strictly dominant strategy example

March 9, 2021

0000009889 00000 n -l��R w�#!��)j4��,0 A strategy is weakly dominant if, regardless of what any other players do, the strategy earns a player a payoff at least as high as any other strategy, and, the strategy earns a strictly higher payoff for some profile of other players' strategies. One method is called Nash Equilibrium.What (if any) are the equilibrium for Battle of the Sexes? %PDF-1.3 %�� 0000007790 00000 n }�&~��Y�wy�(T'�JP��^7lx��\�.�5dE��g��`�M��o=^ �^� endstream endobj 453 0 obj 740 endobj 454 0 obj << /Filter /FlateDecode /Length 453 0 R >> stream 0000006104 00000 n Hence, a strategy is strictly dominant if it is always strictly better than any other strategy, for any profile of other players' actions. 0000001750 00000 n For example: How to map your drive in the morning (or equivalently how to route your network traﬃc). The following game doesn't have payoffs defined:In order for (T,L) to be an equilibrium in dominant strategies (which is also a Nash Equilibrium), the following must be true: 1. a > e 2. c > g 3. b > d 4. f > h 1. a > or = e 2. b > or = d To determine if there is a dominant strategy for Motorola, we first start by comparing the possible outcomes for Motorola if they decide to put user needs first versus the possible outcomes if they decide to put carrier needs first. 0000003691 00000 n A strategy is weakly dominant if, regardless of what any other players do, the strategy earns a player a payoff at least as high as any other strategy, and, the strategy earns a strictly higher payoff for some profile of other players' strategies. Corollary 7 There can only be at most one IESDS solution. 0000006126 00000 n H��U�N�@}�W�c+��x �J�J��dC܆�ځ4�Y'kwM��3g��~YG�s��Y�!ξHwKخ[� �.��濲c&s�PK�0��۲�@��/~��F��9"�L$"O� |O�o`�7��q��{��P��$� J��eYV5�b��u��Y+��z[n��/u�,ר��f��k�.��u$G��GD�U;��kh��#� ~|��w��ۣx;!�i"��=,�f^��v�RwŞ@�g��\^^��n �uuu}3ˮ��"�q��/3*�ܔe��*�Q� ��&��(u��t��Ѵo��Aw�Wo{��3-��.Ή�zS%��YɃ�m��v��y�tԄ�vE$�ň 2�F+f�q܉Ə�2�EELT�n�m�1\��lV�0�14KAG�C&Bz-�슺Op�8��j6ZGBƙ��8A��Y\��!��x�Q��@3�dx�8"ZApQ0��d"��C��.�$%��AF��h4�Tڡ�T0�|�+m��ߔ�5e��qCh�G�X��OS3T'��!�g ��>a��Ai1U&�n� ��ƍP�ő97DպE�cci�2��#�D� �d.�%:�@ąs��ӈɃ��&B�&KG{��q?�4C��)n��nΦf�\�)�h��6��:l� �4" endstream endobj 455 0 obj 668 endobj 456 0 obj << /Filter /FlateDecode /Length 455 0 R >> stream Dominant strategies are considered as better than other strategies, no matter what other players might do. BG introduces incomplete information into games in a very exible way. This lecture shows how to handle such a situation. For example, (hire, shirk) is a dominant strategy equilibrium in game (4.2). Then it is a Nash equilibrium of G. Moreover, if G is ﬁnite, then it is a unique Nash equilibrium. . In game theory, a dominant strategy is the course of action that results in the highest payoff for a player regardless of what the other player does. We say s’i is strictly dominated by si if, for every choice of strategies of the other players, i’s payoff from choosing si is strictly greater than i’s payoff from choosing s’i. The result of the comparison is one of: Requirement for strictly dominant strategies is quite stringent Therefore other, Requirement for strictly dominant strategies is quite stringent. *-��N��-�r��>j�͢�D�>��` �N� endstream endobj 447 0 obj 646 endobj 448 0 obj << /Filter /FlateDecode /Length 447 0 R >> stream . There may be situations where it is not a priori clear which strategy the other player will choose. Game theory is the science of strategic decision making in situations that involve