Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Romanuke, Vadim

doi:10.1515/ecce-2015-0002

Cited by 5 publications

(9 citation statements)

References 42 publications

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“…Traditional game theory tells people that there are many possible Nash equilibriums in one game. Evolutionary game theory further states which one is the real equilibrium in reality and it is not necessarily Pareto optimal equilibrium [23][24][25].…”

Section: Game Strategy Selection and Evolutionary Stabilizationmentioning

confidence: 99%

Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application

Wang

et al. 2018

Complexity

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Coal mine safety management involves many interested parties and there are complex relationships between them. According to game theory, a multiparty evolutionary game model is established to analyze the selection of strategies. Then, a simplified three-party model is taken as an example to carry out detailed analysis and solution. Based on stability theory of dynamics system and phase diagram analysis, this article studies replicator dynamics of the evolutionary model to make an optimization analysis of the behaviors of those interested parties and the adjustment mechanism of safety management policies and decisions. The results show how the charge of supervision of government department and inspection of coal mine enterprise impact the efficiency of safety management and the effect of constraint measures and incentive and other measures in safety management.

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Section: Game Strategy Selection and Evolutionary Stabilizationmentioning

confidence: 99%

Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application

Wang

et al. 2018

Complexity

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“…The refinement must be turned on if 1 S  . In the being considered non-repeatable bimatrix game, from the view of players that can "think truly and rationally" [1,7,10,14,15,26,27], it is best to use pure strategies from subsets (10). But how can their actions guarantee an appropriate result?…”

Section: Appending the Maximin And Superoptimality Rulementioning

confidence: 99%

“…Typically, such a refinement refers to the selection of a subset of Nash equilibria, and this subset is believed to include equilibria that are more plausible than other equilibria. A great deal of the refinements exists, e. g. [7], strong Nash equilibrium [8,9], Mertens-stable equilibrium [10], trembling hand perfect equilibrium [11], proper equilibrium [12,13], sequential equilibrium [14,15], quasi-perfect equilibrium [13,16,17]. However, none of them can guarantee a single (refined) Nash equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Pure Strategy Nash Equilibria Refinement in Bimatrix Games by Using Domination Efficiency along with Maximin and the Superoptimality Rule

Romanuke

2018

Nauk. Visti KPI

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Background. Multiple Nash equilibria bring a new problem of selecting amongst them but this problem is solved by refining the equilibria. However, none of the existing refinements can guarantee a single refined Nash equilibrium. In some games, Nash equilibria are nonrefinable. Objective. For solving the nonrefinability problem of pure strategy Nash equilibria in bimatrix games, the goal is to develop an algorithm which could facilitate in refining the equilibria as much further as possible. Methods. A Nash equilibria refinement is suggested, which is based on the classical refinement by selecting only efficient equilibria that dominate by their payoffs. The suggested refinement exploits maximin subsequently. The superoptimality rule is involved if maximin fails to produce just a single refined equilibrium. Results. An algorithm of using domination efficiency along with maximin and the superoptimality rule has been developed for refining Nash equilibria in bimatrix games. The algorithm has 10 definite steps at which the refinement is progressively accomplished. The developed concept of the equilibria refinement does not concern games with payoff symmetry and mirror-like symmetry. Conclusions. The suggested pure strategy Nash equilibria refinement is a contribution to the equilibria refinement game theory field. The developed algorithm allows selecting amongst nonrefinable Nash equilibria in bimatrix games. It partially removes the uncertainty of equilibria, without going into mixed strategies. There are only two negative cases when the refinement fails. For a case when more than a single refined equilibrium is produced, the superoptimality rule may be used for a player having multiple refined equilibrium strategies but the other player has just a single refined equilibrium strategy.

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“…The trimatrix game rendering can be fulfilled regardless of the pure strategy complexity [18,15,12,21]. Obviously, such rendering is impossible if the set of the player's strategies is either infinite or continuous.…”

Section: Introductionmentioning

confidence: 99%

“…This is so because of the continuity of possible values of the strategy on a subinterval. However, the continuity might be removed also by sampling [21,16]. Then the set of function-strategies becomes finite.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

Romanuke

2022

Foundations of Computing and Decision Sciences

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A method of solving a three-person game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous. The method is based on stacking equilibria of “short” three-person games, each defined on an interval where the pure strategy value is constant. In the case of finite three-person games, which factually are trimatrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any interval-wise combination (succession) of the respective equilibria of the “short” trimatrix games. Apart from the stack, there are no other equilibria in this “long” trimatrix game. An example is presented to show how the stacking is fulfilled for a case of when every “short” trimatrix game has a pure-strategy equilibrium. The presented method, further “breaking” the initial “long” game defined on a product of staircase-function finite spaces, is far more tractable than a straightforward approach to solving directly the “long” trimatrix game would be.

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Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Cited by 5 publications

References 42 publications

Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application

Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application

Pure Strategy Nash Equilibria Refinement in Bimatrix Games by Using Domination Efficiency along with Maximin and the Superoptimality Rule

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

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