Population dynamical embedding of iterated games of different lengths

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http://urn.fi/URN:NBN:fi-fe201804208633
Title: Population dynamical embedding of iterated games of different lengths
Author: Ollikainen, Jyri
Contributor: University of Helsinki, Faculty of Science, Department of Mathematics and Statistics
Publisher: Helsingin yliopisto
Date: 2018
Language: eng
URI: http://urn.fi/URN:NBN:fi-fe201804208633
http://hdl.handle.net/10138/273576
Thesis level: master's thesis
Discipline: Applied Mathematics
Soveltava matematiikka
Tillämpad matematik
Abstract: Topic: - This thesis addresses the problem of comparing payoffs from iterated games of varying lengths in a meaningful way. Shorter games can be played more often than longer games in same amount of time. Direct comparison of payoffs per game therefore leads to systematic error for the shorter games. On the other hand if it is difficult to find a playing partner, shorter games have extra disadvantage and per game payoff calculation is more accurate. This thesis calculates payoffs as time averages instead of per game averages taking into account rate of finding a new playing partner. - Games can be of different lengths because of random termination of the game or by a strategic choice of the player. Latter case is known as quitting strategy, which is given in the form of a quitting rule as a part of a players strategy, e.g. ""quit after two subsequent rounds with low payoff"". Quitting can prevent further losses in a single iterated game, but becomes more effective when a player can start a new game with another opponent after quitting in a game. Opponents are randomly chosen from a pool of potential players and after the termination of a game they are returned to the pool to be paired off randomly again. This is called ""pooling"". The strategies utilized by the players in the pool change over time as strategies with longer games become more rare in the pool. - Quitting traditionally has not been considered a strategic choice. Method: This thesis constructs a model for iterated games with quitting and pooling. Then it is explored further with an example of iterated Hawk-Dove-Bully-Retaliator (HDBR) game. Results: - Strategies that tend to lead to long games become less frequent in the pool than strategies with shorter games. - Greedy strategies, when pooled with quitting strategies, will eventually spend most of their time playing against each other or in the pool. This reduces their payoffs to the point that they are no longer competitive compared to more altruistic strategies. - High termination rate increases the relevance of the first few rounds. This causes more greedy strategies to benefit from high termination rate when more naive or altruistic strategies cannot play in beneficial games for long.


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