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Scaffolding

From Wikipedia, the free encyclopedia
Bamboo scaffolding in Hong Kong
condominium in periodical (every 10-15 years) large scale repairing/maintenance in Japan under regulation. In most cases the entire building is covered by steel scaffolding and mesh for easy work and safety. Typically it continues 3-5 weeks per planned schedule.
Scaffolding, 10 months after Tokyo Skytree construction start
Scaffolding is a temporary structure used to support people and material in the construction or repair of buildings and other large structures. It is usually a modular system of metal pipes or tubes, although it can be from other materials. Bamboo is frequently used in Asia.[1]

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[edit]In the ancient world

The Berlin Foundry Cup depicts scaffolding in ancient Greece (early 5th century BC). The ancient Egyptians, Nubians and Chinese are also recorded as having used scaffolding-like structures to build tall buildings.

[edit]In the modern day

This European Standard specifies performance requirements and methods of structural and general design for access and working scaffolds. Requirements given are for scaffold structures that rely on the adjacent structures for stability. In general these requirements also apply to other types of working scaffolds.
The purpose of a working scaffold is to provide a safe place of work with safe access suitable for the work being done. This document sets out performance requirements for working scaffolds. These are substantially independent of the materials of which the scaffold is made. The standard is intended to be used as the basis for enquiry and design.
Thus the requirements of BS EN 12811-1. TG20 is largely based on BS 5973 with extracts taken directly from the old code, it also uses permissible stress design method. However, TG20 received a mixed response from the UK industry and as a result TG20 is being re-written and the new version is due for release sometime in 2008. This is the reason for the 'limbo' situation. Until the release of the revised TG20 the HSE continue to allow scaffold to be built in accordance with BS 5973.[2][clarification needed (technical jargon)]

[edit]Materials

The basic components of scaffolding are tubes, couplers and boards.
Extensive scaffolding on a building in downtown Cincinnati, Ohio. This type of scaffolding is called pipe staging.
Assembly of bamboo scaffolding cantilevered over a Hong Kong street
The basic lightweight tube scaffolding that became the standard and revolutionised scaffolding, becoming the baseline for decades, was invented and marketed in the mid-1950s. With one basic 24 pound unit a scaffold of various sizes and heights could be assembled easily by a couple of labourers without the nuts or bolts previously needed.[3]
Tubes are usually made either of steel or aluminium, although there is composite scaffolding, which uses filament-wound tubes of glass fibre in a nylon or polyester matrix, because of the high cost of composite tube, it is usually only used when there is a risk from overhead electric cables that cannot be isolated. If steel, they are either 'black' or galvanised. The tubes come in a variety of lengths and a standard diameter of 48.3 mm. (1.5 NPS pipe). The chief difference between the two types of metal tubes is the lower weight of aluminium tubes (1.7 kg/m as opposed to 4.4 kg/m) and also their greater flexibility and so their lower resistance to force. Tubes are generally bought in 6.3 m lengths and can then be cut down to certain typical sizes. Most large companies will brand their tubes with their name and address in order to deter theft.
Boards provide a working surface for scaffold users. They are seasoned wood and come in three thicknesses (38 mm (usual), 50 mm and 63 mm) are a standard width (225 mm) and are a maximum of 3.9 m long. The board ends are protected either by metal plates called hoop irons or sometimes nail plates, which often have the company name stamped into them. Timber scaffold boards in the UK should comply with the requirements of BS 2482. As well as timber, steel or aluminium decking is used, as well as laminate boards. In addition to the boards for the working platform, there are sole boards which are placed beneath the scaffolding if the surface is soft or otherwise suspect, although ordinary boards can also be used. Another solution, called a scaffpad, is made from a rubber base with a base plate moulded inside; these are desirable for use on uneven ground since they adapt, whereas sole boards may split and have to be replaced.
A short section of steel scaffold tube.
Couplers are the fittings which hold the tubes together. The most common are called scaffold couplers, and there are three basic types: right-angle couplersputlog couplers and swivel couplers. To join tubes end-to-end joint pins (also called spigots) or sleeve couplers are used. Only right angle couplers and swivel couplers can be used to fix tube in a 'load-bearing connection'. Single couplers are not load-bearing couplers and have no design capacity.
Other common scaffolding components lnclude base plates, laddersropes, anchor ties, reveal ties, gin wheels, sheeting, etc. Most companies will adopt a specific colour to paint the scaffolding with, in order that quick visual identification can be made in case of theft. All components that are made from metal can be painted but items that are wooden should never be painted as this could hide defects. Despite the metric measurements given, many scaffolders measure tubes and boards in imperial units, with tubes from 21 feet down and boards from 13 ft down.
Bamboo scaffolding is widely used in Hong Kong, with nylon straps tied into knots as couplers.[4]

