Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces

• Autorzy: Romanuke Vadim

Identyfikatory

DOI

10.2478/fcds-2021-0012

• Języki publikacji: EN

Abstrakty

EN

A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that 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 coefficients at the squared variable.

Słowa kluczowe

EN

game theory; payoff functional; sinusoidal strategy; finite approximation; attractive situation; continuous games

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2021
• Tom: Vol. 46, No. 2
• Strony: 173--197
• Opis fizyczny: Bibliogr. 25 poz., rys.,

Twórcy

autor

Romanuke Vadim

• Polish Naval Academy, Gdynia, Poland

Bibliografia

• [1] Agapova A., Madura J., Market uncertainty and earnings guidance, The Quarterly Review of Economics and Finance, 61, 2016, 97-111.
• [2] Basso B., Liu L., Chapter 4. Seasonal crop yield forecast: Methods, applications, and accuracies, Advances in Agronomy, 164, 2019, 201-255.
• [3] Bazerman M.H., Moore D.A., Judgment in Managerial Decision Making (8th ed.), Wiley, River Street, Hoboken, NJ, 2013.
• [4] Blalock H.M., Social Statistics, McGraw-Hill, New York, NY, 1979.
• [5] Branke J., Deb K., Miettinen K., Słowiński R. (eds.), Multiobjective Optimization: Interactive and Evolutionary Approaches (Lecture Notes in Computer Science (5252), Springer, Berlin, 2008.
• [6] Castelli A.F., Moretti L., Manzolini G., Martelli E., A robust rolling-horizon algorithm for the optimal operation of multi-energy systems with yearly constraints and seasonal storage, Computer Aided Chemical Engineering, 48, 2020, 1513-1518.
• [7] Harsanyi J.C., Selten R., A General Theory of Equilibrium Selection in Games, The MIT Press, Cambridge, MA, 1988.
• [8] Hirshleifer D., Jiang D., DiGiovanni Y.M., Mood beta and seasonalities in stock returns, Journal of Financial Economics, 137 (1), 2020, 272-295.
• [9] Kalaiselvam S., Parameshwaran R., Chapter 7. Seasonal Thermal Energy Storage, Thermal Energy Storage Technologies for Sustainability. Systems Design, Assessment and Applications, Academic Press, 2014, 145-162.
• [10] Lan Y., Liu Y.K., Sun G., Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels, Journal of Computational and Applied Mathematics, 231 (1), 2009, 208-221.
• [11] Loesche F., Ionescu T., Mindset and Einstellung Effect, Encyclopedia of Creativity, 3, 2020, 174-178.
• [12] Martinez J.M.G., Martin J.M.M., del Sol Ostos Rey M., An analysis of the changes in the seasonal patterns of tourist behavior during a process of economic recovery, Technological Forecasting and Social Change, 161, Elsevier, 2020, 120280.
• [13] Nisan N., Roughgarden T., Tardos É., Vazirani V.V., Algorithmic Game Theory, Cambridge University Press, Cambridge, UK, 2007.
• [14] Romanuke V.V., Uniform sampling of fundamental simplexes as sets of players’ mixed strategies in the finite noncooperative game for finding equilibrium situations with possible concessions, Journal of Automation and Information Sciences, 47 (9), 2015, 76-85.
• [15] Romanuke V.V., Approximate equilibrium situations with possible concessions in finite noncooperative game by sampling irregularly fundamental simplexes as sets of players’ mixed strategies, Journal of Uncertain Systems, 10 (4), 2016, 269-281.
• [16] Romanuke V.V., Interval uncertainty reduction via division-by-2 dichotomization based on expert estimations for short-termed observations, Journal of Uncertain Systems, 12 (1), 2018, 3-21.
• [17] Romanuke V.V., Acyclic-and-asymmetric payoff triplet refinement of pure strategy efficient Nash equilibria in trimatrix games by maximinimin and superoptimality, KPI Science News, 4, 2018, 38-53.
• [18] Romanuke V.V., Ecological-economic balance in fining environmental pollution subjects by a dyadic 3-person game model, Applied Ecology and Environmental Research, 17 (2), 2019, 1451-1474.
• [19] Romero L.M., Bauer C.M., de Bruijn R., Lattin C.R., Chapter 42. Seasonal Rhythms, Stress: Neuroendocrinology and Neurobiology. Handbook of Stress Series, 2, Academic Press, 2017, 421-427.
• [20] Vorob’yov N.N., Game theory fundamentals. Noncooperative games, Nauka, Moscow, 1984. (in Russian).
• [21] Vorob’yov N.N., Game theory for economists-cyberneticists, Nauka, Moscow, 1985. (in Russian).
• [22] White E.R., Hastings A., Seasonality in ecology: Progress and prospects in theory, Ecological Complexity, 44, Elsevier, 2020, 100867.
• [23] Yang J., Chen Y.-S., Sun Y., Yang H.-X., Liu Y., Group formation in the spatial public goods game with continuous strategies, Physica A: Statistical Mechanics and its Applications, 505, 2018, 737-743.
• [24] Yang Y., DeFrain J., Faruqui A., Conceptual discussion on a potential hidden cross-seasonal storage: Cross-seasonal load shift in industrial sectors, The Electricity Journal, 33 (8), Elsevier, 2020, 106846.
• [25] Young P., Zamir S. (eds.), Handbook of Game Theory. Volume 4, North Holland, 2015.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).