Karpowicz, Anna and Szajowski, Krzysztof (2010): Anglers’ Fishing Problem. Published in: Annals of the International Society of Dynamic Games , Vol. 12, No. Advances in Dynamic Games (August 2012): pp. 327349.

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Abstract
The model considered here will be formulated in relation to the “fishing problem,” even if other applications of it are much more obvious. The angler goes fishing, using various techniques, and has at most two fishing rods. He buys a fishing pass for a fixed time. The fish are caught using different methods according to renewal processes. The fish’s value and the interarrival times are given by the sequences of independent, identically distributed random variables with known distribution functions. This forms the marked renewal–reward process. The angler’s measure of satisfaction is given by the difference between the utility function, depending on the value of the fish caught, and the cost function connected with the time of fishing. In this way, the angler’s relative opinion about the methods of fishing is modeled. The angler’s aim is to derive as much satisfaction as possible, and additionally he must leave the lake by a fixed time. Therefore, his goal is to find two optimal stopping times to maximize his satisfaction. At the first moment, he changes his technique, e.g., by discarding one rod and using the other one exclusively. Next, he decides when he should end his outing. These stopping times must be shorter than the fixed time of fishing. Dynamic programming methods are used to find these two optimal stopping times and to specify the expected satisfaction of the angler at these times.
Item Type:  MPRA Paper 

Original Title:  Anglers’ Fishing Problem 
Language:  English 
Keywords:  Stopping time Optimal stopping Dynamic programming SemiMarkov process Marked renewal process Renewal–reward process Infinitesimal generator Fishing problem Bilateral approach Stopping game 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games 
Item ID:  41800 
Depositing User:  Krzysztof Szajowski 
Date Deposited:  08. Oct 2012 13:28 
Last Modified:  20. Feb 2013 08:12 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/41800 