Meta tags:

Headings (most frequently used words):

proper, equilibrium, contents, definition, example, equilibria, of, extensive, games, references,

Text of the page (most frequently used words):
game (48), the (38), #equilibrium (22), player (21), proper (18), theory (17), strategy (16), games (14), and (12), perfect (12), penny (11), form (10), this (9), with (8), extensive (8), edit (8), that (8), wikipedia (7), displaystyle (7), search (6), myerson (6), stable (6), nash (6), epsilon (6), move (6), information (6), heads (6), tails (6), probability (6), hide (6), about (5), page (5), bayesian (5), for (5), dilemma (5), trembling (5), hand (5), strategic (5), equilibria (5), contents (4), non (4), concepts (4), complete (4), auction (4), theorem (4), mechanism (4), core (4), robert (4), evolutionarily (4), tools (4), win (4), roger (4), point (4), matching (4), pennies (4), guess (4), normal (4), grab (4), sidebar (4), view (3), may (3), commons (3), was (3), different (3), from (3), cooperative (3), bertrand (3), design (3), price (3), john (3), key (3), people (3), dominance (3), ways (3), david (3), kuhn (3), rational (3), read (3), one (3), competition (3), pure (3), mixed (3), escalation (3), talk (3), model (3), strategies (3), payoff (3), rationality (3), concept (3), two (3), whether (3), has (3), sigma (3), main (3), languages (2), toggle (2), table (2), contact (2), privacy (2), policy (2), terms (2), apply (2), categories (2), link (2), defined (2), short (2), description (2), wikidata (2), portal (2), agent (2), complexity (2), paradox (2), other (2), goods (2), applications (2), satterthwaite (2), theorems (2), vickrey (2), principle (2), algorithmic (2), axelrod (2), william (2), donald (2), selection (2), stag (2), hunt (2), set (2), variation (2), tree (2), sum (2), combinatorial (2), reinhard (2), selten (2), jean (2), mertens (2), cournot (2), aumann (2), shapley (2), arrow (2), herbert (2), eric (2), contract (2), behavioral (2), fixed (2), gibbs (2), war (2), problem (2), prisoner (2), bargaining (2), switch (2), dominated (2), markov (2), commitment (2), cheap (2), efficiency (2), incomplete (2), edgeworth (2), related (2), subgame (2), sequential (2), quasi (2), response (2), coalition (2), correlated (2), international (2), journal (2), relationship (2), van (2), damme (2), references (2), notion (2), hides (2), variant (2), are (2), profiles (2), where (2), grabs (2), any (2), such (2), intuitively (2), expects (2), not (2), however (2), can (2), unique (2), prepares (2), event (2), example (2), profile (2), expected (2), playing (2), smaller (2), than (2), assigned (2), definition (2), costly (2), solution (2), appearance (2), upload (2), file (2), changes (2), links (2), history (2), article (2), log (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, text, available, under, additional, using, site, you, agree, registered, trademark, profit, organization, wikimedia, foundation, inc, use, creative, attribution, sharealike, license, rendered, parsoid, last, edited, 2026, utc, hidden, category, locally, articles, retrieved, https, org, index, php, title, proper_equilibrium, oldid, 1357089958, wikiproject, mathematics, ppad, multi, system, helly, metric, computational, chainstore, topics, truthful, cake, cutting, knapsack, digital, border, revenue, equivalence, virtual, valuation, clarke, groves, strategyproofness, revelation, participation, constraint, monotonicity, ironing, market, incentive, compatibility, optimal, hamilton, george, maynard, smith, terminal, investment, hypothesis, mobbing, fisher, cultural, group, chicken, weak, stochastically, risk, replicator, equation, state, evolution, bishop, cannings, evolutionary, von, neumann, conway, claude, shannon, principal, paranoid, negamax, monte, carlo, minimax, expectiminimax, alpha, beta, pruning, algorithms, winning, your, mathematical, plays, surreal, number, star, numbers, nimber, mex, math, toads, frogs, sylver, coinage, subtract, square, notakto, nim, hackenbush, domineering, cram, clobber, chomp, chess, zugzwang, stealing, argument, sprague, grundy, solved, partisan, misère, impartial, first, second, disjunctive, determinacy, explosion, oskar, morgenstern, olga, bondareva, ken, binmore, françois, tirole, hervé, moulin, gillies, kreps, levine, ariel, rubinstein, antoine, augustin, amos, tversky, albert, tucker, thomas, schelling, suzanne, scotchmer, samuel, bowles, wilson, peyton, young, paul, milgrom, merrill, flood, melvin, dresher, martin, shubik, lloyd, leonid, hurwicz, kenneth, jennifer, tour, chayes, scarf, simon, harold, maskin, drew, fudenberg, gale, alvin, roth, social, software, quantum, negotiation, mean, field, heresthetic, graphical, drama, confrontation, compositional, subfields, zermelo, sperner, irrationality, ignorance, prim, shot, deviation, kakutani, glicksberg, gibbard, folk, competitive, altruism, brouwer, agreement, impossibility, attrition, volunteer, ultimatum, traveler, stackelberg, rock, paper, scissors, rendezvous, public, pirate, optional, obligationes, lewis, signaling, poker, keynesian, beauty, contest, average, gift, exchange, electronic, mail, farol, bar, dollar, diner, trust, dictator, deadlock, coordination, centipede, blotto, battle, sexes, all, pay, stay, lose, tit, tat, max, hobbesian, trap, grim, trigger, focal, fictitious, play, deterrence, device, collusion, bid, shading, appeasement, value, rationalizable, anarchy, pareto, open, loop, iterated, elimination, individual, inequity, aversion, contracts, cycle, backward, induction, self, confirming, satisfaction, quantal, program, proof, strong, cursed, berge, bayes, zero, uncorrelated, asymmetry, tragedy, topological, succinct, interaction, complements, spite, simultaneous, action, preference, ply, recall, outcome, credible, threat, mutual, knowledge, nature, hierarchy, beliefs, semantics, farsightedness, dynamic, inconsistency, coopetition, contingent, cooperator, conjectural, mixing, bounded, best, regret, asynchrony, definitions, traditional, theorists, glossary, 