sequential equilibrium example

Overview of Experience. COVID … A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson.A sequential equilibrium specifies not only a strategy for each of the players but also a belief for each of the players. C. Hurtado (UIUC - Economics) Game Theory 9 / 25. Please help to demonstrate the notability of the topic by citing, Relationship to other equilibrium refinements, Learn how and when to remove this template message, extensive-form trembling hand perfect equilibrium, https://en.wikipedia.org/w/index.php?title=Sequential_equilibrium&oldid=845686180, Articles with topics of unclear notability from June 2018, All articles with topics of unclear notability, Creative Commons Attribution-ShareAlike License, This page was last edited on 13 June 2018, at 13:11. 0000014444 00000 n 0000005242 00000 n Player 2 is able to observe the action taken by player 1, then respond accordingly. �>�풭-��Ӷ�.�c̻�D�5R��T[k��}�hwv�Y�'*��΋r�GF0X�LdKe"��-��uJ�b8W��ʛ]x8�qZ a��8;Z(O��>��z�Z?\��+��0j:ek�̂��yw�M��صԅ=�d)� C�,��eM�@��=j��x��:X+�ܵ��T�UnG�^��|��B�!�e�I�� 5�?Y��0ы�c;w�=�� EB$ endstream endobj 60 0 obj << /Type /Font /Subtype /Type0 /BaseFont /IHFJGE+Cmmi7 /Encoding /Identity-H /DescendantFonts [ 90 0 R ] /ToUnicode 65 0 R >> endobj 61 0 obj << /Filter /FlateDecode /Length 235 >> stream In Section 5 we present the consistency criterion that we subsequently use, and we motivate this criterion by a series of examples. This for example happens in Chess. 0000003432 00000 n The Leadership. R0L��=Q ��-�a&��ns��]9� �EQ��ݧ��4�x1:U��:�v�g��gi��)��{u#��:kiY^��.��oH� ��y��^�82H.��^��Q/ 0000054223 00000 n 0000002647 00000 n We conclude with some discussion in Section 5. 0000011038 00000 n Game Theory Game theory is a mathematical framework developed to address problems with conflicting or cooperating parties who are able to make rational decisions.The. Example 67 9.D.1 a This is a weak perfect Bayesian equilibrium. The information set where 2 moves might look like a subgame, but if you go back to the deﬁnition you will see that it isn’t. In fact, it is a sequential equilibrium. Sequential equilibrium outcomes: (L; l) and A Unique equilibrium leading to (L; l) Two families of equilibria with outcome A...2 must choose r with positive probability. We shall develop the notion of a sequential equilibrium, due to David Kreps and Robert Wilson. admissible. 1. We shall develop the notion of a sequential equilibrium, due to David Kreps and Robert Wilson. 0000037433 00000 n Sequential games are solved via backwardsinduction– starting at the end of the game and working backwards. Game theorists refer ... Sequential or Simultaneous. 124 5 Games with Sequential Actions: Reasoning and Computing with the Extensive Form good news: not only are we guaranteed to n d a subgame-perfect equilibrium (rather than possibly n ding a Nash equilibrium that involves non-c redible threats) but also this procedure is computationally simple. Mihai Manea (MIT) Equilibrium Reﬁnements. 7. 