[edit]Basic scaffolding

The key elements of a scaffold are standardsledgers and transoms. The standards, also called uprights, are the vertical tubes that transfer the entire mass of the structure to the ground where they rest on a square base plate to spread the load. The base plate has a shank in its centre to hold the tube and is sometimes pinned to a sole board. Ledgers are horizontal tubes which connect between the standards. Transoms rest upon the ledgers at right angles. Main transoms are placed next to the standards, they hold the standards in place and provide support for boards; intermediate transoms are those placed between the main transoms to provide extra support for boards. In Canada this style is referred to as "English". "American" has the transoms attached to the standards and is used less but has certain advantages in some situations. Since scaffolding is a physical structure, it is possible to go in and come out of scaffolding.
Scaffolding in Tretyakovsky Proyezd, Moscow
As well as the tubes at right angles there are cross braces to increase rigidity, these are placed diagonally from ledger to ledger, next to the standards to which they are fitted. If the braces are fitted to the ledgers they are called ledger braces. To limit sway a facade brace is fitted to the face of the scaffold every 30 metres or so at an angle of 35°-55° running right from the base to the top of the scaffold and fixed at every level.
Of the couplers previously mentioned, right-angle couplers join ledgers or transoms to standards, putlog or single couplers join board bearing transoms to ledgers - Non-board bearing transoms should be fixed using a right-angle coupler. Swivel couplers are to connect tubes at any other angle. The actual joints are staggered to avoid occurring at the same level in neighbouring standards.
Basic scaffold dimensioning terms. No boards, bracing or couplers shown
The spacings of the basic elements in the scaffold are fairly standard. For a general purpose scaffold the maximum bay length is 2.1 m, for heavier work the bay size is reduced to 2 or even 1.8 m while for inspection a bay width of up to 2.7 m is allowed.
The scaffolding width is determined by the width of the boards, the minimum width allowed[where?] is 600 mm but a more typical four-board scaffold would be 870 mm wide from standard to standard. More heavy-duty scaffolding can require 5, 6 or even up to 8 boards width. Often an inside board is added to reduce the gap between the inner standard and the structure.
The lift height, the spacing between ledgers, is 2 m, although the base lift can be up to 2.7 m. The diagram above also shows a kicker lift, which is just 150 mm or so above the ground.
Transom spacing is determined by the thickness of the boards supported, 38 mm boards require a transom spacing of no more than 1.2 m while a 50 mm board can stand a transom spacing of 2.6 m and 63 mm boards can have a maximum span of 3.25 m. The minimum overhang for all boards is 50 mm and the maximum overhang is no more than 4x the thickness of the board.

[edit]Foundations

Good foundations are essential. Often scaffold frameworks will require more than simple base plates to safely carry and spread the load. Scaffolding can be used without base plates on concrete or similar hard surfaces, although base plates are always recommended. For surfaces like pavements or tarmac base plates are necessary. For softer or more doubtful surfaces sole boards must be used, beneath a single standard a sole board should be at least 1,000 cm² with no dimension less than 220 mm, the thickness must be at least 35 mm. For heavier duty scaffold much more substantial baulks set in concrete can be required. On uneven ground steps must be cut for the base plates, a minimum step size of around 450 mm is recommended. A working platform requires certain other elements to be safe. They must be close-boarded, have double guard rails and toe and stop boards. Safe and secure access must also be provided.
Scaffolding showing required protection of a working platform with maximum dimensions. Butt-board not visible. No couplers shown

