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Topic: Pure strategies

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	Game Theory Notes 3
		In essence, a pure strategy is a collection of rules governing behavior during the course of a play of the game, while a mixed strategy is a method of selecting, before the play of the game commences, which collection of rules (i.e.
		The extension should be such that the mixed strategy expected payoff is identical to the pure strategy expected payoff when the mixed strategies are in fact associated mixed strategies for some pure strategies.
		As before, since pure strategies correspond to associated mixed strategies, we wish the extension to be consistent with pure strategy equilibrium pairs.
	mathematics.monmouth.edu /coursenotes/kuntz/math499/GTNotes09.htm (1475 words)

	Untitled Document (Site not responding. Last check: 2007-11-04)
		One may define a concept of an n-person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n-tuple of pure strategies, one strategy being taken for each player.
		For mixed strategies, which are probability distributions over the pure strategies, the pay-off functions are the expectations of the players, thus becoming polylinear forms in the probabilities with which the various players play their various pure strategies.
		Any n-tuple of strategies, one for each player, may be regarded as a point in the product space obtained by multiplying the n strategy spaces of the players.
	www.bcs.rochester.edu /~dlee/projects/Nash.htm (355 words)

	A Taxonomy of Decomposition Strategies Based on Structures, Behaviors, and Goals
		By grouping strategies, it provides generalizations that could in the future be used as the basis for selection guidelines in a methodical design approach.
		It is possible to employ heterogeneous strategies, in which one portion of a design is decomposed with one strategy, and the remainder of the design is decomposed using a second strategy.
		A pure structural decomposition is used to divide the design into a mechanical portion and an electrical/electronic portion in order to accommodate the fact that two engineers from those two disciplines will be designing the system.
	www.ece.cmu.edu /~koopman/decomp/decomp.html (5108 words)

	Chapter G Summary Finite
		If one pure strategy is dominated by another, the player can ignore the dominated strategy without losing any advantage.
		strategy is a method of playing a game where the rows or columns are played at random so that each is used a given fraction of the time.
		An optimal mixed strategy for the column player is a mixed strategy for which the highest expected payoff (over all possible row player mixed strategies) is as small as possible.
	www.zweigmedia.com /ThirdEdSite/Summary9.html (1450 words)

	Well-mixed populations: pure strategies
		The replicator equation simply states that the success of a strategy depends on its relative performance in the population.
		may equally refer to the propensity of cooperation in a continuous strategy space.
		Time evolution of the mean payoff of each strategy together with the average population payoff.
	www.univie.ac.at /virtuallabs/Snowdrift/mixed.pure.html (698 words)

	Game Theory Notes 3
		In the matrix game of figure 12.1, we notice that for each of the three possible player I selections of a pure strategy, the expected payoff to player I when the player selects the second strategy is as good or better than this expected payoff if the first strategy were selected.
		Since each player is fully cognizant of the rules of the game, a second principle is that each strategy of one of the players, which is determined by him to be to his advantage, is known to the other player.
		We observe that strategy 1 for player II is also his security level and also that -1 is a saddle point for the matrix.
	mathematics.monmouth.edu /coursenotes/kuntz/math499/GTNotes12.htm (1534 words)

	Repeated game
		A strategy can become very complicated as actions in say the tenth repetition of the stage game can be made conditional on prior decisions of the other player or outcomes in preceding stage game encounters.
		A strategy may then be a simple "always do the same thing in each stage game regardless of what has happened before" or a much more complex set of instructions.
		For example, a strategy of “permanent retaliation” (AKA the “grim reaper” strategy) in a repeated prisoner’s dilemma game requires that the player cooperate in the initial stage game and continue to cooperate in subsequent stage games as long as the other player has cooperated in the preceding stage game.
	www.carleton.ca /~kacheson/T490_2001_6.htm (1776 words)