0000078450 00000 n Example 1. About Our Degree Programs. • Player 1’s strategy EJ is sequentially rational given player 2’s G. Player 2’s strategy G is also sequentially rational given her beliefs and player 2’s strategy EJ. 0000011582 00000 n 0000028588 00000 n Subgame Perfect Nash Equilibrium Lets consider the example of Predation with Niches: Firm E, (the Entrant) ﬁrst chooses to enter or not. 0000004288 00000 n 0000009523 00000 n Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs and its beliefs are confirmed on the outcome path given by its strategies. Well-known example of board games are Chess, Go, Nine Men's Morris, Checkers, Pachisi, Backgammon with a very long history, or the more recent games of Monopoly, Hex, Tic-tac-toe or others. Courtesy of The MIT Press. Updates. Conditions 2 and 3 of the Theorem above are fulfilled, but not condition 1. I A sequential equilibrium is a Nash equilibrium. 0000004068 00000 n 0000078655 00000 n Whereas Weak Sequential Equilibria (sometimes referred to as Weak Perfect Bayesian) also necessitates sequential rationality, but has a weaker consistency requirement,which is my main source of confusion. 0000008508 00000 n 0000007689 00000 n Consider a sequential game with two players called the entrant (or potential entrant) and the monopolist. For example, beliefs along the equilibrium path should be computed from the strategy via Bayes' rule. ing sequential equilibrium in the presence of imperfect recall (see, for example, [Piccione and Rubinstein, 1997]). 2 chooses r with probability in [2 = 5; 1]believes. Let™s show this with an example. H��T��0��+r�%bf�v숥'N�)�-7diPɖ4ڿg�i�]�ĥ�=��7��d�Z(3Ȫ� QVի��7�d��)�2'e�S�`�mwBW7�s�q��Pg�U�+�� 1�]W��%�r��2嘱��U�8��î�˂�$)-��mض�v��T)�#;RV��O��9��/K�C>ܵ�$�@��a��/�>��#o<3�Qa��H@k~)y�(dY�g#uM��gT+�A>�UGeJ7"�2��2A�\;�f�A;p��9gN��ḋQບ'Vh۷��#uj�s��O��Ͼ��,��Ɖ��mgoAi_��7��d1�n�9:��u��*�q}��-�ZO)9;I��L�y��]Ʀ��_wg��3�KE^��H�߼5��$ l��je��_�K��}�׈x;�K�$/'�NU��YvzL thatanequilibriumissequential.PBEisequivalenttosequential equilibrium in multistage games provided thateach playerhas onlytwo possible types;the conceptsdifferwhen the number oftypesper player is endstream endobj 48 0 obj << /Type /Font /Subtype /Type0 /BaseFont /IHFHOK+SymbolMT /Encoding /Identity-H /DescendantFonts [ 107 0 R ] /ToUnicode 47 0 R >> endobj 49 0 obj << /Type /Font /Subtype /Type0 /BaseFont /IHFJCD+Cmmi10 /Encoding /Identity-H /DescendantFonts [ 98 0 R ] /ToUnicode 46 0 R >> endobj 50 0 obj 569 endobj 51 0 obj << /Filter /FlateDecode /Length 50 0 R >> stream This means that players who move later in the game have additional information about the actions of other players or states of the world. You're signed out. 0000010155 00000 n 2 chooses r with probability 1 and believes (x) 2[0; 1 = 2] 2. 9 / 26 A sequential equilibrium is a sequentially rational assessment that meets ... For example, beliefs along the equilibrium path should be computed from the strategy via Bayes' rule. For example, suppose we had two players, and player 1 was able to choose their action before player 2 could choose theirs. 1.3 Reﬁnements of PBE While PBE is a bread and butter solution concept for dynamic games with incomplete information, there are many examples where PBE arguably al- lwos for equilibria that seem quite unreasonable. Keywords: Nash equilibrium, sequential game, non-determinism, partial order, constructive, proof assistant 1 Introduction Neumann and Morgenstern (1944) described the basis of modern game theory. �䑻 A sequential equilibrium specifies not only a strategy for each sequential rationality (as SPNE, but applied to contexts of incomplete information). 