| Article |
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| Article name |
The Problem of Fair Sharing of the Cake with the Arbitrator |
| Authors |
Tokareva J.S. Candidate of Physics and Mathematics, jtokareva2@mail.ru |
| Bibliographic description |
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| Section |
Scientific Research |
| UDK |
В 11 |
| DOI |
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| Article type |
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| Annotation |
We consider the stochastic procedure of multicomponent resource allocation presented as a problem of fair sharing of the pie. The model of two different resource allocation of a single size between three playersis presented. A multistage non- cooperative game with the arbitration procedure using a random mechanism with the multi-dimensional Dirichlet distribution is studied. Time intervalis given for the negotiations. At each step, the arbitrator generates random proposals for each of the two resources for each of the players. Optimal players’ behavior in the model for the three negotiators is studied, the Nash equilibrium strategies of threshold type are foundand analytical expressions for the winningsare obtained. We consider the case where the random number generator (the arbitrator’s opinion) is represented by theDirichlet distribution with asymmetrical distribution parameters. To study the model, threshold strategies of the players are introducedas probabilities of the fact that the player at this stage will accept a current proposal of the arbitrator on two resources. The game value satisfies the recurrence relations. We found the optimal solution in full consensus. Research methods are based on game-theoretic analysis of non-cooperative games.
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| Key words |
negotiation, arbitrator, discounting, Dirichlet distribution, threshold strategies |
| Article information |
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| References |
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| Full article | The Problem of Fair Sharing of the Cake with the Arbitrator |
