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We would like to show you a description here but the site won’t allow us. As an added bonus, they could use the model to incentivise/encourage the self-interested players to take actions, while trying to avoid a “tragedy of the commons” situation. The type space is merely a representation of the inﬁnite posterior belief hierarchies; Is there a meaningful prior stage? For example, internationally agreed upon taxe/fines could force removing or preventing the growth of space debris to become a highly prioritized task for certain countries/organizations. The word 'space' is used here as a metaphor and must not be taken too literally! We don’t think about this topic very often, but it is a fact: many of our modern day technologies such as GPS devices, smartphones, and television, all depend primarily on satellites that are revolving around the earth, floating in outer space. One organisation attempting to remove debris would benefit everyone operating in space. "Game theory is a complex subject dealing with independent agents, choice, probability, and forecasting. 6�ߢ�Z,aR�,��{j{+Ү���Wv:.fY�'��Pn>��aщk�h�Ph������:[�ái��ɾ���Y�|�6��/�[- �b����-- (�) �TNA@�s��8*���\�E6OͣB��|FD�@�f�1�Smv^}�Ò$����7aI��91~��H��@��9'�0^����Y��eV�L&�qz���q ����LDDѲ�wMea��%͊���{����a/���^�dѰ���6!��%�:��T�V�8K�^���1����~�r(��*ݛ:]4Z�^���y0ce��Ć�����A�T��McdWJ���4ݙ(|��܃r 5ԹEI �k/�&G�g��^-]f�TV�� ��d���Ps�L]^�c�xc5�YXG83���������:�,o��r�8 The Normal Form Representation Basic Notation n: number of players. For example, internationally agreed upon taxe/fines could force removing or preventing the growth of space debris to become a highly prioritized task for certain countries/organizations. %ȫ҄@l�s�e�V+_�~:Ҵ�|���y�F�:1q!$m�5#��*״���N,Ɇd�%��� �������z��晛����y2���I�&�{ Theory Wear. �J�֦�b�ti�Ggz-"�aj�2�"l+�e�XI��c���e��A/V��5�&�й" �Q Strategy space $${\displaystyle \Sigma \ =\prod _{i\in \mathrm {N} }\Sigma \ ^{i}}$$, where Player i's strategy space $${\displaystyle \Sigma \ ^{i}}$$ is the space of all possible ways in which player i can play the game. Game Theory: Lecture 6 Continuous Games Proof Since S is a compact metric space, the utility functions ui are uniformly continuous, i.e., for all α > 0, there exists some > 0 such that ui (s) − ui (t) ≤ α for all d(s, t) ≤ . Imagine the damage that would occur from one piece of debris that small. Military defense systems rely on satellites to provide them with accurate geo-location data; satellites help climatologists and meteorologists create accurate weather forecasts and climate change models for the news. ���� �Z�t���_�U��)����-��b����M�?Up�{����Z����c�����RUy�;l���Y������F��[�����1��x�j�&�ح����u �\��.o+�� ���%�D>-� 廯͊�m"�)�i�(�u�Z�� Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. Space debris poses a significant collision risk for an operational spacecraft, especially in low-Earth orbit (LEO). It is used to identify the most-effective strategies possible in contests The section that describes Tulys’ solution reminded me the most of what we learned in class, that strategic situations can often times be represented as a game featuring several players that each have a choice of several actions, and each player chooses which action to take based on their own preferences and the strategies of the opposing players. ��w20S��L����{Q��0�h)��ˢ���1�Q!���K�빴�tJ��J/���T���n p����,0�]��kњ��0븎���K� �����6�nV8n����#$Sʛɘ����_̅�0#���Pκ����"��$5ڥ�ajju�H��1G̨�#�,9�&cE��Y�A�.Y����k��Z�)]�l�)��|˂Ԕ5���i�uJ�I�����s��ܦY�w9�������)��3aR�Ƚ�M�k��e����1��ΑG �iX�c�)�]�������cw�/�'!�R���-�{d@�?�|��Ņ�s8!��P(�S9�.e�����������s�Ѭ2aR���&LM���Y!��?B��g��y�2ܹ�8�Z��U�WO�J��Ȇ1 Extensive Games Subgame Perfect Equilibrium Backward Induction Illustrations Extensions and Controversies Concepts • Some concepts: The empty history (∅): the start of the game A terminal history: a sequence of actions that speciﬁes what may happen in the game from the start of the game to an Game theoretic analysis of the space debris removal dilemma. si: a (pure) strategy of player i. 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