0000086372 00000 n 0000003204 00000 n 5.5 Sequential Games [5.2 Using Game Theory] [5.3 Classic Game Models] [5.4 Simultaneous Games] [5.6 Oligopoly] [5.7 Network Effects] What Are Sequential Games? Player 1’s strategy EJ is sequentially rational given player 2’s G. Player 2’s strategy G is also sequentially rational given his beliefs and player 1’s strategy EJ. �SC��gB��=O;x��i˩||�|�7��` �9 endstream endobj 58 0 obj 655 endobj 59 0 obj << /Filter /FlateDecode /Length 58 0 R >> stream 0000007840 00000 n A profile of strategies and beliefs is called an assessment for the game. Sequential rationality implies that pleray 2 must play B , so the unique PBE is ( R,B ) . Two approaches: Arrow-Debreu set-up and sequential markets. endstream endobj 62 0 obj << /Type /Font /Subtype /TrueType /FirstChar 40 /LastChar 61 /Widths [ 446 446 0 877 0 0 0 0 0 569 569 569 569 0 0 0 0 0 0 0 0 877 ] /Encoding /WinAnsiEncoding /BaseFont /IHFJHL+Cmr7 /FontDescriptor 63 0 R >> endobj 63 0 obj << /Type /FontDescriptor /Ascent 704 /CapHeight 0 /Descent -216 /Flags 32 /FontBBox [ -27 -250 1120 750 ] /FontName /IHFJHL+Cmr7 /ItalicAngle 0 /StemV 0 /FontFile2 95 0 R >> endobj 64 0 obj << /Type /Font /Subtype /Type0 /BaseFont /IHFJGP+Cmsy7 /Encoding /Identity-H /DescendantFonts [ 111 0 R ] /ToUnicode 61 0 R >> endobj 65 0 obj << /Filter /FlateDecode /Length 235 >> stream Sequential Equilibrium (S.E.) H�b```f`�he`g``�� Ȁ �@1v�Y[�004��@.hq�6� `��%vM��Zd��Ҟ^5�g��nO�|]8��R��]W��Ƭl�c��f>��M�v��F1 The common equilibrium type is subgame perfect equilibrium in pure strategies (SPEPS). 0000069023 00000 n E: entrant I: incumbent 24 Draw as normal form: E/I Fight Accomodate Out 0,2 0,2 In -3,-1 2,1 There are two Nash equilibria in this game. I Thm: Every nite extensive-form game with perfect recall has a sequential equilibrium. I ˙: perfect equilibrium of the extensive-form game)9(˙ m) m 0!˙ totally mixed strategies in the agent-normal form s.t. I A sequential equilibrium is a Nash equilibrium. 1. )\\�Nz�R��R ��ev�}j�M@ߢ�&�3g�D�p��:��@ۭ'�fs�� ,�)��N@_��hݘ�Z||f�[B�� ]R��U�5!��k@��ƨ܈�0�*Y��I��n��R��V��,H��zמ%ɝO�Y&��K�9��-d�g�7|(I�!? This for example happens in Chess. Sequential Equilibrium I An assessment (s; ) is asequential equilibriumof a nite extensive-form game with perfect recall if it issequentially rationalandconsistent. Copy link. )��et��ӕ��]\�%@ڄTCa�>v�m �I`Q>��1��$��!��z`H1�=��YA��aN�6V gN�M�, � �M, �f \58N;(`��P�p@Z�'A�Y 0000016359 00000 n To compute an optimal strategy in a perfect information game, an agent traverses the game tree and evaluates individual nodes. is a Perfect Bayesian Equilibrium (PBE) if: (1) sequential rationality—at each information set, each player’s strategy speciﬁes optimal actions, given her be-liefs and the strategies of the other players, and (2) consistent beliefs—given the strategy proﬁle, the be-liefs are consistent with Bayes’ rule whenever possible. The player with the white pieces start and the player with the black pieces has the next turn, and so on. H�TP�n� ��-sJ��nN�h. • But there is no weak sequential equilibrium in which the strategy proﬁle is (DJ,G). Problems ytpically arise Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. H�tT�N1}�W�Ѯ�}y% T�V�2o��0,:IZ��s�@��H_��s�v��,7��gF+m�Ư�l*G�tR�kǻ ;Y�#��H�}�e'+��lm 0000016146 00000 n 0000054748 00000 n A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. H�TP�N�0��AI+ƪ�N�p��=��%u"7��$Q{��ly�^;r�;{�c�ёe\��ᆓ#�j��Ľ+��:�L�~["��Fȏ4\"o�0Փz��є��+!��H�-X�A�8l�. 