more than one actor. A player™s strategy is (strictly) dominant if, for any combination of actions by other players, it gives that player a strictly higher payo⁄ than all her other strategies. On the Agenda 1 The Extensive Form Representation of a Game 2 Strategies and the Normal Form Representation of a Game 3 Randomized Choices 4 Exercises 5 Formalizing the Game 6 Dominant and Dominated Strategies 7 Iterated Delation of Strictly Dominated Strategies 8 Iterated Delation of Dominated Strategies 9 Exercises C. Hurtado (UIUC - Economics) Game Theory Dominant Strategy Equilibria A strategy is strictly (resp., weakly, very weakly) dominant for an agent if it strictly (weakly, very weakly) dominates any other strategy for that agent A strategy profile (s 1, . When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. Iterated Deletion of Dominated Actions Iterated Deletion of Strictly Dominated Actions Remark. Imagine a scenario where you are given two choices: You can get $10 now. 0000008560 00000 n EC202, University of Warwick, Term 2 13 of 34 . Requirement for strictly dominant strategies is quite stringent. In the above cases, the. Game Theory: Lecture 2 Introduction Motivation In many social and engineered systems, agents make a variety of choices. Hence, we can conclude that not hiring a lawyer is the dominated strategy for both firms. Therefore solution (Opera, Bullfight), In the above examples, it was clear that given the strategy of Player 1, you could infer the strategy of, Player 2 and vice versa. 20. The dominant strategy is not always apparent, though, and often depends on the sum of everyone else's choices and consequences. Too complicated to go over here, but is the equilibrium stable? in which the strictly dominant strategies are followed. H�b```f``�� 6P��Ù`�$#�b�LW�5x,�`a``K�20�=``� �� },�7%�2X3��V ��Tĸ��1V �gb? Dominated strategies and iterative elimination of strictly dominated strategies Nash Equilibrium Examples Reading: Fudenberg and Tirole, Chapter 1. ***, I enjoy going to parties at my Indian friends’ houses. H��V�n�@��+xl��^r�@�C�P�zNm%u�؅��ߗ+Y�VYٲ���W��`�T��KnL��: lV��Z}��#�翫�yu�p[;��8��> ��ܰZ�g%H��*Dd��с%T. This is because it is optimal for a player to choose the Nash equilibrium strategy. - We know, firm 2 has a dominant strategy( low price) - Firm A does not a dominant strategy. Proof. If both A and B have strictly dominant strategies, there exists a unique Nash equilibrium in which each plays their strictly dominant strategy. H��UMo�@��W̱��awv�^KQ!9��R-�ҋ6��lԊ�1�cwc RX`v��͛7��W��_^��KM��@BVF��~�M1�?0R`�_YG_~~��D�)$��0�`l��2 � � �C�d1NB,�/~t��-��ާ��6��Ӥ�9�j>=�˞`j��$F�H��:�:��B�~y�㜑1�:-Q�cm=�v�y�؉ crﷻ��V{��j�_��M��8�q��}H�p֞�.B�7c�_;��$(Ұ}��(��E��ٲ�f�%0��ۢ*��n�_��|_4�CؠFSqj0=�5�U��ɻ�P?A��.K(�z�s�s��K]Mu[mw &)1%��e��t��AG��3]�Ibt^ƄOҢ�#ؾ��ɡK �b`�� , s n) in which every s i is dominant for agent i (strictly, weakly, or very weakly) is a Nash equilibrium 0000009968 00000 n Example 8 A nice example of a game that is solved by IESDS is the loca-tion game. Q: How do you interpret the Opera-Bullfight game? Example 10 Let us return to the beauty contest game introduced in Ex-ample 2 of Chapter 1. Using the example of Rock-Paper-Scissors, if a person’s probability of employing each pure strategy is equal, then the probability distribution of the strategy set would be 1/3 for each option, or approximately 33%. When it exists, the dominant strategy equilibrium has an obvious attraction. Example of a dominant strategy. uc��S��Si ��ʢ��K4��Q��|ݏ��!