
Bernhard von Stengel

Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1872
Author(s):  
Chenwei Liu ◽  
Shuwen Xiang ◽  
Yanlong Yang

We define the mixed strategy form of the characteristic function of the biform games and build the Shapley allocation function (SAF) on each mixed strategy profile in the second stage of the biform games. SAF provides a more detailed and accurate picture of the fairness of the strategic contribution and reflects the degree of the players’ further choices of strategies. SAF can guarantee the existence of Nash equilibrium in the first stage of the non-cooperative games. The existence and uniqueness of SAF on each mixed strategy profile overcome the defect that the core may be an empty set and provide a fair allocation method when the core element is not unique. Moreover, SAF can be used as an important reference or substitute for the core with the confidence index.


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