0000013690 00000 n guarantees admissibility is quasi-perfect equilibrium. Let™s show this with an example. We give a deﬁnition of sequential equilibrium in a companion paper [Halpern and Pass, 2011b] for standard games of imperfect recall that we extend here to take computation into account. 0000005438 00000 n It is far from straightforward to define what a sensible belief should be for those information sets that are reached with probability zero, given the strategies. equilibrium behavior has focused on the normal ‐ form ... • Example: Consider the following game, describing an industry with a single incumbent firm (a monopolist). Player … H�TP�n� ��-��K�¢�K�"�Nzk)��0��R ��fg�yn��@�ì[�0Xg.�4B��u��Q��D�7�Pׄ~��w]��U��+!��N�"0��^^�U-�?��4�F��1�d~�^:�ODQ��V�\�Bp!�!��$I�,~Ք/2�T,� 0000014925 00000 n We develop and advocate for this hindsight rationality framing of learning in general sequential decision-making settings. Example: Ultimatum game: In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. 0000070818 00000 n is a Perfect Bayesian Equilibrium (PBE) if: (1) sequential rationality—at each information set, each player’s strategy speciﬁes optimal actions, given her be-liefs and the strategies of the other players, and (2) consistent beliefs—given the strategy proﬁle, the … Weak sequential equilibrium: example • Does the game have a weak sequential equilibrium in which the strategy proﬁle is (EJ,G) and player 2 assigns probability 2 3 to history C and 1 3 to history D? Loosely, a sequential equilibrium is a Nash Equilibrium that Preliminary Concepts Sequential Equilibrium Signaling Game Application: The Spence Model Application: Cheap Talk Weak sequential equilibrium: example (cont.) Some Examples Example 1. Example 1, cont. }�k{�K�Yӄ�(Ua{$�~�n��,��R�H�;�y��2'��b$[p��Z�+� bk About Stanford GSB. The information set where 2 moves might look like a subgame, but if you go back to the deﬁnition you will see that it isn’t. In Section 5 we present the consistency criterion that we subsequently use, and we motivate this criterion by a series of examples. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. The equilibrium outcome derived through backwards induction is known as a subgameperfectequilibrium. b3�O;6++�ࠕ��dZe�=_e��;��J�XW� �)��Or��\X��Zo]E��{��M�b��o�'�= f�|n�dLv-�s I��x��.B�-#�Qj�%U�jqO�Y�e��?�J�Eږn��J*Մ�a�?�wR��!��Vxi7�F�C��c�*�7��Fr)#|wR��v?��Q�\ ��P�|�$v㸓֣ �Ö*m��]>��cC��\M��Z~��GnP��_��Ư�5��j��!O��/��7orQ>r�˃�H@pYE?K=��I��~�Y�T�9�,Tx61��T@jA'�g�$��e4�s�-�1��|B��ƕ�Ď��Co�yՁb��k=|�B�zd��ؗ@��X(G��-��[2��)*�k_��H��d�V%�{{@4��0�{dQ��,�*%'�}a�~��G!�%�*) g�X��H��VF7P�hs��Q�N�t��N�L�ƙ�5G�L,��T� �� We also discuss interim sequential equilibrium. endstream endobj 47 0 obj << /Filter /FlateDecode /Length 245 >> stream 0000092577 00000 n O�p��:K3s�M��4�h2��@��d+A��Y��A�U1��|C�uwsw��j�5ޱ2Z��Yc�ke@��I%1��4� +��,h�!8��ty�`��Ƴ��f(�'��=��l��,=�x�\)Ǉjr�x��A�>o�%="�ɇ�Q}n��L��v�F��>��j��s��@~iِ��©f9t��Ժ}d)$��ͷ�P�s��u��A��AW.�r��MWrԮ[6�L5��,�v�h�B��'D� ��׮ݏ�SN�B)J��'/x��[aɾ��]��ۍf?��,��6s4��1y�a ��Nf�o��ϧ�G� `�)� endstream endobj 52 0 obj << /Type /FontDescriptor /Ascent 706 /CapHeight 0 /Descent -217 /Flags 32 /FontBBox [ -40 -250 1008 750 ] /FontName /IHFJDJ+Cmr10 /ItalicAngle 0 /StemV 0 /FontFile2 99 0 R >> endobj 53 0 obj << /Type /Font /Subtype /TrueType /FirstChar 40 /LastChar 109 /Widths [ 389 389 0 778 0 0 0 0 500 500 500 500 500 0 0 0 0 0 278 278 0 778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 0 278 0 0 0 0 0 0 0 0 0 0 0 278 0 0 278 833 ] /Encoding /WinAnsiEncoding /BaseFont /IHFJDJ+Cmr10 /FontDescriptor 52 0 R >> endobj 54 0 obj << /Type /Font /Subtype /Type0 /BaseFont /IHFHEK+Dcr10 /Encoding /Identity-H /DescendantFonts [ 92 0 R ] /ToUnicode 55 0 R >> endobj 55 0 obj << /Filter /FlateDecode /Length 216 >> stream Belief system: $latex \mu: X - T \rightarrow [0,1]$ such that $latex \sum_{x\in h} \mu(x)=1$ for all information set h. Sometimes, we write it by $latex… H��Tˎ�0��+|��%�7P쩽��n�Իq�&�c�؟