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PDF How to Solve Strategic Games? - tayfunsonmez.net However, neither of these methods is guaranteed to return a tractably small set of expected outcomes. << /S /GoTo /D (Outline0.1) >> Some authors allow for elimination of strategies dominated by a mixed strategy in this way. If Player 2 chooses U, then the final equilibrium is (N,U). Equilibria of a game obtained by eliminating a -dominated strategy are guaranteed to be approximate equilibria of the original game, with degree of approximation bounded by the dominanceparameter,. uX + uZ uX A dominated strategy in game theory occurs when one player has a more dominant strategy over another player. Why do men's bikes have high bars where you can hit your testicles while women's bikes have the bar much lower? Thanks for creating and sharing this! For this method to hold however, one also needs to consider strict domination by mixed strategies. A dominant strategy in game theory occurs when one player has a stronger, more effective strategy over another player. 2, or that R is strictly dominated by L for Player 2. /Subtype /Form Your reply would be so much appreciated. (Note this follows directly from the second point.) This gives Bar B a total of 20 beers sold at a price of $5 each, or $100 in revenue. Game Theory: Finding a table with two or more weakly dominant equilibriums? This is the premise that allows a player to make a value judgment on the actions of another player, backed by the assumption of rationality, into Both methods have in common one major shortcoming, they do not always narrow down what may happen in a game to a tractably small number of possibilities. There are instances when there is no pure strategy that dominates another pure strategy, but a mixture of two or more pure strategies can dominate another strategy. More on Data Science4 Essential Skills Every Data Scientist Needs. F+=S}73*t&N$9y#f:&"J /FormType 1 33 0 obj << Sorted by: 2. That is, when Bar A charges $2 and Bar B charges $5. EconPort - Example of Iterated Deletion of Dominated Strategies 2. In the game below, which strategies survive the | Chegg.com Game Theory - Mixed strategy Nash equilibria, Game Theory 2x2 Static Game: Finding the Pure Strategy and Mixed Strategy Nash Equilibria with Weakly Dominant Strategies, The hyperbolic space is a conformally compact Einstein manifold, Checks and balances in a 3 branch market economy, Counting and finding real solutions of an equation. B:R>)`Q. /Matrix [1 0 0 1 0 0] Find startup jobs, tech news and events. $$ The only rationalizable strategy for Players 1 and 2 is then (M,Z) or (3,5). Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Is the reverse also true? >> The result of the comparison is one of: This notion can be generalized beyond the comparison of two strategies. xXKs6WH0[v3=X'VmRL+wHc5&%HnEiP$4'V( 'kT.j!J4WpK'ON_oUC]LD[/RJ%X.wJGy4Oe=x\9G"cQKOx5Ni~7dUMZ\K#?y;U sR8S:ix@4AA Built Ins expert contributor network publishes thoughtful, solutions-oriented stories written by innovative tech professionals. /Resources 50 0 R Why he do not make himself his own calculator. We can delete dominated strategies from the payoff matrix like so: By doing this, weve lost all cells corresponding to a strategy profile in which a dominated strategy is played. $u_1(U,x) = 5-4a$, $u_1(M,x) = 1$, $u_1(B,x) = 1$. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. PDF 6.891 Games, Decision, and Computation February 5, 2015 Lecture 2 1 Games Joel., Watson,. I only found this as a statement in a series of slides, but without proof. /BBox [0 0 16 16] : Whereas looking for an equilibrium in strictly dominant strategies involves finding a strategy that is always the best response for each player, looking for an equilibrium via iterated deletion involves iteratively discounting from consideration strategies that are never best responses. Thinking about this for a moment, a follow up question emerges. arXiv:2304.13901v1 [cs.GT] 27 Apr 2023 19 0 obj /Type /XObject Are all strategies that survive IESDS part of Nash equilibria? dominated. Pingback: Desegregating the Electorate: Aren't we All Americans - Big Sky Headlines, Pingback: Desegregating the Electorate: Aren't we All Americans. +(91)-9821210096 | paula deen meatloaf with brown gravy. Pricing at $5 would be. Strategic dominance - Wikipedia /Shading << /Sh << /ShadingType 2 /ColorSpace /DeviceRGB /Domain [0.0 8.00009] /Coords [0 0.0 0 8.00009] /Function << /FunctionType 3 /Domain [0.0 8.00009] /Functions [ << /FunctionType 2 /Domain [0.0 8.00009] /C0 [1 1 1] /C1 [0.5 0.5 0.5] /N 1 >> << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [0.5 0.5 0.5] /N 1 >> ] /Bounds [ 4.00005] /Encode [0 1 0 1] >> /Extend [false false] >> >> Nash-equilibrium for two-person zero-sum game. 