strictly dominated strategy

The dominated strategy produces the absolute worst result, regardless of the choices made by the other players. As a result, the Nash equilibrium found by eliminating weakly dominated strategies may not be the only Nash equilibrium. The process stops when no dominated strategy is found for any player. If Player 2 chooses U, then the final equilibrium is (N,U), This page was last edited on 1 March 2021, at 13:47. Strictly dominated strategies cannot be a part of … Because information sets represent points in a game where a player must make a decision, a player's strategy describes what that player will do at each information set. Procede with iterated elimination of strictly dominated strategies as usual, if possible. Therefore, Player 2 will never play strategy Z. Many simple games can be solved using dominance. Learn how and when to remove this template message, Jim Ratliff's Game Theory Course: Strategic Dominance, Creative Commons Attribution/Share-Alike License, https://en.wikipedia.org/w/index.php?title=Strategic_dominance&oldid=1009621008, Articles lacking in-text citations from January 2016, Wikipedia articles incorporating text from PlanetMath, Creative Commons Attribution-ShareAlike License, C is strictly dominated by A for Player 1. Strict DominanceDominant Strategy EquilibriumWeak DominanceIESDSCournot Duopoly Strictly Dominant Strategies In some games like prisoner’s dilemma, avoiding strictly dominated strategies leaves a unique strategy that is always best, regardless of what other players do. If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria. ��-��%Į�e2`+��.su�Ъp�-pZ��ЅNas9�pk�L�WZ� h��,\,%��_'J(0 ��r��R�}��l��0��1��~a.b��M�_��٭�oḒ�:�Sg�7��"�GB��5��!�A��п�~��Y�tؿ g��8s�8��[p�?��I㜩]ƾ)c�5Ib�.b$t�_c�a?`k��g#��p��-��o�5��g7uz��O�4�y�N��JϬʁ:o�Q�Y��|�Y�L��2��0^��虒�8��6u{ɞ�G�qT'�D�(��_(z��0ɘ !J�� QA�-��¥s�:��Y�D1ގ?�j��` ��G��E��`ӄ1^��VOC-�pb �(��#��`��M��J2�L�{:��f|�q�8W"C��r'�d(��ƽ��O�J�K�Υ| %.=�ƺT��\^1��Wװ�Q�z4��m$g�؋��ƷiKZ�r �G4��,�.p7�`� Ã?�g�-��k��\��_�!tkb�^KXmvߜH�A��$. In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. But action T is dominated by the mixed strategy (M,p;B,1 p), with 1 4 < p < 2 3. And rationality strictly… They would like to wait if the other one presses, they would prefer to, to press if the other one waits, so no domination here, but notice that the small pig always gets a higher payoff, four versus one, zero versus negative one, they would always prefer to wait. Player 2 knows this. The first step is repeated, creating a new even smaller game, and so on. This results in a new, smaller game. Well where does anyone have a strictly dominated strategy? And yes, strictly dominated strategies can (and should) be eliminated in the process of IEWDS. A strictly dominant strategy is always played in equilibrium, and thus strictly dominated strategies never are. We call this kind of rationality, strong-dominance rationality, and deﬁne it formally later. If a mixture of two strategies strictly dominates a third strategy, you may eliminate the third strategy. Formally: De nition A strategy s i 2S i isstrictly dominantfor i Recall from last time that a strategy is strictly dominated if another strategy exists that always pays strictly more regardless of what other players are doing. the big pig, the large pig doesn't have a strictly dominated strategy. Therefore, Player 1 will never play strategy C. Player 2 knows this. Compare this to D, where one gets 0 regardless. Player 2 L R Player 1 T 1, a 1, b M 4, c 0, d B 0, e 3, f • A strictly dominated action is not used in any mixed strategy Nash equilibrium.. . Therefore, Player 1 will never play B. However, several games cannot be solved using them. (Note that there are no other strictly dominated strategies in the game in the video.) [2], Rationality: The assumption that each player acts in a way that is designed to bring about what he or she most prefers given probabilities of various outcomes; von Neumann and Morgenstern showed that if these preferences satisfy certain conditions, this is mathematically equivalent to maximizing a payoff. Thus, any time a strategy is strictly dominant (or strictly dominated) it is also weakly dominant (or weakly dominated). Hence, a strategy is dominated if it is always better to play some other strategy, regardless of what opponents may do. For each player i, choose a subset Si of her set Ai of actions 3. Procede with iterated elimination of strictly dominated strategies as usual, if possible. The classic game used to illustrate this is the Prisoner's Dilemma. M. We now focus on iterated elimination of pure strategies that are strictly dominated by a mixed strategy. B is strictly dominated by A: choosing B always gives a worse outcome than choosing A, no matter what the other player(s) do. 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. An intransitive strategy is one that depends upon the strategies chosen by others. If, at the end of the process, there is a single strategy for each player, this strategy set is also a Nash equilibrium. The result of the comparison is one of: http://economicsdetective.com/Game theory is the study of human behaviour in strategic settings. Back to Game Theory 101 Show also that it cannot be played with positive probability in a mixed strategy Nash equilibrium. Only one rationalizable strategy is left {A,X} which results in a payoff of (10,4). However, unlike the first process, elimination of weakly dominated strategies may eliminate some Nash equilibria. 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 Also, strategy s i is strictly dominated by s i.