Ecological-Economic Balance in Fining Environmental Pollution Subjects  by a Dyadic 3-Person Game Model

Romanuke, Vadim

doi:10.15666/aeer/1702_14511474

Cited by 7 publications

(31 citation statements)

References 14 publications

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“…In the simplest case, the strategy is a linear function of time. The time interval is usually short, through which a short-term trend of economic activity is realized [11,9]. Thus, a whole process is modeled as a series of those noncooperative games.…”

Section: Motivationmentioning

confidence: 99%

“…Then an approximating game is solved easily and faster. Besides, an approximated solution (with respect to the initial game) can be selected in order to meet demands and rules of the economic system [11,9]. In the case when the game is defined on a product of functional spaces, a strict substantiation is required to sample the functional sets of players' pure strategies.…”

Section: Motivationmentioning

confidence: 99%

“…Continuous noncooperative two-person games model interactions of a pair of subjects (players or persons) possessing continuums of their pure strategies [5,10]. A specificity of such games consists in that finding and practicing a solution in mixed strategies is often intractable [11,6,9]. Even if a solution exists in pure strategies, it often is revealed not to be a single one.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the problem of the single solution selection (or uniqueness) arises. However, even if the solution is unique, it is not guaranteed to be simultaneously profitable and symmetric [11,9,2,1].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite Approximation of Continuous Noncooperative Two-person Games on a Product of Linear Strategy Functional Spaces

Romanuke¹

2020

JMA

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Section: Motivationmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite Approximation of Continuous Noncooperative Two-person Games on a Product of Linear Strategy Functional Spaces

Romanuke¹

2020

JMA

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“…Such games are typical for economic interaction processes, where the player may use short-term time-varying strategies [3,4]. Continuous noncooperative two-person games are specic due to that nding and practicing a solution in mixed strategies is almost intractable even for the case when the players act within nite-dimensional Euclidean subspaces [3,5,6]. Moreover, a continuous game may have multiple solutions in pure strategies, so the problem of the single solution selection (or the problem of uniqueness) arises.…”

Section: Introductionmentioning

confidence: 99%

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2020

VAM

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A noncooperative two-person game is a model of an economic interaction process considered on a short interval. A whole process, which is a stack of a multitude of the short intervals, is modeled as a series of such noncooperative games. The series of the games is required to be solved without delay, so a method of the nite approximation of continuous noncooperative two-person games is presented. The method is based on sampling the functional spaces, which serve as the sets of pure strategies of the players. The pure strategy is a sinusoidal function of time, in which the phase lag is variable. The spaces of the players' pure strategies are sampled uniformly so that the resulting nite game is a bimatrix game whose payo matrices are square. The approximation procedure starts with not a great number of intervals. Then this number is gradually increased, and new, bigger, bimatrix games are solved until an acceptable solution of the bimatrix game becomes suciently close to the same-type solutions at the preceding iterations. The closeness is expressed in terms of the respective functional spaces, in which the player's strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. These requirements are transformed into the relaxed conditions which allow sampling the players' sets of pure strategies: the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coecients at the squared variable. The acceptable solution is not only a situation, but rather a sub-rectangle of situations, associated with just the phase lags, dened by its center, which is the most attractive situation for the players.

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Equilibrium stacks for a non-cooperative game defined on a product of staircase-function continuous and finite strategy spaces

Vadim Romanuke

2023

Stat., optim. inf. comput.

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A method of finite uniform approximation of 3-person games played with staircase-function strategies is presented. A continuous staircase 3-person game is approximated to a staircase trimatrix game by sampling the player’s pure strategy value set. The set is sampled uniformly so that the resulting staircase trimatrix game is cubic. An equilibrium of the staircase trimatrix game is obtained by stacking the equilibria of the subinterval trimatrix games, each defined on an interval where the pure strategy value is constant. The stack is an approximate solution to the initial staircase game. The (weak) consistency, equivalent to the approximate solution acceptability, is studied by how much the players’ payoff and equilibrium strategy change as the sampling density minimally increases. The consistency includes the payoff, equilibrium strategy support cardinality, equilibrium strategy sampling density, and support probability consistency. The most important parts are the payoff consistency and equilibrium strategy support cardinality (weak) consistency, which are checked in the quickest and easiest way. However, it is practically reasonable to consider a relaxed payoff consistency, by which the player’s payoff change in an appropriate approximation may grow at most by epsilon as the sampling density minimally increases. The weak consistency itself is a relaxation to the consistency, where the minimal decrement of the sampling density is ignored. An example is presented to show how the approximation is fulfilled for a case of when every subinterval trimatrix game has pure strategy equilibria.

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Ecological-Economic Balance in Fining Environmental Pollution Subjects by a Dyadic 3-Person Game Model

Cited by 7 publications

References 14 publications

Finite Approximation of Continuous Noncooperative Two-person Games on a Product of Linear Strategy Functional Spaces

Finite Approximation of Continuous Noncooperative Two-person Games on a Product of Linear Strategy Functional Spaces

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Equilibrium stacks for a non-cooperative game defined on a product of staircase-function continuous and finite strategy spaces

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