1984, between, 133, 154, 1978, refinements, properness, completely, analogous, applied, leads, notions, shown, behaviorally, equivalent, perfection, row, column, guesses, correctly, gets, third, option, grabbing, without, guessing, pair, even, since, concerned, leaving, uncertain, seen, motivated, follows, fully, still, unlikely, does, instead, some, reason, decides, make, making, sure, exactly, original, twist, right, said, limit, approaches, sequence, given, parameter, whenever, then, most, times, totally, refinement, further, refines, assuming, more, trembles, made, significantly, less, ones, proposed, significance, subset, free, encyclopedia, item, projects, printable, version, download, pdf, print, export, legacy, parser, get, shortened, url, cite, permanent, what, here, general, actions, english, русский, 日本語, español, top, personal, special, pages, recent, community, learn, help, contribute, random, current, events, navigation, jump, content,

Text of the page (random words):
proper equilibrium wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 definition 2 example 3 proper equilibria of extensive games 4 references toggle the table of contents proper equilibrium 4 languages español 日本語 русский 粵語 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia solution concept in game theory proper equilibrium solution concept in game theory relationship subset of trembling hand perfect equilibrium significance proposed by roger b myerson proper equilibrium in game theory is a refinement of nash equilibrium by roger b myerson proper equilibrium further refines reinhard selten s notion of a trembling hand perfect equilibrium by assuming that more costly trembles are made with significantly smaller probability than less costly ones definition edit given a normal form game and a parameter ϵ 0 displaystyle epsilon 0 a totally mixed strategy profile σ displaystyle sigma is defined to be ϵ displaystyle epsilon proper if whenever a player has two pure strategies s and s such that the expected payoff of playing s is smaller than the expected payoff of playing s that is u s σ i u s σ i displaystyle u s sigma _ i u s sigma _ i then the probability assigned to s is at most ϵ displaystyle epsilon times the probability assigned to s the strategy profile of the game is said to be a proper equilibrium if it is a limit point as ϵ displaystyle epsilon approaches 0 of a sequence of ϵ displaystyle epsilon proper strategy profiles example edit the game to the right is a variant of matching pennies matching pennies with a twist guess heads up guess tails up grab penny hide heads up 1 1 0 0 1 1 hide tails up 0 0 1 1 1 1 player 1 row player hides a penny and if player 2 column player guesses correctly whether it is heads up or tails up he gets the penny in this variant player 2 has a third option grabbing the penny without guessing the nash equilibria of the game are the strategy profiles where player 2 grabs the penny with probability 1 any mixed strategy of player 1 is in nash equilibrium with this pure strategy of player 2 any such pair is even trembling hand perfect intuitively since player 1 expects player 2 to grab the penny he is not concerned about leaving player 2 uncertain about whether it is heads up or tails up however it can be seen that the unique proper equilibrium of this game is the one where player 1 hides the penny heads up with probability 1 2 and tails up with probability 1 2 and player 2 grabs the penny this unique proper equilibrium can be motivated intuitively as follows player 1 fully expects player 2 to grab the penny however player 1 still prepares for the unlikely event that player 2 does not grab the penny and instead for some reason decides to make a guess player 1 prepares for this event by making sure that player 2 has no information about whether the penny is heads up or tails up exactly as in the original matching pennies game proper equilibria of extensive games edit one may apply the properness notion to extensive form games in two different ways completely analogous to the two different ways trembling hand perfection is applied to extensive games this leads to the notions of normal form proper equilibrium and extensive form proper equilibrium of an extensive form game it was shown by van damme that a normal form proper equilibrium of an extensive form game is behaviorally equivalent to a quasi perfect equilibrium of that game references edit roger b myerson refinements of the nash equilibrium concept international journal of game theory de 15 133 154 1978 eric van damme a relationship between perfect equilibria in extensive form games and proper equilibria in normal form games international journal of game theory de 13 1 13 1984 v t e game theory glossary game theorists games traditional game theory definitions asynchrony bayesian regret best response