Stochastic Learning in Kolkata Paise Restaurant Problem: Classical and Quantum Strategies

Abstract

We review the results for stochastic learning strategies, both classical (one-shot and iterative) and quantum (one-shot only), for optimizing the available many-choice resources among a large number of competing agents, developed over the last decade in the context of the Kolkata Paise Restaurant (KPR) Problem. Apart from few rigorous and approximate analytical results, both for classical and quantum strategies, most of the interesting results on the phase transition behavior (obtained so far for the classical model) uses classical Monte Carlo simulations. All these including the applications to computer science [job or resource allotments in Internet-of-Things (IoT)], transport engineering (online vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Traveling Salesman problem) will be discussed.

Quantum affective processes for multidimensional decision-making

“…Recently, quantum strategies have been proposed as a stochastic solution of a game that allows enhanced capabilities of judgment for better utility [45][46][47] . Modeling usually begins with a "bottom-up" formulation of unitary operations that abide by mathematical rules as the strategies of choice 48 . Given a set of preset payoffs for each state of choice and an initial state, the unitary operations are parametrized and optimized for a maximum expected payoff.…”

“…Given a set of preset payoffs for each state of choice and an initial state, the unitary operations are parametrized and optimized for a maximum expected payoff. Such methodology has been employed in classic games such as Prisoner's dilemma 45,49 , snowdrift 45 , stag-hunt 45,50 , and Kolkata Paise Restaurant [46][47][48]51 . To compare, the Coppélia system reveals complex affective and cognitive processes during decision-making.…”

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.…”

“…Learning in KPRP is considered in [12,18,29] with both classical and quantum learning considered in [12]. 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].…”