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Partitions as a Model for Numerical Simulation

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We propose a new approach to investigating such non-cooperative games, as tournaments and evolutionary games. Our model of symmetric game is based on partition classes of integers, and the rules are similar to those of well-known Colonel Lotto game. We present detailed model of dynamics of evolutionary game with two populations of matrix strategies. A win (according to Lotto game’s rules) leads to precise replication of the winning strategy, a loss leads to eliminating the losing strategy. We specify efficiently computable properties of partitions allowing to classify the set of partitions according to their winning ability and present detailed simulation results for the evolutionary Lotto game with (100,10)-partitions. The results of the simulations fully support the classification principles we are proposing.
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Partition; Composition; Partition Game; Colonel Lotto Game; Population Dynamic; Reproduction; Fitness; Balance; Relative Strength

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D.E. Knuth, The Art of Computer Programming, Vol. 4A: Combinatorial Algorithms, Part 1.Addison-Wesley Professional, 2011.

E. Borel, The theory of play and integral equations with skew symmetric kernels, Econometrica, Vol. 21(1):97–100, 1953.

D. Kovenock, B. Roberson, Coalitional colonel blotto games with application to the economics of alliances, Journal of Public Economic Theory, Vol. 14 (4):653-676, 2012

O. Gross, R. Wagner, A Continuous Colonel Blotto Game, Technical Report, 1950.

B. Roberson, The Colonel Blotto game, Economic Theory, Vol. 29(1):1–24, 2006.

S. Hart, Discrete Colonel Blotto and General Lotto games, International Journal of Game Theory, Vol. 36(3):441–460, 2008.

S. Hart, Allocation games with caps: From captain lotto to all-pay auctions, International Journal of Game Theory, 1–24, July 2015 2015.

Cox, B., Juditsky, A., Nemirovski, A. Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators on Domains Given by Linear Minimization Oracles.arXiv:1506.02444, June 12, 2015.

E. Dechenaux, D. Kovenock, R. M. Sheremeta, A Survey of Experimental Research on Contests, All-Pay Auctions and Tournaments,Experimental Economics, 1–64, 2014.

S.M.Chowdhury, D.Kovenock, R.M. Sheremeta(2013a). An experimental investigation of Colonel Blotto games. Economic Theory, Vol. 52(3):833–861, 2013.

A. Arad, A. Rubinstein, Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game. Journal of Economic Behavior and Organization, Vol. 84(2)571–585, 2012.

A. Arad, The tennis coach problem: A game-theoretic and experimental study. The B.E. Journal of Theoretical Economics, 12(1), 2012.

D.O. Stahl, P.W. Wilson, Experimental evidence on players' models of other players, Journal of economic behavior& organization, Vol. 25(3):309–327, 1994.

P. Bocharov, A. Goryashko, E. V. Nikulchev, Partition Games as Contests: Numerical Simulation Results, Applied Mathematical Sciences,Vol. 9(104):5149–5167, 2015.

P. Bocharov, Partition Games ResearchToolbox, 2015.

C. Taylor, D. Fudenberg, A. Sasaki, M. Nowak, Evolutionary Game Dynamics in Finite Populations, Bulletin of Mathematical Biology, Vol. 66(6):1621–1644, 2004.

D. Vilone, A. Robledo, A. Sanchez, Chaos and Unpredictability in Evolutionary Dynamics in Discrete Time, Physical review letters, Vol. 107(3), 038101, 2011.

E. Walkingshaw, M. Erwig, A Domain-Specific Language for Experimental Game Theory, Journal of Functional Programming, Vol. 19(6):645–661, 2009 .

I. Alger, J. W. Weibull, Kinship, Incentives, and Evolution,The American Economic Review, Vol.100(4):1725–1758, 2010.

D. Easley, J. Kleinberg, Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge University Press, 2010.

K. A. Konrad, F. Morath, Bargaining with incomplete information: Evolutionary stability in finite populations, Working Paper of the Max Planck Institute for Tax Law and Public Finance, 2014.

I. Alger, J. Weibull. Homo Moralis– Preference Evolution under Incomplete Information and Assortative Matching, Econometrica, Vol. 81(6):2269-2302, 2013,


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