	Nat' Academies Press, Governance and Opportunity in Metropolitan America (1999)
		Another set of strategies is inclusionary, seeking to require local governments or developers to include housing for low-and moderate-income households in the community.
		Household mobility strategies, which attempt to open up housing opportunities for residents of distressed areas in other areas where housing conditions, employment, and other opportunities are presumably better.
		Some critics of mobility strategies suggest that they are unlikely to succeed because physical access is only part of the problem; suburban employers will continue to discriminate against central-city residents, particularly fl central-city residents, either through racism or through a belief that a central-city address is a proxy for poor education and work readiness.
	www.nap.edu /books/0309065534/html/79.html (8791 words)

	Mixed Strategies
		Given that neither of the pure strategy equilibria is a focal point of the game, the solution to the game is for both of them to play a mixed strategy.
		of a mixed strategy is the set of pure strategies used to construct the mixed strategy.
		The worst case payoff of a mixed strategy may be better than the worst case payoff of a pure strategy.
	isc.temple.edu /economics/Econ_92/Game_Lectures/6th-MixedStrat/mixed_strategies.htm (1041 words)

	Scientific American: What is game theory and what are some of its applications? (Site not responding. Last check: 2007-11-04)
		Here the optimal strategy, given that the game is being played many times, is a specialized random mix of the individual pure strategies.
		We can show that heads-tails is a fair game and that both players have the same optimal mix of strategies that randomizes the selection of heads or tails 50 percent of the time for each.
		An equilibrium solution is a set of mixed strategies, one for each player, such that each player has no reason to deviate from that strategy, assuming all the other players stick to their equilibrium strategy.
	www.sciam.com /print_version.cfm?articleID=000B8A10-F94C-1ECC-8E1C809EC588EF21 (1471 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Likewise to player A, B must mix its pure strategies in such a way that A is indifferent to any of its pure strategies (and B is indifferent to A’s pure strategies).
		In summary, there is no pure strategy Nash equilibrium for A or B. There is one mixed strategy Nash equilibrium in which A randomly mixes its pure strategies according to the probabilities p1, p2, p3; and b randomly mixes its pure strategies according to the probabilities q1, q2, q3.
		Since there are only two pure strategies for each player, I am going to take advantage of the graphical method of modeling this game to ensure locating all mixed strategy Nash equilibrium, not because I expect to find pure strategy equilibria, but because I want to look at boundary conditions.
	www.peter.norman.name /images/MidTermFinal.doc.doc (2405 words)

	Introduction to Game Theory -- simple, two-strategy examples
		Strategies can be behaviors that are on some continuum (e.g., how long to wait or display) or they may represent discrete behavior types (e.g., display, fight, or flee).
		Thus, as long as the two strategies do not have identical payoffs ( see this note to understand what would happen if both did have identical payoffs), then at some frequencies one will be more fit while at other frequencies the other strategy will be more fit.
		It means that as either strategy increases from being rare, its relative fitness must begin to decrease and eventually, by the time it is very common, it must be less than the fitness of the other strategy.
	www.holycross.edu /departments/biology/kprestwi/behavior/ESS/games_intro.html (7092 words)

	Science & Technology at Scientific American.com: Ask the Experts: Mathematics: What is game theory and what are ... (Site not responding. Last check: 2007-11-04)
		After learning how to play the game tick-tack-toe, you probably discovered a strategy of play that enables you to achieve at least a draw and even win if your opponent makes a mistake and you notice it.
		And a pure strategy--such as the one you found for tick-tack-toe--is an overall plan specifying moves to be taken in all eventualities that can arise in a play of the game.
		But whereas you may be able to describe all such pure strategies for tick-tack-toe, it is not possible to do so for chess, hence the latter's age-old intrigue.
	www.sciam.com /askexpert_question.cfm?articleID=000B8A10-F94C-1ECC-8E1C809EC588EF21&catID=3&chanID=sa005 (1079 words)