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=1147355371, Articles lacking in-text citations from January 2016, Wikipedia articles incorporating text from PlanetMath, Creative Commons Attribution-ShareAlike License 3.0, C is strictly dominated by A for Player 1. In fact, the logic can grow more complicated. eliminate right from player 2's strategy space. Dominated Strategies & Iterative Elimination of Dominated Strategies 3. Some strategies that werent dominated before, may be dominated in the smaller game. Were told that each bar only cares about maximizing revenue (number of beers sold multiplied by price.) /ProcSet [ /PDF ] Why did DOS-based Windows require HIMEM.SYS to boot? /Resources 48 0 R [2], Common Knowledge: The assumption that each player has knowledge of the game, knows the rules and payoffs associated with each course of action, and realizes that every other player has this same level of understanding. 20 0 obj Games in which all players have dominant strategies are still strategic in the sense that payoff depends on what other players do, but best response does not. Consider the following strategic situation, which we want to represent as a game. But what if Bar B does not price at $5 and instead prices its beer at $2? Proof It is impossible for a to dominate a 1 and a 1 to dominate a. This solver uses the excellent lrs - David Avis's . If B prices its beer at $4, matching that nets $120, and pricing at $5 nets $100. [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. consideration when selecting an action.[2]. 17 0 obj << grassroots elite basketball ; why does ted lasso have a southern accent . ; Thus regardless of whether player 2 chooses left or right, player 1 gets more from playing this mixed strategy between up and down than if the player were to play the middle strategy. If, at the end of the process, there is a single strategy for each player, this strategy set is also a Nash equilibrium. : When iterated deletion of dominated strategies results in just one strategy profile, the game is said to be dominance solvable. I finished my assignment with the help of those, and just checked my answers on your calculator I got it right! As an experimental feature, on can exercise the controversial method of iterated elimination of Pareto-dominated strategies as well (eliminating weakly dominated strategies). Proposition 2 If (a ;b ) is a dominant solution, then (a ;b ) is a Nash equi-librium. This follows from the earlier comment that a strictly dominated strategy is never a best response. In this case, all the locals will go to bar A, as will half the tourists. Two dollars is a strictly dominated strategy for Bar B, and Bar A knows this, too. x}V[7SHQu'X6Yjuf`a5IG*YR|QRJz?uhn~~}?Ds&>y: endstream Im sure that the people who have gone out their way to tell you how much they appreciate your work are only a fraction of the people out there who have used it, but its the least I can do! Tourists will choose a bar randomly in any case. Q: (2) Consider the following two-player norma. stream When a gnoll vampire assumes its hyena form, do its HP change? Did the Golden Gate Bridge 'flatten' under the weight of 300,000 people in 1987. i-gq;E6LMsZYRw=?O;yX9{^54aL%*,u{xpt6>P[bh1KiR3A+{2Bpw\m~UL52Z`XwQ@ EkBxEW._661ROEK-\,Q) .^^_z h6:10a&_M ; d82a06/qJb[0JP"HQ@ipJGs+n^!V*?z!_^CKyi=0#8x;T: 5/' oS94W0'|>4d~o4Kp5YhJ %0^ bT5! There are two versions of this process. $$ Thus if player 1 knows that player 2 is rational then player 1 can /Filter /FlateDecode 4.2 Iterated Elimination of Strictly Dominated Pure Strategies. 