��$�GQlB�!�CIţ2M��+��jT�ų�t�e��B'y�Ǩ��_ The issue in both of the following examples is oﬀthe equilibrium path beliefs, namely I assigning positive probability to E playing a strictly dominated strategy oﬀthe equilibrium path. Another example Considerthegameinﬁgure 7. sequential rationality requires that at the last note in the upper branch player 1 goes down, and at the last node of the Then Nash (1950) intro-duced his key notion of non-cooperativeequilibrium. 0000009062 00000 n Example: In the simultaneous Battle of the Sexes with outside option, there are two subgame perfect equilibria: (N, B), B) and ((E, F), F). I ˙: perfect equilibrium of the extensive-form game)9(˙ m) m 0!˙ totally mixed strategies in … This example shows that the notions of perfect Bayesian equilibrium and sequential equilibrium are generically distinct, because $(E_{1},C_{2},R_{3})$ is a perfect Bayesian equilibrium but not a sequential equilibrium. 9 / 26. and (x=) 1 = 2. The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expected payoff in every information set. Example: (F,(B,F)) is (the only) subgame perfect equilibrium of the sequential Battle of the Sexes. Connection to Sequential Equilibrium. Example. 0000006452 00000 n follows. 0000015643 00000 n Whereas Weak Sequential Equilibria (sometimes referred to as Weak Perfect Bayesian) also necessitates sequential rationality, but has a weaker consistency … Sequential equilibrium outcomes: (L; l) and A Unique equilibrium leading to (L; l) Two families of equilibria with outcome A...2 must choose r with positive probability. 0000005672 00000 n formal models and analyses have been lacking. Every perfect equilibrium of a ﬁnite extensive-form game is a sequential equilibrium (for some appropriately chosen beliefs). sets ). David M. Kreps and Robert Wilson. The simplest example of such signaling games involves two players, who each take an action in sequence. Consider the following extensive game: 1 2 ab c L RRL 1 4 0 0 2 1 0 1 2 2 Notice that this game has no subgames. A sequential equilibrium is a sequentially rational assessment that meets certain further consistency criteria. 2 chooses r with probability in [2 = 5; 1]believes. “Alles” — 2014/5/8 — 11:36 — page ii — #2 c 2014by the Mathematical Associationof America,Inc. The first player is privately informed with some payoff-relevant information, which is unavailable to the second player. Asking for sequential rationality in sequential-move games with incomplete information." A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. , where k are the beliefs derived from ˙k using Bayes rule 0000018337 00000 n Y Z A 5,2 3,1 B 6,3 4,4 Sequential Equilibrium I An assessment (s; ) is asequential equilibriumof a nite extensive-form game with perfect recall if it issequentially rationalandconsistent. However an example shows that backward induction no longer implies Nash equilibrium (which does not mean that there is no Nash equilibrium). 