	Pure Arbitrage, Forex, Currencies, Futures, Options, Trading Strategy, Hedge Fund, Alternative Investment (Site not responding. Last check: 2007-11-04)
		Pure arbitrage strategies aim to take advantage of transient mispricings of securities relative to a basket of other securities, or to theoretical pricing laws.
		The set of strategies employed also is large, and each strategy is tailored to the particular securities under consideration.
		Another example is a strategy exploiting mispricing between a futures contract and a put and a call contract (of the same exercise price), all with the same underlying security.
	www.finlabs.net /docs/purearb.html (205 words)

	UO Stratics - Hall of Warfare - Pure Mage Strategies (Site not responding. Last check: 2007-11-04)
		he almost pure mages that we can make now days can be quite deadly, but they also have a few weaknesses.
		If it becomes neccessary for you to use a melee skill try to ensure that your blade is poisoned, GM made, and fast.
		Pure mages dex's are generally low and a heavy, slow weapon won't do you a whole lot of good when you don't have armor but your opponent does.
	uo.stratics.com /warfare/puremage.shtml (592 words)

	Structured populations: pure strategies
		In the spatial Snowdrift or Hawk-Dove game it is favorable to adopt a strategy which opposes the neighboring ones.
		In the Snowdrift and Hawk-Dove game cooperators and defectors co-exist in well-mixed populations as opposed to the Prisoner's Dilemma where cooperators are doomed and go extinct.
		The shades of grey of the payoff scale are augmented by blueish and reddish shades indicating payoffs for mutual cooperation and defection, respectively.
	www.univie.ac.at /virtuallabs/Snowdrift/struct.pure.html (1342 words)

	Evanson Asset Management - Asset Allocation for Bears
		A pure passive and index strategy therefore ignores current economic and financial market events and opinions and focuses on probable long-term risks and returns available from highly diversified equity and fixed income portfolios.
		A second simple strategy passive and index equity investors can use if they believe a long-term bear may be coming is to maintain a lower equity/fixed ratio than they might ordinarily hold.
		A third simple strategy passive and index investors can use is to make sure that they have maximum global and asset class diversification in their equity holdings.
	www.evansonasset.com /index.cfm/Page/18.htm (4046 words)

	Prisoner's Dilemma
		Since the strategies are deterministic, we must distinguish between the versions that cooperate on the first round and those that defect on the first round.
		For any strategy i in the IPD (or indeed in any iterated finite game), however, there are strategies j different from i such that j mimics the way i plays when it plays against i or j.
		One way to distinguish among the strategies that meet BS is by the size of the invasion required to overturn the natives, or, equivalently, by the proportion of natives required to maintain stability.
	plato.stanford.edu /entries/prisoner-dilemma (14189 words)

	A game of Structural Optimization by Andrej and Elena Cherkaev (Site not responding. Last check: 2007-11-04)
		The best strategy for the force is to be applied in a certain way and the best strategy for the structure is to resist that force.
		Here the strategy is different: an optimal design offers equal resistance against a class of equally harmful loadings, rather then the extremal resistance to a single loading.
		The mixed strategies correspond to the multiplicity of the minimal eigenvalue.
	www.math.utah.edu:8080 /~cherk/comics2/ab.html (808 words)

	2002-15: On Nash-solvability in pure stationary strategies of finite games with perfect information which may have ... (Site not responding. Last check: 2007-11-04)
		The players are allowed only pure stationary strategies, that is the move in any position is deterministic, and may depend only on this present position, not on the preceding positions or moves.
		Hence, the resulting play $p$ is a directed path which begins in the initial position $v_0$ and either (i) ends in a final position or (ii) results in a simple directed cycle.
		A game is called Nash-solvable if it has at least one Nash equilibrium in pure stationary strategies and properly Nash-solvable if the corresponding play results in a final position, not in a cycle.
	dimacs.rutgers.edu /TechnicalReports/abstracts/2002/2002-15.html (492 words)

	Social Conformity And Equilibrium In Pure Strategies In Games With Many Players (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		In fact, every mixed strategy equilibrium can be used to construct an z-equilibrium in pure strategies, an 'z-purification' resuit.
		8 the existence of pure and mixed strategy Nash equilibria in..
		2 the existence of pure strategy equilibria with a continuum o..
	citeseer.ist.psu.edu /550864.html (758 words)