12 0 obj 6D7wvN816sIM" qsG;!_maeq"Mw]Vn1cJf}?!!u"\W,v,hTc}yZoV]}_|u_F+tA@1g(,* ^ZR~@Om8eY Oqy*&C3FW1J"&2Nm*z}y}^ a6`wC(=h:*4"0xSdgE+;>ef,XV> W*8}'n~oP> Watch on. As in Chapter 3 we would like to clarify whether it aects the Nash equilibria, in this case equilibria in mixed strate-gies. A: Pure strategy nash equilibrium is the one in which all the players are doing their best, given the. 5,1 & 1,5 & 1,2 \\ (Dominant and Dominated Strategies) 38 0 obj << There is no point frustrating the people who appreciate you and patron your site. Thank you so much! endobj By the well known path independence of iterated elimination of strictly dominated strategies [1, 19, 41], fully reducing and results in the same game. we run into many situations where certain issues are bookend policies (0 or 1), but for which one side has a distribution of options that can be used to optimize, based on previous decisions made using such policies (a priori info from case studies). /Length 1154 Strictly and Weakly Dominated Stategies - Blitz Notes 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. ( Here is a quick Python implementation for . outcome of an iterated elimination of strictly dominated strategies unique, or in the game theory parlance: is strict dominance order independent? Does the 500-table limit still apply to the latest version of Cassandra? The strategy $2 always gives lower payoffs to Bar A than either $4 or $5. Lets see why the strategy is strictly dominated by the strategy $4 for Bar A: Therefore, Bar A would never play the strategy $2. That is, if a strategy is strictly dominated, it can't be part of a Nash equilibrium. /ProcSet [ /PDF ] ;UD(`B;h n U _pZJ t \'oI tP*->yLRc1,[j11Y(25"1U= A straightforward example of maximizing payoff is that of monetary gain, but for the purpose of a game theory analysis, this payoff can take any desired outcome. (Game Theory) : 1 - : Thep Excel 50 0 obj << De nition 1. cZiAIF}$\ScQME >> endobj Untitled - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This is great if a dominant strategy exists, however, there often isnt a dominant strategy. If a single set of strategies remains after eliminating all strictly dominated strategies, then we have a prediction for the games outcome. stream Iterated elimination of strictly dominated strategies (IESDS). (e) Is this game dominance solvable? endobj Enjoy! So, is there any way to approach this? This is an Excel spreadsheet that solves for pure strategy and mixed strategy Nash equilibrium for 22 matrix games. Examples. endobj better than up if 2 plays right (since 2>0). We can demonstrate the same methods on a more complex game and solve for the rational strategies. In the game \guess two-thirds of the average" from Lecture 1, the all-0 strategy pro le was the unique pro le surviving the iterated elimination of strictly dominated strategies. is a Nash equilibrium. Theorem 4 (Order Independence I) Given a nite strategic game all it-erated eliminations of strictly dominated strategies yield the same outcome. This satisfies the requirements of a Nash equilibrium. Expected average payoff of Strategy Y: (4+0+4) = 4 Your excel spreadsheet doesnt work properly. 28 0 obj $$. PDF Rationalizability and Iterated Elimination of Dominated Actions In this case, we should eliminate the middle strategy for player 1 since its been dominated by the mixed strategy of playing up and down with probability (,). We can generalize this to say that rational players never play strictly dominated strategies. A player's strategy is dominated if all associated utility values (rewards) are strictly less than those of some other strategy (or a mixing of other strategies, but that can be left out for now). Nash Equilibrium Dominant Strategies Astrategyisadominant strategy for a player if it yields the best payo (for that player) no matter what strategies the other players choose. stream I know that Iterated Elimination of Strictly Dominated Strategies (IESDS) never eliminates a strategy which is part of a Nash equilibrium. Bar A knows that it will not play $2, and neither will its opponent. Is the reverse also true? %PDF-1.4 $u_1(U,x) = 1$, $u_1(M,x) = 1$, $u_1(B,x) = 1+4a$. Was Aristarchus the first