0000078862 00000 n ... Nash equilibrium of the game; cf. Consider the following extensive game: 1 2 ab c L RRL 1 4 0 0 2 1 0 1 2 2 Notice that this game has no subgames. 0000018537 00000 n Mihai Manea (MIT) Equilibrium Reﬁnements. Selten [22, 23, 241. ��mO��o��ϣ�C~ xQ{Z Extensive Form Games with Imperfect Information. Consider the following extensive game: 1 2 ab c L RRL 1 4 0 0 2 1 0 1 2 2 Notice that this game has no subgames. Info. 0000003849 00000 n I Thm: Every nite extensive-form game with perfect recall has a sequential equilibrium. Sequential games entail strategic situations in which there is a strict order of play: players take turns in making there moves and they know what the other players have done. 0000002088 00000 n Connection to Sequential Equilibrium. Sequential auctions. Up Next. 0000011347 00000 n 0000009212 00000 n What is the other recipient of such a signal (the employer in the example above) to believe when she sees that signal? 0000011935 00000 n 0000012448 00000 n Sequential rationality implies that pleray 2 must play B , so the unique PBE is ( R,B ) . 0000072795 00000 n 0000094491 00000 n 0000010134 00000 n counter example to equilibrium existence. Typical behavioral strategies are represented in the ﬁgure; for instance εis the probability with which player 1 plays L, etc. Example: Sequential Battle of the Sexes First mover advantage Football Opera Football 5, 1 0, 0 Opera 0, 0 1, 5 b b b b b b b Mike Nancy Nancy F O F O F O 5 1 0 0 0 0 1 5 c b b b b b b b Nancy Mike Mike F O F O F O 5 1 0 0 0 0 1 5 c. Example: Stackelberg competition perfect Bayesian equilibrium. 0000010888 00000 n subgame constitute a Nash equilibrium when the subgame is considered as a game by itself. �T�G�&`Cߺ�1��س� Q1'U endstream endobj 44 0 obj << /Type /Font /Subtype /TrueType /FirstChar 222 /LastChar 222 /Widths [ 555 ] /Encoding /MacRomanEncoding /BaseFont /IHFIPK+Dcr10 /FontDescriptor 45 0 R >> endobj 45 0 obj << /Type /FontDescriptor /Ascent 706 /CapHeight 671 /Descent -217 /Flags 32 /FontBBox [ -40 -250 1008 896 ] /FontName /IHFIPK+Dcr10 /ItalicAngle 0 /StemV 90 /XHeight 437 /FontFile2 110 0 R >> endobj 46 0 obj << /Filter /FlateDecode /Length 286 >> stream If it enters, then the two ﬁrms simultaneously choose a niche of the market to compete in: a (A) or b (B). perfect Bayesian Nash equilibrium in which player 1 orders quiche independent of this type, and player 2 ﬁghts when he observes a beer. 0000088763 00000 n Sequential Equilibrium (S.E.) Deﬁnition A Nash equilibrium, σ∗, in the extensive form game, E, is a Subgame Perfect Nash Equilibrium (SPNE) if it induces a Nash equilibrium in every subgame of E. C. Hurtado (UIUC - … 0000002669 00000 n shall develop the notion of a sequential equilibrium, due to David Kreps and Robert Wilson. This cannot be a proper subgame either This cannot be a … Example. %PDF-1.3 %�� Indeed, this is the main conceptual contribution of Kreps and Wilson. 0000008711 00000 n Sequential Rationality, Backward Induction, and Subgame Perfection Example 42 Predation Game A component of the chain store paradox, which will be discussed later. 1. and (x=) 1 = 2. They are also very often sequential games, where the players take turns to move. Sequential games entail strategic situations in which there is a strict order of play: players take turns in making there moves and they know what the other players have done. About Us. Backward Induction and SP Beliefs and PBE Forward Induction Remarks: 1. 