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	PlanetMath: strategy
		A mixed strategy is an assignment of a probability to each pure strategy.
		It defines a probability over the strategies, and reflect that, rather than choosing a particular pure strategy, the player will randomly select a pure strategy based on the distribution given by their mixed strategy.
		This is version 4 of strategy, born on 2002-07-24, modified 2002-07-28.
	planetmath.org /encyclopedia/Strategy2.html (192 words)

	Payoff matrix - Wikipedia, the free encyclopedia
		In both these examples, the strategy sets for both players have the same cardinality; more significantly, the payoff matrices are symmetric in regard to the players.
		A mixed strategy profile is an association of mixed strategies to players, that is an m-tuple of mixed strategies
		The expectation of F relative to Pr is the extension of F to mixed strategies.
	en.wikipedia.org /wiki/Payoff (814 words)

	[No title]
		That is, some mixed strategy guarantees P1 a higher (expected) payoff than his maximin pure strategy does.
		That is, some mixed strategy for P2 holds P1 down to a lower (expected) payoff than P2's minimax pure strategy does.
		Moreover, when P1 and P2 use their maximin and minimax (respectively) mixed strategies, the result is an equilibrium, i.e., given the strategy choice of the other player, neither player could do better by using any other pure or mixed strategy.
	userpages.umbc.edu /~nmiller/POLI388/MIXED.htm (803 words)

	Nash equilibrium - Wikipedia, the free encyclopedia
		In game theory, the Nash equilibrium (named after John Nash, who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy.
		If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
		Let (S, f) be a game, where S is the set of strategy profiles and f is the set of payoff profiles.
	en.wikipedia.org /wiki/Nash_equilibrium (2253 words)

	Street-Works (Site not responding. Last check: 2007-11-03)
		With our track record as developers and consultants in over 25 million square feet of mixed- use development, we know better than most when mixed-use as a strategy is appropriate and when it is not.
		With the ability to develop, evaluate and test strategies in the market, we are then able to create “realistic expectations” that help us form viable program solutions and physical plans that survive the scrutiny of your equity.
		It should be a strategy to help leverage and spread the risk of your development across many uses, making it an even stronger concept from a financial standpoint.
	www.street-works.com /news.asp?nid=17 (545 words)

	Evolutionary Games Glossary
		Put another way, when its frequency is 1.0 other strategies cannot enter the population and in situations where it appears as a mutant, it increases to fixation.
		Satelliting may be an evolutionarily stable strategy (where at some frequency it produces the same lifetime reproductive success as alternative strategies such as advertisement) or a simple contingent behavior induced by, for example, poor physiological state.
		As with other definitions, the human term strategy that implies conscious thought is used as a shorthand; no conscious planning is required, even though it might appear that the behaviors are rational and planned in the human sense.
	www.holycross.edu /departments/biology/kprestwi/behavior/ESS/game_defs.html (1909 words)

	Notes to Evolutionary Game Theory
		In a mixed strategy, a player assigns a probability to each pure strategy, and chooses which strategy to play using a randomization device.
		For the Hawk-Dove game, one mixed strategy would assign equal probabilities to playing Hawk or Dove, and decide which to play in a given case by flipping a fair coin.
		Of course, Nowak and May were speaking somewhat loosely when they referred to this behavior as "chaotic." Since there are only finitely many states of the population, it must be the case that this dynamical system will eventually settle into a cycle (although it may not repeat itself for a very long time).
	plato.stanford.edu /entries/game-evolutionary/notes.html (578 words)

	Lecture 4 Bräss' Paradox, and more on Mixed Strategy (Site not responding. Last check: 2007-11-03)
		Playing a mixed strategy means that the moves made by the players (in the second step above) are not made deterministically.
		Each player wants to maximize his profit, and since he does not know what strategy the other one is using, he wants to maximize his expected profit irrespective of what the opponent plays.
		The reason for this is if column player knows row player's mixed strategy, the column player can choose the column to maximize the expected payoff (instead of getting a weighted average over all columns).
	www.cse.iitd.ernet.in /~rahul/cs905/lecture4 (700 words)

	[No title]
		A mixed strategy with p = 0 or p = 1 is called a “degenerate” mixed strategy.
		It can be seen that P1's maximin mixed strategy is [p =.75], and that this mixed strategy guarantees P1 a higher payoff (2.50) than P1's maximin pure strategy does (2.00).
		It is only “non-strictly” determined because the equilibrium outcome is in mixed strategies rather than pure strategies.
	research.umbc.edu /~nmiller/POLI388/MIXED.EXAMPLE.htm (391 words)

	Constructing and manipulating games (Site not responding. Last check: 2007-11-03)
		A mixed strategy profile is a specification of a numeric value (usually interpreted as a probability) for each strategy in the support.
		Similarly, a behavior strategy profile is a specification of a numeric value (usually interpreted as a probability) for each action in the support.
		In most cases, the value assigned to an action or strategy is interpreted as the probability with which a player adopts the corresponding action or strategy.
	econweb.tamu.edu /gambit/doc/manual-0.97.0.6/x1367.html (4292 words)