��i�Ŀ:A��;y��%�zyƝ��N�Z5�q3BM��0 �� endstream endobj 449 0 obj 701 endobj 450 0 obj << /Filter /FlateDecode /Length 449 0 R >> stream i is a strictly dominant strategy. - Firm A can either earn 20 or loose 100 by low prices. Therefore other solution methods can be used. However, this game has two other Nash equilibria, (T,R) and (B,L). If a mixture of two strategies strictly dominates a third strategy, you may eliminate the third strategy. "�1��Ái�qMd:��v;�M>��͡O��>1`/%��v�)qTK)�O'N�9�؁76��a�e�W��I�D��5��[/2��־쪝��H�3��̳�c쎉� Battle of the Sexes FemalePlayer Male Player Strategy Opera Bullfight Opera (1,2) (0,0) Bullfight (0,0) (2,1) Likewise, with multi-dimensional values, BIC mechanisms may result in higher revenues than can be attained by any DIC mechanism. It is possible that an action is not strictly dominated by any pure strategy, but strictly dominated by a mixed strategy. 0000004553 00000 n 0000005301 00000 n Furthermore, the timing of the decisions are important. Iterated Dominance and Nash Equilibrium In the previous chapter we examined simultaneous move games in which each player had a dominant strategy; the Prisoner’s Dilemma game was one example. P��~�ݫ�{(��&P2l�69�S�1��n�˛�|�,��lƥ��N\d�Kʫة׌F^��{. A strategy is strictly dominant if, regardless of what any other players do, the strategy earns a player a strictly higher payoff than any other. 0000002156 00000 n 0000001772 00000 n Use Nash Equilibrium solution concept to illustrate that neither player has incentive to deviate. It’s not so. This was great when I was a kid. Assume that Firm A and Firm B are firms who must decide about … Obara (UCLA) Bayesian Nash Equilibrium February 1, 2012 4 / 28. _��Pw� � �)� endstream endobj 467 0 obj 140 endobj 438 0 obj << /Type /Page /Parent 434 0 R /Resources << /ColorSpace << /CS2 443 0 R /CS3 444 0 R >> /ExtGState << /GS2 461 0 R /GS3 462 0 R >> /Font << /TT2 440 0 R /TT3 442 0 R >> /ProcSet [ /PDF /Text ] >> /Contents [ 446 0 R 448 0 R 450 0 R 452 0 R 454 0 R 456 0 R 458 0 R 460 0 R ] /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 /StructParents 0 >> endobj 439 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 98 /FontBBox [ -498 -307 1120 1023 ] /FontName /EAHDFL+TimesNewRoman,Italic /ItalicAngle -15 /StemV 0 /FontFile2 464 0 R >> endobj 440 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 146 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 250 333 250 0 500 500 500 500 500 500 500 500 500 500 278 0 0 0 0 0 0 722 667 667 722 611 556 722 722 333 389 0 611 0 722 0 0 0 667 556 611 0 0 944 0 0 0 0 0 0 0 0 0 444 500 444 500 444 333 500 500 278 0 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 ] /Encoding /WinAnsiEncoding /BaseFont /EAHDBD+TimesNewRoman /FontDescriptor 441 0 R >> endobj 441 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2028 1007 ] /FontName /EAHDBD+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 463 0 R >> endobj 442 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 146 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 0 0 250 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 500 444 500 444 278 500 500 278 0 444 278 722 500 500 0 500 389 389 278 500 0 667 0 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 ] /Encoding /WinAnsiEncoding /BaseFont /EAHDFL+TimesNewRoman,Italic /FontDescriptor 439 0 R >> endobj 443 0 obj [ /ICCBased 465 0 R ] endobj 444 0 obj /DeviceGray endobj 445 0 obj 760 endobj 446 0 obj << /Filter /FlateDecode /Length 445 0 R >> stream

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strictly dominant strategy example

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