<> Basic Setup¶. More recent work has used stochastic games to model a wide range of topics in industrial organization, including advertising (Doraszelski, 2003) capacity accumulation (Besanko and x��Zێ���� o���x��_��+� Y��l?�fW�X��je��s���.�=����Y]�S���|ӉAv������ͣ�{u���^m�ld��+�W�gX�B�Dw�r�_�=�U���ή6�����w�*!� ����.�7���?ux��=Wb{������Hy�V��f��)�/�);���:��h����������[1��1����Ai�C�v�3�wQ���.����݉�E��۝��$��C�.����$@y����P��2N���N�ko�߯����N�8��ق��Xb�S(��Xi�Ķ7;��hq��t0� �N��LV���S����Z��d����n1�{~:��F�!� .�Bvg��W[5Xk����,�{��j�%�۪�h���߷;9X�7pOO����_�W1��W������_ֵ5�L��g^[È���BAy$����p��5������,��Tp�돞#������M�8��'���5�w��zJO �ڔ�;i5��AJLZ�� �`��AX V�?�흂RP*z'S�q��Tx6$�i����i�1Q!���� �}�Wޱ�L+��sE8�I 3Y�']�p ������*)#S�h���=�a�A�o�*���� ���yC�j�Y����zw����GP��1�.&g����Ey��U���rN�X���,ϲ�4s~bwh* ]�t��!����6�T�:�t��:d>����A�&�!��d��݋˜UQ��b�� ��r؏��l 5ip=i0FZ��H� i�Tq�2B�l-#-$1��˔o]m�"a�8�2M�I6���e4@��]Q/��-v��U�$�Lي��c��okf2ǰ0MfՕ9H� �u;����^�m�0�Ƞ{@�^�} ��Y�qo)�ڬ�_l�X+������h{��!�pE�Ց�o'�(L�ơ���Y�Y��$[584��#�fD���.�t~ �**ތ �"�Ë�Hybh��uMz��p���m�劏g��'���4f�٥&U�Qo�q���Nu`R�p4h�;�| 0��Y�v1�|[w��+�u�"_j�J�'0�$�Š애F!�t�fP�����9��3܍� �0x���Ե6k���(Iƒ"�/��v���*�;E�����(�hT�c_c�f YmW[k�~���>!�����SAC�e����Ǜ-�U(9��D���g�qO����y���O� 3T2����͍ZF w�Nqx��Z/'�)�RTbń% �7�p�ϖZṴ��l�`d\g�qJ�5��F��6�M�3Z1�b� | ̃"D��O$̾P20�`jԔkP>! 7For this set up, one can guess the unique subgame perfect Nash equilibrium strategies of the nite horizon model. D�hi-5���+��P� 4.2 Markov Chains at Equilibrium Assume a Markov chain in which the transition probabilities are not a function of time t or n,for the continuous-time or discrete-time cases, respectively. Every n-player, general-sum, discounted-reward stochastic game has a MPE The role of Markov-perfect equilibria is similar to role of subgame-perfect We define Markov strategy and Markov perfect equilibrium (MPE) for games with observable actions. ޮ)[y[��V�٦~�g�W7��~�t�)5:k��95l\��8�]�S�+�:8�{#�������tXC�$. Browse our catalogue of tasks and access state-of-the-art solutions. Competition between the two firms (i= 1,2) takes place in discrete time with an infinite horizon. We should also mention a very interesting papers byCurtat(1996),Cole and Kocherlakota(2001), Following convention in the literature, we maintain that players do not switch between equilibria within the process of a dynamic game. Markov perfect equilibrium is a key notion for analyzing economic problems involving dy-namic strategic interaction, and a cornerstone of applied game theory. Equilibrium Entry/Exit (Theorem 3): If p t = D t(Q) is nondecreasing in t, and q(p t=x) is strictly concave in x, then the equilibrium price sequence is constant p t= pfor each t, and entry and exit occurs in equilibrium at each t. Key elements of the proof: { x t = E(x t+1jI(t)) is a random-walk. VP�*y� Get the latest machine learning methods with code. stream Markov perfect equilibrium Eggertsson: Federal Reserve Bank of New York (e-mail: gauti.eggertsson@ny.frb.org). (PM1) and (PM2) provide algorithms to compute a Markov perfect equilibrium (MPE) of this stochastic game. Informally, a Markov strategy depends only on payoff-relevant past events. Keywords and Phrases: Oligopoly_Theory, Network_Externalities, Markov_Perfect-Equilibrium Markov perfect equilibrium is a refinement of the concept of Nash equilibrium. KEYWORDS: Markov perfect equilibrium, dynamic games, incomplete models, bounds estimation. • Linear Markov perfect equilibria 4 • Application 5 • Exercises 6 • Solutions 7 2 Overview This lecture describes the concept of Markov perfect equilibrium. a Markov perfect equilibrium of a dynamic stochastic game must satisfy the conditions for a Nash equilibrium of a certain reduced one-shot game. The MPE solutions determine, jointly, both the expected equilibrium value of coalitions and the Markov state transition probability that describes the path of coalition formation. 4. stream MPE equilibrium cannot be taken for granted. 5 0 obj 5A Markov Perfect Equilibrium is a profile of time-homogeneous pure strategies that map a player’s information in each single time period to a choice. �KX3���R^S�ҏ6������eG*z��Zh�4��Y�<20� $瀁E�eə��Ȇr r��������^X�:ɑ�a�����(m-� In this lecture, we teach Markov perfect equilibrium by example. QRE as a Structural Model for Estimation 141 Markov-perfect equilibrium where the equilibrium path market share difference is linear in the price differences between the firms in the preceding period. 25 0 obj Equilibrium exists and is unique (refer to the paper) The overwhelming focus in stochastic games is on Markov perfect equilibrium. Markov perfect equilibrium is a key notion for analyzing economic problems involving dy-namic strategic interaction, and a cornerstone of applied game theory. • a pair of equations that express linear decision rules for each agent as functions of that agent’s continuation value function as well as parameters of preferences and state tran-
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