	Introduction to Game Theory -- simple, two-strategy examples
		Strategies: The particular behavior or suite of behaviors that a player uses is termed a strategy (see important note).
		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.
	www.holycross.edu /departments/biology/kprestwi/behavior/ESS/games_intro.html (7040 words)

	Mixed Strategies
		Every pure strategy that is played as part of a mixed strategy equilibrium has the same expected value.
		An important case where mixed strategies at equilibrium are always efficient is the case of constant-sum games.
		Interestingly, the optimal mixed strategies can be computed using linear programming, one linear program for each of the two players.
	mat.gsia.cmu.edu /QUANT/NOTES/chap10/node5.html (631 words)

	Mixed Strategy
		The mixed strategy selects an action with some probability based on the EW of the action.
		On the other hand, if the curves were squeezed towards the centre of the horizontal axis, a deterministic strategy would be employed with the action with the greatest EW always being selected.
		Against an experienced human player, we would expect that the mixed strategy would perform better than a deterministic one, but due to the difficulty in obtaining results from games played against human players, a significant number of results have not been collected.
	www.csse.monash.edu.au /hons/projects/2000/Jason.Carlton/html/node38.html (744 words)

	Zero-Sum
		In addition to the two obvious strategies, head and tail, a player can "randomize" her strategy by offering either a head or a tail, at random, with specific probabilities.
		Such a randomized strategy is called a "mixed strategy." The obvious two strategies, heads and tails, are called "pure strategies." There are infinitely many mixed strategies corresponding to the infinitely many ways probabilities can be assigned to the two pure strategies.
		The game of matching pennies has a solution in mixed strategies, and it is to offer heads or tails at random with probabilities 0.5 each way.
	william-king.www.drexel.edu /top/eco/game/zerosum.html (1643 words)

	voluntaryXchange: Is Santa a Mixed Strategy?
		Perhaps Santa Claus is a way for a parent to pursue a mixed strategy.
		The parents strategies in a child-rearing game are a mix of carrots and sticks.
		Parents' stick strategies usually involve punishment, but not new toy starvation (of course, that could be more of a general proposition invoked by rote on every trip to the store).
	voluntaryxchange.typepad.com /voluntaryxchange/2004/12/is_santa_a_mixe.html (264 words)

	EconPapers: Mixed-Strategy Equilibrium Implementation
		It is shown that, in environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure.
		Mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure.
		The key condition, mixed virtual monotonicity, is shown to be very weak.
	econpapers.repec.org /paper/ecmnasm04/485.htm (351 words)

	Mixed Strategy in Game Theory - Game Theory .net
		A strategy consisting of possible moves and a probability distribution (collection of weights) which corresponds to how frequently each move is to be played.
		A player would only use a mixed strategy when she is indifferent between several pure strategies, and when keeping the opponent guessing is desirable - that is, when the opponent can benefit from knowing the next move.
		Try to generate mixed strategies on the applets page.
	www.gametheory.net /Dictionary/MixedStrategy.html (101 words)

	E-commerce Technology: Game Theory (Site not responding. Last check: 2007-11-03)
		This analysis has led us to the dominant strategy equilibrium of the game---neither agent could, through a unilateral action, improve his payoff.
		Interestingly, this is the only outcome that is not a Pareto efficient outcome---both agents could be better off had they been able to coordinate on {UP, LEFT}.
		Notice that there is no dominant strategy equilibrium to this game.
	www.ecommerce.ncsu.edu /technology/topic_GameTheory.html (748 words)

	Mixed strategy profiles (Site not responding. Last check: 2007-11-03)
		returns the behavior strategy profile corresponding to this mixed strategy profile.
		sets the profile to the centroid of the strategy space, in which each player plays all of his strategies with equal probability.
		Probabilities for all strategies that appear in the unrestricted game, but not the restricted game, are set to zero.
	econweb.tamu.edu /gambit/doc/libgambit-0.97.1.6/x1908.html (348 words)

	Unknown (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath (Site not responding. Last check: 2007-11-03)
		This paper reports on a set of experiments designed to discriminate among the possible sources of the failure of the unique mixed strategy minimax equilibrium of the O'Neill (1987) game.
		Second, the design allows one to discriminate among a set of mixed strategies which generate distributions over actions and wins similar to the distributions generated by the minimax strategy.
		This is accomplished by introducing a new methodology for eliciting mixed strategies, which overcomes some of the difficulties with previous experimental attempts to directly observe mixed strategies.
	smealsearch2.psu.edu /590.html (375 words)

	MPR: Mixed reaction to Bush's bird flu strategy
		A fresh outbreak of the bird flu virus strain H5N1 that is potentially deadly for humans has been confirmed in a village in the Urals, according to Russian health officials.
		President Bush outlined a $7.1 billion strategy Tuesday to prepare for the danger of a pandemic outbreak of avian flu.
		Paul, Minn. — (AP) - President Bush outlined a $7.1 billion strategy Tuesday to prepare for the danger of a pandemic influenza outbreak, saying he wanted to stockpile enough vaccine to protect 20 million Americans against the current strain of bird flu as a first wave of protection.
	news.minnesota.publicradio.org /features/2005/11/01_tonessb_birdflureax (1012 words)

