Simulation of Concurrent Games

A. N. Ivutin; E. V. Larkin

doi:10.14529/mmp150204

Authors

A. N. Ivutin Tula State University
E. V. Larkin Tula State University

DOI:

https://doi.org/10.14529/mmp150204

Keywords:

competition, concurrent game, Petri-Markov net, distance, distributed forfeit, waiting time, common winning, paired competition, multiple competition.

Abstract

Concurrent games, in which participants run some distance in real physical time, are investigated. Petri-Markov models of paired and multiple competitions are formed. For paired competition formula for density function of time of waiting by winner the moment of completion of distance by loser is obtained. A concept of distributed forfeit, which amount is defined as a share of sum, which the winner gets from the loser in current moment of time is introduced. With use of concepts of distributed forfeit and waiting time the formula for common forfeit, which winner gets from loser, is obtained. The result, received for a paired competition, was spread out onto multiple concurrent games. Evaluation of common wins and loses in multiple concurrent game is presented as a recursive procedure, in which participants complete the distance one after another, and winners, who had finished the distance get forfeits from participants, who still did not finish it. The formula for evaluation of common winning in concurrent game with given composition of participants is obtained. The result is illustrated with numerical example.

Author Biographies

A. N. Ivutin, Tula State University

Candidate of Physico-Mathematical Sciences, Associate Professor

E. V. Larkin, Tula State University

Doctor of Physico-Mathematical Sciences, Professor

References

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