to propose heliocentrism? Stall Wars: When Do States Fight to Hold onto the StatusQuo? This results in a new, smaller game. The iterated elimination (or deletion, or removal) of dominated strategies (also denominated as IESDS, or IDSDS, or IRSDS) is one common technique for solving games that involves iteratively removing dominated strategies. And I highly doubt there is anything particularly unique or creative about your coding. Wow, this article is fastidious, my younger sister is analyzing Note that even if no strategy is strictly dominant, there can be strictly dominated strategies. /Font << /F45 4 0 R /F50 5 0 R /F46 6 0 R /F73 7 0 R /F15 8 0 R /F27 9 0 R /F28 10 0 R /F74 11 0 R /F76 12 0 R /F25 13 0 R /F32 14 0 R /F62 15 0 R /F26 16 0 R >> &BH 6a}F~DB ]%pg BZ8PT LAdku|u! For player 1, neither up nor down is strictly 24 0 obj Much more helpful than my *actual* lecturer. I obviously make no claim that the math involved in programming it is special. The logic of equilibrium in dominant strategies is that if a player has a strategy that is always best, we would expect him to play it. It also ensures that there is a strictly dominant strategy pro le s 2S satisfying u i(s ) > u i(s) for all i 2N and all s 2S satisfying s 6= s . L R U M D 5 1 5 1 2 2 (5,1) (1,5) (2,2) D is not strictly dominated by any pure strategy, but strictly dominated by 1=2U + 1=2M. Lets define the probability of player 1 playing up as p, and let p = . Game Theory 101: The Complete Textbook on Amazon: https://www.amazon.com/Game-Theory-101-Complete-Textbook/dp/1492728152/http://gametheory101.com/courses/gam. Elimination of weakly dominated strategies - example It only takes a minute to sign up. player 2 is rational then player 1 can play the game as if it was the game bm'n^ynC-=i)yJ6#x,rcTHHNYwULy2:Mjw'jjn!C}<4C[L,HO[^#B>9Fam%'QvL+YN`LRoOrD{G%}k9TiigB8/}w q#Enmdl=8d2 (o BmErx `@^PB2#C5h0:ZM[L,x4>XLHNKd88(qI#_kc&A's ),7 'beO@nc|'>E4lpC Exercise 2. M. We now focus on iterated elimination of pure strategies that are strictly dominated by a mixed strategy. Thanks! /Shading << /Sh << /ShadingType 3 /ColorSpace /DeviceRGB /Domain [0.0 8.00009] /Coords [8.00009 8.00009 0.0 8.00009 8.00009 8.00009] /Function << /FunctionType 3 /Domain [0.0 8.00009] /Functions [ << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [0.5 0.5 0.5] /N 1 >> << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [1 1 1] /N 1 >> ] /Bounds [ 4.00005] /Encode [0 1 0 1] >> /Extend [true false] >> >> I am supposed to solve a game by iterated elimination of weakly dominated strategies: ECON 459 Exam 3 Flashcards | Quizlet Once weve identified the players and the strategies, we can begin to create our payoff matrix: Now, we can fill in the payoffs. Proof. The second version involves eliminating both strictly and weakly dominated strategies. Uncertainty and Incentives in NuclearNegotiations, How Uncertainty About Judicial Nominees Can Distort the ConfirmationProcess, Introducing -CLEAR: A Latent Variable Approach to Measuring NuclearProficiency, Militarized Disputes, Uncertainty, and LeaderTenure, Multi-Method Research: A Case for FormalTheory, Only Here to Help? For example, a price of $4 gives Bar A higher payoffs than any other price if Bar B prices at $5. Strictly dominated strategies cannot be a part of a Nash equilibrium, and as such, it is irrational for any player to play them. PDF A Primer In Game Theory Solutions Pdf (2023) Strict Dominance Deletion Step-by-Step Example: Another version involves eliminating both strictly and weakly dominated strategies. knows that the second game applies) then player 2 can eliminate down from S2={left,middle,right}. Now Bar A is comparing the strategies of $4 and $5 and notices that, once the strategy of $2 is taken off the table for both players, the strategy $5 is dominated by the strategy $4. Consider the following game to better understand the concept of iterated elimination of strictly dominated strategies. 64. Its just math, you dont have a copyright privilege to pure mathematics. My bad you are right. First note that strategy H is strictly dominated by strategy G (or strategy E), so we can eliminate it from consideration. /k\MI\R}n%-(vvao5 %K6~hfmake/@v.6v]ko]cq"AI X4/F B{T% How to Identify a Dominated Strategy in Game Theory, There are two versions of this process. Now let us put ourselves in the shoes of Bar A again. Bar B knows Bar As payoffs. 