[edit]Ties

The Holy Trinity Church in Vladimir, with scaffolding wrapped in safety mesh.
Scaffolds are only rarely independent structures. To provide stability for a scaffolding (at left) framework ties are generally fixed to the adjacent building/fabric/steelwork.
General practice is to attach a tie every 4m on alternate lifts (traditional scaffolding). Prefabricated System scaffolds require structural connections at all frames - ie.2-3m centres (tie patterns must be provided by the System manufacturer/supplier). The ties are coupled to the scaffold as close to the junction of standard and ledger (node point) as possible. Due to recent regulation changes, scaffolding ties must support +/- loads (tie/butt loads) and lateral (shear) loads.
Due to the different nature of structures there is a variety of different ties to take advantage of the opportunities.
Through ties are put through structure openings such as windows. A vertical inside tube crossing the opening is attached to the scaffold by a transom and a crossing horizontal tube on the outside called a bridle tube. The gaps between the tubes and the structure surfaces are packed or wedged with timber sections to ensure a solid fit.
Box ties are used to attach the scaffold to suitable pillars or comparable features. Two additional transoms are put across from the lift on each side of the feature and are joined on both sides with shorter tubes called tie tubes. When a complete box tie is impossible a l-shaped lip tie can be used to hook the scaffold to the structure, to limit inward movement an additional transom, a butt transom, is place hard against the outside face of the structure.
Sometimes it is possible to use anchor ties (also called bolt ties), these are ties fitted into holes drilled in the structure. A common type is a ring bolt with an expanding wedge which is then tied to a node point.
Scaffolding by Balfour & Beatty during refurbishment of the Waverley Station roof, Edinburgh 2011
The least 'invasive' tie is a reveal tie. These use an opening in the structure but use a tube wedged horizontally in the opening. The reveal tube is usually held in place by a reveal screw pin (an adjustable threaded bar) and protective packing at either end. A transom tie tube links the reveal tube to the scaffold. Reveal ties are not well regarded, they rely solely on friction and need regular checking so it is not recommended that more than half of all ties be reveal ties.
If it is not possible to use a safe number of ties rakers can be used. These are single tubes attached to a ledger extending out from the scaffold at an angle of less than 75° and securely founded. A transom at the base then completes a triangle back to the base of the main scaffold.

[edit]Specialty scaffolding

[edit]Putlog scaffold

In addition to the putlog couplers (discussed above, there are also putlog tubes. These have a flattened end or have been fitted with a blade. This feature allows the end of the tube to be inserted into or rest upon the brickwork of the structure.
A putlog scaffold may also be called a bricklayer's scaffold. As such, the scaffold consists only of a single row of standards with a single ledger. The putlogs are transoms - attached to the ledger at one end but integrated into the bricks at the other.
Spacing is the same on a putlog scaffold as on a general purpose scaffold, and ties are still required. In recent years a number of new innovations have meant an increased scope of use for scaffolding, such as ladderbeams for spanning spaces that cannot accommodate standards and the increased used of sheeting and structure to create temporary roofs.

[edit]Pump-jack

A pump-jack is type of portable scaffolding system. The scaffold rests on supports attached to two or more vertical posts. The user raises the scaffolding by pumping the foot pedals on the supports, like an automobile jack. For U.S. requirements and guidelines on pump-jacks – including a diagram – see the U.S. Department of Labor website.

[edit]Standards

The widespread use of scaffolding systems, along with the profound importance that they earned in modern applications such as civil engineering projects and temporary structures, led to the definition of a series of standards covering a vast number of specific issues involving scaffolding. Among the standards there are:[5]

[edit]See also

[edit]References


Chicken (game)

From Wikipedia, the free encyclopedia
The game of chicken, also known as the hawk-dove game or snow-drift game, is an influential model of conflict for two players in game theory. The principle of the game is that while each player prefers not to yield to the other, the worst possible outcome occurs when both players do not yield.
The name "chicken" has its origins in a game in which two drivers drive towards each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a "chicken," meaning a coward; this terminology is most prevalent in political science and economics. The name "Hawk-Dove" refers to a situation in which there is a competition for a shared resource and the contestants can choose either conciliation or conflict; this terminology is most commonly used in biology andevolutionary game theory. From a game-theoretic point of view, "chicken" and "hawk-dove" are identical; the different names stem from parallel development of the basic principles in different research areas.[1] The game has also been used to describe the mutual assured destruction ofnuclear warfare, especially the sort of brinkmanship involved in the Cuban Missile Crisis.[2]