0000015664 00000 n 0000088520 00000 n �ĐR遐mY*�|*�e�h!��ږT�/��Dy��8Ζ.��G��%�$[@��' ~�� oV�� w>ޛ73)t�lW�r��B͗U�*�lѬWB��z�4��q��.�˸x#�I��U��iGv��D�n�f0�(�طҤ��_#%%0lDq��'�lx��q �E)o��R��v*%(']/��a��]��gb��S5��{��;�ViS�� 4|N_�j�#͈-eY��Tܥ��/sF /pN Sequential equilibrium is a further refinement of subgame perfect equilibrium and even Shopping. 0000002181 00000 n equilibrium exist in games of imperfect recall, under our de nitions. Example: In the simultaneous Battle of the Sexes with outside option, there are two subgame perfect equilibria: ((N, B), B) and ((E, F), F). When the buyers have full information (i.e., they know the sequence of auctions in advance), and a single item is sold in each round, a SPEPS always exists. Example of sequential equilibrium Consider the following game 1 2 3 a b 0,0,0 3,2,2 0,0,1 4,4,0 1,1,1 1−ε 1−η 1−δ ε η δ 1−δ δ Each player has two actions (left and right). 0000063718 00000 n 2 chooses r with probability 1 and believes (x) 2[0; 1 = 2] 2. 0000013861 00000 n Example: (F,(B,F)) is (the only) subgame perfect equilibrium of the sequential Battle of the Sexes. 0000012244 00000 n 0000011784 00000 n 0000012708 00000 n X�,3;,�4/�5�9�b��XM8��c��@6�o5Jh��+��{�螺�"u��#��6@B�ƞ�˫�orD��Pe\nӝ��K�$�PEy�. It is also straightforward to define what a sensible belief should be for those information sets that are reached with positive probability given the strategies; the beliefs should be the conditional probability distribution on the nodes of the information set, given that it is reached. 0000007216 00000 n An Example Consider a sequential equilibrium and a non-equilibrium announcement (such as a nonequi-librium choice of education in the Spence model). Sequential Equilibrium De–nition Strategies ˙and beliefs form a sequential equilibrium if 1 ˙is sequentially rational given 2 There is a sequence of completely mixed strategies ˙k!˙ such that the resulting beliefs k! 0000009502 00000 n Example 1. The Experience. Example 1, cont. Belief system: such that for all information set h. Sometimes, we write it by to emphasize it is a conditional probability. Theorem 4. • Sequential Equilibrium is our first attempt at doing this. concept that determines the optimal solution in a non-cooperative game in which each player lacks any incentive to change his/her initial strategy. Scherer [ 211, for example, points to the demonstration effect that sharp price cutting in one market can have on the ... Selten [24]. It is itself refined by extensive-form trembling hand perfect equilibrium and proper equilibrium. 8�{)��Y�Y��$:�"�� B��p�K�Ŋq 0000007861 00000 n Nash Equilibrium is a game theory. 0000007535 00000 n 0000013400 00000 n The player with the white pieces start and the player with the black pieces has the next turn, and so on. 0000076516 00000 n 0000076721 00000 n 0000012687 00000 n In a sequential auction, items are sold in consecutive auctions, one after the other. Niche b is the ”larger” niche. About Us ; The Leadership ; Updates ; COVID-19 Information In particular, it can be implemented as a Cancel. Yes. If playback doesn't begin shortly, try restarting your device. 