Evolution of iterated Hawk-Dove games with quitting : adaptive dynamics approach with population embedding

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Title: Evolution of iterated Hawk-Dove games with quitting : adaptive dynamics approach with population embedding
Author: Laurén, Toni
Other contributor: Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta
University of Helsinki, Faculty of Science
Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten
Publisher: Helsingin yliopisto
Date: 2020
Language: eng
URI: http://urn.fi/URN:NBN:fi:hulib-202011254596
Thesis level: master's thesis
Discipline: Soveltava matematiikka
Abstract: The Hawk-Dove game has been used as a model of situations of conflict in diverse fields as sociology, politics, economics as well as animal behavior. The iterated Hawk-Dove game has several rounds with payoff in each round. The thesis is about a version of the iterated Hawk-Dove game with the additional new feature that each player can unilaterally decide when to quit playing. After quitting, both players return to the pool of temporally inactive players. New games can be initiated by random pairing of individuals from within the pool. The decision of quitting is based on a rule that takes into account the actions of oneself or one's opponent, or on the payoffs received during the last or previous rounds of the present game. In this thesis, the quitting rule is that a player quits if its opponent acts as a Hawk. The additional feature of quitting dramatically changes the game dynamics of the traditional iterated Hawk-Dove game. The aim of the thesis is to study these changes. To that end we use elements of dynamical systems theory as well as game theory and adaptive dynamics. Game theory and adaptive dynamics are briefly introduced as background information for the model I present, providing all the essential tools to analyze it. Game theory provides an understanding of the role of payoffs and the notion of the evolutionarily stable strategies, as well as the mechanics of iterated games. Adaptive dynamics provides the tools to analyze the behavior of the mutant strategy, and under what conditions it can invade the resident population. It focuses on the evolutionary success of the mutant in the environment set by the current resident. In the standard iterated Hawk-Dove game, always play Dove (all-Dove) is a losing strategy. The main result of my model is that strategies such as all-Dove and mixed strategy profiles that are also not considered as worthwhile strategies in the standard iterated Hawk-Dove game can be worthwhile when quitting and the pool are part of the dynamics. Depending on the relations between the payoffs, these strategies can be victorious.
Subject: Game theory
adaptive dynamics
invasion fitness
mixed strategy
iterated games
singular strategy

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