bounded rationality cheap talk coalition complete contract complete information complete mixing conjectural variation contingent cooperator coopetition cooperative game theory dynamic inconsistency escalation of commitment farsightedness game semantics hierarchy of beliefs incomplete information information set move by nature mutual knowledge non cooperative game non credible threat outcome perfect information perfect recall ply preference rationality sequential game simultaneous action selection spite strategic complements strategic dominance strategic form strategic interaction strategic move strategy subgame succinct game topological game tragedy of the commons uncorrelated asymmetry win win game zero sum game equilibrium bayes correlated berge correlated cursed epsilon gibbs equilibrium markov perfect mertens stable nash strong coalition proof perfect bayesian program proper quantal response quasi perfect satisfaction self confirming sequential subgame perfect trembling hand perfect related backward induction bayesian efficiency bayesian game bertrand edgeworth model core edgeworth price cycle incomplete contracts inequity aversion individual rationality iterated elimination of dominated strategies open loop model pareto efficiency payoff dominance price of anarchy rational agent rationalizable strategy shapley value strategies appeasement bargaining model of war bid shading cheap talk collusion commitment device de escalation deterrence escalation fictitious play focal point grim trigger hobbesian trap markov strategy max dominated strategy mixed strategy pure strategy tit for tat win stay lose switch games all pay auction battle of the sexes nash bargaining game bertrand competition blotto game centipede game coordination game cournot competition deadlock dictator game trust game diner s dilemma dollar auction el farol bar problem electronic mail game gift exchange game guess 2 3 of the average keynesian beauty contest kuhn poker lewis signaling game matching pennies obligationes optional prisoner s dilemma pirate game prisoner s dilemma public goods game rendezvous problem rock paper scissors stackelberg competition stag hunt traveler s dilemma ultimatum game volunteer s dilemma war of attrition theorems arrow s impossibility aumann s agreement brouwer fixed point competitive altruism folk gibbard satterthwaite gibbs glicksberg s kakutani fixed point kuhn s one shot deviation prim read rational ignorance rational irrationality sperner s zermelo s subfields algorithmic behavioral behavioral strategy compositional confrontation contract theory drama theory graphical heresthetic mean field negotiation theory quantum social software key people us alvin e roth david gale drew fudenberg eric maskin harold w kuhn herbert simon herbert scarf jennifer tour chayes kenneth arrow leonid hurwicz lloyd shapley martin shubik melvin dresher merrill m flood paul milgrom peyton young robert aumann robert axelrod robert b wilson roger myerson samuel bowles suzanne scotchmer thomas schelling william vickrey albert w tucker amos tversky antoine augustin cournot ariel rubinstein david k levine david m kreps donald b gillies hervé moulin jean tirole jean françois mertens ken binmore olga bondareva oskar morgenstern reinhard selten combinatorial game theory core concepts combinatorial explosion determinacy disjunctive sum first second player win game complexity game tree impartial game misère partisan game solved game sprague grundy theorem strategy stealing argument zugzwang games chess chomp clobber cram domineering hackenbush nim notakto subtract a square sylver coinage toads and frogs math tools mex nimber on numbers and games star surreal number winning ways for your mathematical plays search algorithms alpha beta pruning expectiminimax minimax monte carlo tree search negamax paranoid principal variation key people claude shannon john conway john von neumann evolutionary game theory core concepts bishop cannings theorem evolution and the theory of games evolutionarily stable set evolutionarily stable state evolutionarily stable strategy replicator equation risk dominance stochastically stable equilibrium weak evolutionarily stable strategy games chicken stag hunt applications cultural group selection fisher s principle mobbing terminal investment hypothesis key people john maynard smith george r price william donald hamilton robert axelrod mechanism design core concepts algorithmic mechanism design bayesian optimal mechanism incentive compatibility market design myerson ironing monotonicity participation constraint revelation principle strategyproofness vickrey clarke groves mechanism virtual valuation theorems myerson satterthwaite theorem revenue equivalence border s theorem applications digital goods auction knapsack auction truthful cake cutting other topics bertrand paradox chainstore paradox computational complexity of games helly metric multi agent system ppad complete mathematics portal game theory wikiproject game theory retrieved from https en wikipedia org w index php title proper_equilibrium oldid 1357089958 categories game theory equilibrium concepts non cooperative games hidden categories articles with short description short description is different from wikidata commons category link is locally defined this page was last edited on 31 may 2026 at 18 07 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents proper equilibrium 4 languages add topic