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. /Subtype /Form Explain. The predictive power may not be precise enough to be useful. There are instances when there is no pure strategy that dominates another pure strategy, but a mixture of two or more pure strategies can dominate another strategy. this strategy set is also a Nash equilibrium. There are two versions of this process. Player 1 knows this. endobj I know that Iterated Elimination of Strictly Dominated Strategies (IESDS) never eliminates a strategy which is part of a Nash equilibrium. Strategic Dominance: A Guide to Dominant and Dominated Strategies Solve Iterated Elimination of Dominated Strategy. endobj You said in your video that down-right was the strictly dominated strategy, but your excel spreadsheet says top left is. Bargaining and the Perverse Incentives of InternationalInstitutions, Outbidding as Deterrence: Endogenous Demands in the Shadow of GroupCompetition, Policy Bargaining and MilitarizedConflict, Power to the People: Credible Communication in the Quotidian Use of AuthoritarianInstitutions, Power Transfers, Military Uncertainty, andWar, Sanctions, Uncertainty, and LeaderTenure, Scientific Intelligence, Nuclear Assistance, andBargaining, Shooting the Messenger: The Challenge of National SecurityWhistleblowing, Slow to Learn: Bargaining, Uncertainty, and the Calculus ofConquest. When player 2 plays left, then the payoff for player 1 playing the mixed strategy of up and down is 1, when player 2 plays right, the payoff for player 1 playing the mixed strategy is 0.5. For Bar A, there is no price that will give it higher revenues than any other price it could have set, no matter what price Bar B sets. /Length 4297 Basic Probability Theory and Statistics Terms to Know, 4 Essential Skills Every Data Scientist Needs, What Can We Learn From 4 Superhuman, Game-playing AIs. & L & C & R \\ \hline For symmetric games, m = n. Enter payoff matrix B for player 2 (not required for zerosum or symmetric games). However, there's another way we can use the concept of. (a)How Nash Equilibrium is achieved under Game. If column mixes over $(L, R)$ - $x = (a, 0, 1-a)$ Want to practice what Im learning, and as far as I can find your calculator seems to be the only easiest best option available. Dominance Solvability in Random Games - arXiv >> endobj 9G|zqO&:r|H>1`(N7C\|.U%n,\Ti}=/8{'Q :j!^$Rs4A6iT+bSz;,_/|GGv%ffp ,$ Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. $$ Untitled | PDF | Profit (Economics) | Microeconomics - Scribd Change), You are commenting using your Facebook account. Strictly dominated strategies cannot be played in equilibrium, and you will note that the calculator says that is the PSNE. /Filter /FlateDecode . 3,8 3,1 2,3 4,5 Strategic dominance is a state in game theory that occurs when a strategy that a player can use leads to better outcomes for them than alternative strategies.. There are also no mixed equilibria in which row plays $B$: if column mixes over his entire strategy space - $x = (a, b, 1-a-b)$. So, we can delete it from the matrix. 1. Analytical Services; Analytical Method Development and Validation I developed it to give people who watch my YouTube course or read my game theory textbook the chance to practice on their own and check their solutions. IESDS on game with no strictly dominated strategies. Iterated elimination of strictly dominated strategies is the process that guides that thinking. Is it safe to publish research papers in cooperation with Russian academics? Consequently, if player 2 knows that player 1 is rational, and player 2 se7 gnx(\D4nLfZ[z\nS* l:ZM~_4w>nqtBOO]TS4H1K{!!j$Bu64@D4QsE?