	SSRN-Contests: A Unique, Mixed Strategy Equilibrium by Michael Landsberger, Boris Tsirelson
		Derivation of pure strategy non-monotone equilibria when signals are interdependent and continuously distributed has not been explored in the literature, and it is certainly a non trivial matter; mixed strategy equilibria pose additional problems.
		Assuming a multinormal distribution of signals, we were able to establish a mixed strategy equilibrium and prove that this is the only equilibrium in the class of all equilibria.
		We showed some pitfalls one may encounter when trying to impose a-priori (reasonable) restrictions on strategies, or trying to conduct the analysis assuming a general class of signal distribution.
	papers.ssrn.com /abstract=288810 (282 words)

	[No title]
		This should be compared with a slightly different statement: “If player X plays his optimal mixed strategy, then the expected payoff of player Y is the same no matter which strategy player Y chooses, pure or mixed”.
		For games with 3 or more players, it is not always true that when a player has a dominant strategy, a Nash equilibrium in pure strategy always exists.
		With some thought, it can be seen that Z has a dominant strategy (STUDY), but the game does not have a Nash equilibrium.
	www.cs.pitt.edu /~utp/cs3150/lecture/HW1solution.doc (1294 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Prisoners' dilemma: c > a > d > b (e.g., 3,3 0,5 5,0 1,1) (1,1) is the stable or rational strategy (equilibrium act pair), but (3,3) is a better strategy; that's the dilemma.
		Value of Games Theory Insights on competitive and cooperative strategies and consequences, as well as short-term vs. long-term objectives and public good vs. private interest.
		Repeated plays of the Prisoners' Dilemma game have indicated that Tit-for-Tat beats many other strategies and thus potentially a good genetic strategy.
	www.cob.sjsu.edu /yu_o/bus215/Bus215-6-2002.ppt (290 words)

	[No title]
		Step 1: Remove strategy $6 of each player since $6 is strictly dominated by $5 Step 2: Remove strategy $1 of each player since $1 is strictly dominated by $2 in the reduced game.
		Step 3: Remove strategy $5 of each player since $5 is strictly dominated by $4 in the reduced game.
		Let (r, 1—r) be the mixed strategy played by the Employee, and (q, 1—q) be the mixed strategy played by the manager, as indicated in the above table.
	www.andrew.cmu.edu /user/xinming/gametheory/midtermsol.doc (1376 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Obviously, this applies if player 1 chooses p* such that player 2 is indifferent between his two pure strategies s21 and s22 and any mixture of them, and player 2 chooses q* such that player 1 is indifferent between his two pure strategies s11 and s12 and any mixture of them.
		Cheng, L.K. and M. Zhu (1995), "Mixed strategy Nash equilibrium based upon expected utility and quadratic utility", Games and Economic Behavior, 9, 139-150.
		The "core" of the prove of (a) is: - Let p° = p1 + p+p3 express the frequency of "Pollute", irrespective of its being played as a pure or as a mixed strategy.
	www.igidr.ac.in /~babu/law/slides/session2b.doc (1222 words)

	Midterm Review Questions
		(b) There is a mixed strategy Nash equilibrium combination.
		If one player plays this mixed strategy, what is the expected utility
		the different combinations of strategies, the shape of the diagram is what is important, particularly at
	faculty.washington.edu /wtalbott/phil466/midrev.htm (1404 words)

	Winning Poker Strategy - Jonathan Schaeffer
		Play Winning Poker - Strategy articles, news and a variety of instructional resources for both casino and online play.
		Poker Forums - General discussion forum with sections related to strategy, new players, and bragging about big wins.
		Poker Tips - Strategy articles as well as cardroom reviews and other online playing information.
	hidrogas.i8.com /Jonathan_Schaeffer (1072 words)

	BBC NEWS \| Middle East \| Israel's strategy produces mixed results
		In Gaza, Hamas is pursuing its military strategy to escalate armed resistance so that any Israeli withdrawal would be seen as a defeat rather than a victory for Ariel Sharon.
		Last month Hamas guerrillas in Gaza blew up a hated and heavily fortified Israeli outpost, killing one soldier.
		Most Palestinian analysts believe they'll remain true to that strategy whether through suicide attacks or some other way.
	news.bbc.co.uk /2/hi/middle_east/3896431.stm (694 words)

	EconPapers: Estimating a mixed strategy employing maximum entropy
		Abstract: Generalized maximum entropy may be used to estimate mixed strategies subject to restrictions from game theory.
		We use this method to estimate the mixed strategies of duopolistic airlines.
		This item may be available elsewhere in EconPapers: Search for items with the same title.
	econpapers.repec.org /paper/cdlagrebk/780.htm (198 words)

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