0000004487 00000 n Yes. 0000004526 00000 n 0000076281 00000 n 0000018118 00000 n �z�y�ʮą�*�'i��e�,�� trailer << /Size 114 /Info 25 0 R /Root 28 0 R /Prev 121359 /ID[<34b545121a0d0c0c5a261478fd4f6ec8><6f86d978cb73b8caf849bfe5b17123b0>] >> startxref 0 %%EOF 28 0 obj << /Type /Catalog /Pages 24 0 R /Metadata 26 0 R /PageLabels 23 0 R >> endobj 112 0 obj << /S 256 /L 465 /Filter /FlateDecode /Length 113 0 R >> stream Under some technical conditions both approaches are equivalent. Macroeconomic Theory Dirk Krueger1 Department of Economics University of Pennsylvania January 26, 2012 1I am grateful to my teachers in Minnesota, V.V Chari, Timothy Kehoe and Ed- ward Prescott, my ex-colleagues at Stanford, Robert Hall, Beatrix Paal and Tom �ս�rN��M�s��}eS��w�S�'9\cz�u@�aW)K��>6�efsY��M�m8�t%�A��2��J=ws�'s�CZ��+�fbo� EF@ endstream endobj 113 0 obj 372 endobj 29 0 obj << /Type /Page /Parent 24 0 R /Resources 30 0 R /Contents [ 43 0 R 51 0 R 57 0 R 59 0 R 69 0 R 73 0 R 77 0 R 79 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 >> endobj 30 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT1 54 0 R /TT2 38 0 R /TT4 40 0 R /TT6 32 0 R /TT8 36 0 R /TT10 34 0 R /TT11 48 0 R /TT12 44 0 R /TT13 49 0 R /TT15 53 0 R /TT16 75 0 R /TT17 67 0 R /TT18 60 0 R /TT19 64 0 R /TT21 62 0 R /TT22 71 0 R >> /ExtGState << /GS1 91 0 R >> /ColorSpace << /Cs6 37 0 R >> >> endobj 31 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 98 /FontBBox [ -547 -307 1206 1032 ] /FontName /IHFHND+TimesNewRoman,BoldItalic /ItalicAngle -15 /StemV 133 /FontFile2 86 0 R >> endobj 32 0 obj << /Type /Font /Subtype /TrueType /FirstChar 97 /LastChar 97 /Widths [ 500 ] /Encoding /WinAnsiEncoding /BaseFont /IHFHKJ+TimesNewRoman,Italic /FontDescriptor 33 0 R >> endobj 33 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 98 /FontBBox [ -498 -307 1120 1023 ] /FontName /IHFHKJ+TimesNewRoman,Italic /ItalicAngle -15 /StemV 0 /FontFile2 88 0 R >> endobj 34 0 obj << /Type /Font /Subtype /TrueType /FirstChar 44 /LastChar 52 /Widths [ 250 0 0 0 500 500 500 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /IHFHNP+TimesNewRoman,Bold /FontDescriptor 35 0 R >> endobj 35 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 34 /FontBBox [ -558 -307 2034 1026 ] /FontName /IHFHNP+TimesNewRoman,Bold /ItalicAngle 0 /StemV 133 /FontFile2 84 0 R >> endobj 36 0 obj << /Type /Font /Subtype /TrueType /FirstChar 98 /LastChar 98 /Widths [ 500 ] /Encoding /WinAnsiEncoding /BaseFont /IHFHND+TimesNewRoman,BoldItalic /FontDescriptor 31 0 R >> endobj 37 0 obj [ /ICCBased 94 0 R ] endobj 38 0 obj << /Type /Font /Subtype /TrueType /FirstChar 40 /LastChar 146 /Widths [ 389 389 500 0 278 333 278 0 0 500 500 500 500 0 0 0 0 0 278 278 0 0 0 0 0 0 708 722 0 680 653 785 0 361 0 0 625 0 750 0 680 0 736 555 722 0 0 1028 0 0 0 0 0 0 0 0 0 500 555 444 555 444 305 500 555 278 0 528 278 833 555 500 555 528 392 394 389 555 528 722 528 528 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 ] /Encoding /WinAnsiEncoding /BaseFont /IHFHGJ+Dcr10 /FontDescriptor 39 0 R >> endobj 39 0 obj << /Type /FontDescriptor /Ascent 706 /CapHeight 671 /Descent -217 /Flags 32 /FontBBox [ -40 -250 1008 896 ] /FontName /IHFHGJ+Dcr10 /ItalicAngle 0 /StemV 90 /XHeight 437 /FontFile2 89 0 R >> endobj 40 0 obj << /Type /Font /Subtype /TrueType /FirstChar 49 /LastChar 51 /Widths [ 500 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /IHFHIJ+TimesNewRoman /FontDescriptor 41 0 R >> endobj 41 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2028 1007 ] /FontName /IHFHIJ+TimesNewRoman /ItalicAngle 0 /StemV 0 /FontFile2 93 0 R >> endobj 42 0 obj 702 endobj 43 0 obj << /Filter /FlateDecode /Length 42 0 R >> stream

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