Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

DKPRG or How to Succeed in the Kolkata Paise Restaurant Game via TSP

Version 1 : Received: 2 November 2020 / Approved: 3 November 2020 / Online: 3 November 2020 (14:00:14 CET)

How to cite: Kastampolidou, K.; Papalitsas, C.; Andronikos, T. DKPRG or How to Succeed in the Kolkata Paise Restaurant Game via TSP. Preprints 2020, 2020110150 (doi: 10.20944/preprints202011.0150.v1). Kastampolidou, K.; Papalitsas, C.; Andronikos, T. DKPRG or How to Succeed in the Kolkata Paise Restaurant Game via TSP. Preprints 2020, 2020110150 (doi: 10.20944/preprints202011.0150.v1).

Abstract

The Kolkata Paise Restaurant Problem is a very challenging game, where n agents have to decide where they will have lunch on a busy day during their lunch break. The game is very interesting because there are exactly n restaurants and each restaurant can accommodate only one agent. If two or more agents happen to choose the same restaurants, only one gets served and the others have to return back to work hungry. In this paper, we tackle this problem from an entirely new angle. We abolish certain implicit assumptions, which allows us to propose a novel strategy with greater utilization of the restaurants and overall efficiency. We emphasize the spatially distributed nature of our approach, which, for the first time, perceives the locations of the restaurants as uniformly distributed in the entire city area. This critical change in perspective has profound ramifications in the topological layout of the restaurants, which now makes it completely realistic to assume that every agent has a second chance. Every agent now may visit, in case of failure, more than one restaurants, within the predefined time constraints. From the point of view of each agent, the situation now resembles more that of the iconic travelling salesman, who must compute an optimal route through n cities. Following this shift in paradigm, we advocate the use of metaheuristics, as exacts solution of the TSP are prohibitively expensive, because they can produce near-optimal solutions in a very short amount of time. The use of metaheuristics enables each agent to compute her own personalized solution, incorporating her preferences, and providing alternative destinations in case of successive failures. We analyze rigorously the resulting situation, proving probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The detailed mathematical analysis of our scheme demonstrates that it can achieve utilization ranging from .85 to 0.95 from the first day, while rapidly attaining steady state utilization 1.0. Moreover, the equations we have developed generalize previously presented formulas in the literature, which can be shown to be special cases of our results.

Subject Areas

Game theory; Kolkata Paise Restaurant Problem; TSP; metaheuristics; optimization; probabilistic analysis

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