-a /Filter /FlateDecode If total energies differ across different software, how do I decide which software to use? /Resources << Column 2kare strictly dominated by Row k+1 and Column k+1, respectively. The reason it lists strictly dominated strategies instead of strictly dominant strategies is that there is no guarantee that a player will play a strictly dominant strategy in equilibrium once you extend past 22 matrices. T & 2, 1 & 1, 1 & 0, 0 \\ \hline Bar A also knows that Bar B knows this. (h, h) is the unique profile that survives iterated elimination of strictly dominated strategies. What were the poems other than those by Donne in the Melford Hall manuscript? However, that Nash equilibrium is not necessarily "efficient", meaning that there may be non-equilibrium outcomes of the game that would be better for both players. game theory - Are there strictly dominated strategies? - Economics PDF Chapter 5 Rationalizability - MIT OpenCourseWare 2. Q: If a strategy survives IESDS, is it part of a Nash equilibrium? elimination of strictly dominated strategies. But what if not all players have dominant strategies? Are all strategies that survive IESDS part of Nash equilibria? knows that player 1 knows that player 2 is rational ( so that player 2 I only found this as a statement in a series of slides, but without proof. ^qT4ANidhu z d3bH39y/0$ D-JK^^:WJuy+,QzU.9@y=]A\4002lt{ b0p`lK0zwuU\,(X& {I 5 xD]GdWvM"tc3ah0Z,e4g[g]\|$B&&>08HJ.8vdN.~YJnu>/}Zs6#\BOs29stNg)Cn_0ZI'9?fbZ_m4tP)v%O`1l,>1(vM&G>F 5RbqOrIrcI5&-41*Olj\#u6MZo|l^,"qHvS-v*[Ax!R*U0 (up,middle) as the outcome of the game. $u_1(U,x) > u_1(M,x) \wedge u_1(B,x) > u_1(M,x) \Rightarrow$ if column plays x row plays $M$ with probability zero. If, after completing this process, there is only one strategy for each player remaining, that strategy set is the unique Nash equilibrium. appreciated tremendously! EC202, University of Warwick, Term 2 13 of 34 !mH;'{v(opBaiCX7J9YJ8RxO#C?_3a3b{:mN'7;{5d9FX}-R7Ok:d=6C(~dT*E3En5S)1FgMvhTU}1"6.Kn'9m#* _QfxF[LEN eiDERbJYk+ n?x>3FqT`yUM#:h-I#5 ixhL(5t5+ou\SH-kRmj0 !pTX$1| @v (S5>^"D_%Pym{`;UM35t%hPJVixb[yi ucnh9wHwp3o?fB%:v"B@F~Ch^J87X@,za$pcNJ /ProcSet [ /PDF /Text ] if player 1 is rational (and player 1 knows that player 2 is rational, so Generic Doubly-Linked-Lists C implementation. However, remember that iterated elimination of weakly (not strict) dominant strategies can rule out some NE. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. $\begin{bmatrix} Built In is the online community for startups and tech companies. So playing strictly dominant strategies is Pareto e cient in the \no-talking norm"-modi ed PD. We cannot delete anything else. In iterated dominance, the elimination proceeds in rounds, and becomes easier as more strategies are eliminated: in any given round, the dominating strat- . Since these strategies . In the first step of the iterative deletion process, at most one dominated strategy is removed from the strategy space of each of the players, since no rational player would ever play these strategies. Set up the inequality to determine whether the mixed strategy will dominate the pure strategy based on expected payoffs. In this game, as depicted in the adjacent game matrix, Kenney has no dominant strategy (the sum of the payoffs of the first strategy equals the sum of the second strategy), but the Japanese do have a weakly dominating strategy, which is to go . bubble tea consumption statistics australia. given strategy is strictly (weakly) dominated by some pure strategy is straightforward, by checking, for every pure strat-egy for that player, whether the latter strategy performs . /Length 3114 We can push the logic further: if Player 1 knows that Player 2 is . Games between two players are often . 11 0 obj In this scenario, for player 1, there is no pure strategy that dominates another pure strategy. E.g., cash reward, minimization of exertion or discomfort, promoting justice, or amassing overall utility - the assumption of rationality states that \begin{array}{c|c|c|c} /Shading << /Sh << /ShadingType 3 /ColorSpace /DeviceRGB /Domain [0 1] /Coords [4.00005 4.00005 0.0 4.00005 4.00005 4.00005] /Function << /FunctionType 2 /Domain [0 1] /C0 [0.5 0.5 0.5] /C1 [1 1 1] /N 1 >> /Extend [true false] >> >> Similarly, some games may not have any strategies that can be deleted via iterated deletion. round of the iterated elimination of strictly dominated strategies. It may be that after I factor in your strictly dominated strategy, one of my strategies becomes strictly dominated.