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Approximation in solving the infinite two-person non-cooperative games is studied in the paper. An approximation approach with conversion of infinite game into finite one is suggested. The conversion is fulfilled in three stages. Primarily the players’ payoff functions are sampled variously according to the stated requirements to the sampling. These functions are defined on unit hypercube of the appropriate Euclidean finite-dimensional space. The sampling step along each of hypercube dimensions is constant. At the second stage, the players’ payoff multidimensional matrices are reshaped into ordinary two-dimensional matrices, using the reversible index-to-index reshaping. Thus, a bimatrix game as an initial infinite game approximation is obtained. At the third stage of the conversion, the player’s finite equilibrium strategy support is checked out for its weak consistency, defined by five types of inequalities within minimal neighbourhood of every specified sampling step. If necessary, the weakly consistent solution of the bimatrix game is checked out for its consistency, strengthened in that the cardinality of every player’s equilibrium strategy support and their densities shall be non-decreasing within minimal neighbourhood of the sampling steps. Eventually, the consistent solution certifies the game approximation acceptability, letting solve even games without any equilibrium situations, including isomorphic ones to the unit hypercube game. A case of the consistency light check is stated for the completely mixed Nash equilibrium situation.
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The process of administrative decentralization of the education system in Romania proceeded in chaotic steps. It was done under the pressure, on one hand, of the EU integration requirements and, on the other hand, of the local administrations who wanted more control over how their money were used in the schools and of the parents committees that wanted to have a say in the local schools. The road was scattered with new reform legislations coming with every change in government composition and ministers. The result was a combination of local autonomy and central control that had the potential to produce confusion and conflict. The multiple and complex blend of divided responsibilities and powers turned out in the process of setting up the new form or entry grade in the Romanian primary education cycle in a rational strategic play scholarly designated as anticommons. Each separated actor tries to obtain a maximizing share of the cooperatively generated benefit for a minimum possible cost. The interactions are modeled as a Game of Chicken where, because actors calculate separately, each selects a higher price/lower quantity position than is optimal, resulting in a lower net payoff both individually and collectively.
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