The Distributed Kolkata Paise Restaurant Game

Abstract

The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this problem from a new angle and propose a novel strategy that results in greater utilization. Adopting a spatially distributed approach where the restaurants are uniformly distributed in the entire city area makes it possible for every agent to visit multiple restaurants. For each agent, the situation resembles that of the iconic traveling salesman, who must compute an optimal route through n cities. We rigorously prove probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The derived equations generalize formulas that were previously known in the literature, which can be seen as special cases of our results.

Stability of Dining Clubs in the Kolkata Paise Problem with and without Cheating

“…The Kolkata Paise Restaurant Problem (KPRP) was first introduced in 2007 [1] during work on the Kolkata Paise Hotel Problem. Since then, it has been studied extensively [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] in the econophysics literature. In its simplest form, we assume N ≫ 1 agents will choose among N restaurants.…”

“…Quantum versions of the problem are considered in [12,15,16] and its relevance to other areas of physical modelling are considered in [8,10,14,17] with phase transitions considered recently in [2,9]. Distributed and coordinated solutions to optimizing agent payoff are discussed in [4][5][6]13].…”

An Advanced Multi-Agent Reinforcement Learning Framework of Bridge Maintenance Policy Formulation

“…The multi-agent framework is adopted to solve the problem. Researchers in various fields have tried to extend the existing single-agent to multi-agent [24][25][26], such as Modular Q-Learning in which a single agent problem is divided into different subproblems, and each agent solves different subproblems, Ant Q-Learning of which all the agents share reward, and Nash Q-Learning which has greatly improved the efficiency of Q-Learning algorithms [27][28][29]. In this paper, the training process is completed by multi-agent parallel mode, and the optimal maintenance policy of the bridge is output by calculating the return of the whole structure.…”