Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

Asienkiewicz, Hubert; Balbus, Łukasz

doi:10.1007/s11750-019-00516-2

Cited by 6 publications

(10 citation statements)

References 26 publications

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“…In such a game, and for any given set of strategies, one for each player, the state for which the players obtain the highest possible utility (i.e. minimum possible travel time) is called the Nash equilibrium [23]. The Wardrop equilibrium qualifies further in that the high possible utility must have been achieved through distribution of traffic [24].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Analysing Road Traffic Situation in Lilongwe: An Agent Based Modelling (ABM) Approach

Sibale

Munthali

2021

Adv. J. Grad. Res.

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A 15, 451 km road network forms the main mode of transport for Malawi with 26 % paved. With increasing number of vehicles and elongated travel times during rush hour the study analysed the traffic situation on the M1 road between Mchinji and Area 18 roundabouts in Lilongwe City using an agent-based model (ABM). The methodology used game theory’s traffic grip model to analyse traffic flow by controlling traffic variables such as lights, speed limits and the number of vehicles. Each intersection was treated as non-cooperative game where each agent tried to minimize its queue resulting into Q−Nash’s equilibrium as the solution. The ABM tested the empirical relationships of traffic flow parameters in terms of density, ﬂow, acceleration, deceleration, speed, time lost in traffic congestion and fuel consumption. The model was calibrated using traffic data collected through observing 1,312 vehicles sampled against 24,977. The observation results from the road junctions reveal that on average, a vehicle takes 20 mins 18 seconds, 37 minutes 6 seconds, 44 minutes 21 seconds and 58 minutes 53 seconds to exit Chitukuko, Bwandilo, Chilambula roads and Area 18 roundabout respectively upon entering the M1 at Mchinji roundabout. This data was then used to calibrate the business-as-usual model for the peak hour scenario for the road junctions. The model results show that a selected vehicle entering Chitukuko junction travels at an average speed of 22.60 km/hr, until it exits that junction. On average the selected motorists spend 2.52 l/km with a traffic density of 72 v/km. If dualized average speeds improved to 41.54 km/hr while the traffic density declined to 54.42 v/km, saving motorists MK 3,921,624.00 annually. The predictive model of the dual carriage informed that by 2021, commuters will spend MK 5,187,168 on fuel more than single-lane business as usual scenario of 2019.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Analysing Road Traffic Situation in Lilongwe: An Agent Based Modelling (ABM) Approach

Sibale

Munthali

2021

Adv. J. Grad. Res.

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“…The condition that the players have the same preferences makes a game symmetric. For the results on a stationary Nash equilibrium existence in the symmetric setup of resource extraction games the reader is referred to [6][7][8][9][10]. Studies [11,12] tackled the problem in the non-symmetric case while assuming that the preferences of the players are bounded.…”

Section: Introductionmentioning

confidence: 99%

On a special case of non-symmetric resource extraction games with unbounded payoffs

Sylenko

2022

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The game of resource extraction/capital accumulation is a stochastic infinite-horizon game, which models a joint utilization of a productive asset over time. The paper complements the available results on pure Markov perfect equilibrium existence in the non-symmetric game setting with an arbitrary number of agents. Moreover, we allow that the players have unbounded utilities and relax the assumption that the stochastic kernels of the transition probability must depend only on the amount of resource before consumption. This class of the game has not been examined beforehand. However, we could prove the Markov perfect equilibrium existence only in the specific case of interest. Namely, when the players have constant relative risk aversion (CRRA) power utilities and the transition law follows a geometric random walk in relation to the joint investment. The setup with the chosen characteristics is motivated by economic considerations, which makes it relevant to a certain range of real-word problems.

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“…Rubinstein [3] investigated that bounded rational participants continuously modified their cognition in repeated games in which compared current strategies with previous ones to make optimal strategy choices. Asienkiewicz and Balbus [4] presented the existence analysis of NE for random games under certain conditions. Watkins [5,6] first proposed the Q-learning method, and proved the convergence of Q-learning.…”

Section: Introductionmentioning

confidence: 99%

The Value Function with Regret Minimization Algorithm for Solving the Nash Equilibrium of Multi-Agent Stochastic Game

Liu¹,

Jia²

2021

IJCIS

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In this paper, we study the value function with regret minimization algorithm for solving the Nash equilibrium of multi-agent stochastic game (MASG). To begin with, the idea of regret minimization is introduced to the value function, and the value function with regret minimization algorithm is designed. Furthermore, we analyze the effect of discount factor to the expected payoff. Finally, the single-agent stochastic game and spatial prisoner's dilemma (SDP) are investigated in order to support the theoretical results. The simulation results show that when the temptation parameter is small, the cooperation strategy is dominant; when the temptation parameter is large, the defection strategy is dominant. Therefore, we improve the level of cooperation between agents by setting appropriate temptation parameters.

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Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

Cited by 6 publications

References 26 publications

Analysing Road Traffic Situation in Lilongwe: An Agent Based Modelling (ABM) Approach

Analysing Road Traffic Situation in Lilongwe: An Agent Based Modelling (ABM) Approach

On a special case of non-symmetric resource extraction games with unbounded payoffs

The Value Function with Regret Minimization Algorithm for Solving the Nash Equilibrium of Multi-Agent Stochastic Game

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