Markov Modeling of Cooperative Multiplayer Coupon Collectors' Problems

TL;DR

This paper models a cooperative multiplayer version of the Coupon Collector's Problem using Markov chains, analyzing resource sharing costs and benefits in network contexts.

Contribution

It introduces a Markov framework for the cooperative coupon collector problem, quantifying cooperation costs and benefits based on ensemble parameters.

Findings

Cooperation reduces the average collection time.

Cost depends on number of players and coupons, not on detailed statistics.

Markov modeling effectively captures resource sharing dynamics.

Abstract

The paper introduces a modified version of the classical Coupon Collector's Problem entailing exchanges and cooperation between multiple players. Results of the development show that, within a proper Markov framework, the complexity of the Cooperative Multiplayer Coupon Collectors' Problem can be attacked with an eye to the modeling of resource harvesting and sharing within the context of Next Generation Network. The cost of cooperation is computed in terms of exchange protocol burden and found to be dependent on only ensemble parameters such as the number of players and the number of coupons but not on the detailed collection statistics. The benefits of cooperation are quantified in terms of reduction of the average number of actions before collection completion.