	Pure Marketing, Promoting and marketing UK websites - internet promotion strategies
		Pure Marketing is operated by Peter Yexley the UK internet marketing consultant.
		No doubt you are bombarded with offers from internet marketing ' experts ' to rocket your website so high in the search engine rankings that it will blow Google and Yahoo's tops off !!, the trouble is, they all promise everyone, and everyone can't be at the top of all the search engines.
		He admitted to having egg on his face because he worked on the basis that if I can't be found then how good would my internet marketing skills be with his business.
	www.puremarketing.co.uk (580 words)

	``Quantum strategies'' abstract (Site not responding. Last check: 2007-11-04)
		Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic).
		A mixed strategy deviating from the equilibrium strategy cannot increase a player's expected payoff.
		We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.
	math.ucsd.edu /~dmeyer/papers/qstrat/abs.html (167 words)

	EVOLESS
		Behavioral strategies are frequently analyzed with a series of mathematical techniques called Game Theory - developed by John von Neumann - inspired by games like chess - best move depends on opponents moves.
		An Evolutionarily Stable Strategy (ESS) is defined as a strategy which, if most members of a population adopt it, then no mutant strategy can invade the population under natural selection.
		In general, if strategy I is an evolutionarily stable strategy, it must have the property that, if almost all members of the population adopt I, then the fitness of these typical members is greater than that of any possible mutant - otherwise the mutant could invade the population.
	core.ecu.edu /biol/summersk/summerwebpage/biol3520/EVOLESS.htm (701 words)

	PRACTICE EXAM
		Similarly, hiring and firing workers is not a good strategy when workers are scarce because of low unemployment rates.
		The capacity lag strategy is the most moderate of the strategies and the least conservative.
		The costs involved in using a chase strategy are mainly in holding inventory, including the cost of obsolete or perishable items that may have to be discarded.
	www.cbpa.ewu.edu /~pnemetzmills/OMch9/pracanswers.html (1250 words)

	Finding Mixed Strategies with Small Supports in Extensive Form Games - Koller, Megiddo (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		One measure for the size of a mixed strategy is the number of strategies in its support---the set of pure strategies to which it gives positive probability.
		This paper investigates the existence of "small" mixed strategies in extensive form games, and how such strategies can be used to create more efficient algorithms.
		Mixed strategies are realization equivalent if and only if they have the same realization plan....
	citeseer.lcs.mit.edu /koller95finding.html (564 words)

	Neal E. Young / search
		This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from a multi-set of pure strategies of size logarithmic in the number of pure strategies available to the opponent.
		For exponentially large games, for which even representing an optimal mixed strategy can require exponential space, it follows that there are near-optimal, linear-size strategies.
		These strategies are easy to play and serve as small witnesses to the approximate value of the game.
	www.cs.ucr.edu /~neal/?q=topic:OTHER&t=other (572 words)

	Jupiter Communications - Pure-Plays Must Consider Storefront Strategies (Site not responding. Last check: 2007-11-04)
		All data, opinions, and projections are based on Jupiter's judgment at the time of publication and are subject to change.
		Pure-plays should consider one of three storefront strategies or some combination of the three.
		Dell, on the other hand, which is more likely to sell to seasoned computer users, would accrue fewer benefits from such a channel.
	www-old.jup.com /research/dcs/samples/notes/042 (538 words)

	No Title (Site not responding. Last check: 2007-11-04)
		Description: The goal of this assignment is to build a pure paging memory management component and study the different management strategies: Random, FIFO, LRU, and LFU.
		The study is to determine under what circumstances will one strategy be more efficient over the other by measuring the number of page faults that occur.
		Build 4 job-sets on your own for each strategy such that the strategy is the clear winner as compared to the other strategies.
	www.cse.uconn.edu /~eugene/classes/cse258/project-3/index.html (684 words)

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