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[edit]Popular versions

The game of chicken models two drivers, both headed for a single lane bridge from opposite directions. The first to swerve away yields the bridge to the other. If neither player swerves, the result is a costly deadlock in the middle of the bridge, or a potentially fatal head-on collision. It is presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided). Additionally, a crash is presumed to be the worst outcome for both players. This yields a situation where each player, in attempting to secure his best outcome, risks the worst.
The phrase game of chicken is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain, and only pride stops them from backing down. Bertrand Russell famously compared the game of Chicken to nuclear brinkmanship:
Since the nuclear stalemate became apparent, the Governments of East and West have adopted the policy which Mr. Dulles calls 'brinkmanship'. This is a policy adapted from a sport which, I am told, is practiced by some youthful degenerates. This sport is called 'Chicken!'. It is played by choosing a long straight road with a white line down the middle and starting two very fast cars towards each other from opposite ends. Each car is expected to keep the wheels of one side on the white line. As they approach each other, mutual destruction becomes more and more imminent. If one of them swerves from the white line before the other, the other, as he passes, shouts 'Chicken!', and the one who has swerved becomes an object of contempt. As played by irresponsible boys, this game is considered decadent and immoral, though only the lives of the players are risked. But when the game is played by eminent statesmen, who risk not only their own lives but those of many hundreds of millions of human beings, it is thought on both sides that the statesmen on one side are displaying a high degree of wisdom and courage, and only the statesmen on the other side are reprehensible. This, of course, is absurd. Both are to blame for playing such an incredibly dangerous game. The game may be played without misfortune a few times, but sooner or later it will come to be felt that loss of face is more dreadful than nuclear annihilation. The moment will come when neither side can face the derisive cry of 'Chicken!' from the other side. When that moment is come, the statesmen of both sides will plunge the world into destruction.[2]
Brinkmanship involves the introduction of an element of uncontrollable risk: even if all players act rationally in the face of risk, uncontrollable events can still trigger the catastrophic outcome.[3] In the "chickie run" scene from the film Rebel Without a Cause, this happens when Buzz cannot escape from the car and dies in the crash. The opposite scenario occurs in Footloose where Ren McCormack is stuck in his tractor and hence wins the game as he can't play "chicken". The basic game-theoretic formulation of Chicken has no element of variable, potentially catastrophic, risk, and is also the contraction of a dynamic situation into a one-shot interaction.
The hawk-dove version of the game imagines two players (animals) contesting an indivisible resource who can choose between two strategies, one more escalated than the other.[4] They can use threat displays (play Dove), or physically attack each other (play Hawk). If both players choose the Hawk strategy, then they fight until one is injured and the other wins. If only one player chooses Hawk, then this player defeats the Dove player. If both players play Dove, there is a tie, and each player receives a payoff lower than the profit of a hawk defeating a dove.

[edit]Game theoretic applications

[edit]Chicken

SwerveStraight
SwerveTie, TieLose, Win
StraightWin, LoseCrash, Crash
Fig. 1: A payoff matrix of Chicken
SwerveStraight
Swerve0, 0-1, +1
Straight+1, -1-10, -10
Fig. 2: Chicken with numerical payoffs
A formal version of the game of Chicken has been the subject of serious research in game theory.[5] Two versions of the payoff matrix for this game are presented here (Figures 1 and 2). In Figure 1, the outcomes are represented in words, where each player would prefer to win over tying, prefer to tie over losing, and prefer to lose over crashing. Figure 2 presents arbitrarily set numerical payoffs which theoretically conform to this situation. Here, the benefit of winning is 1, the cost of losing is -1, and the cost of crashing is -10.
Both Chicken and Hawk-Dove are anti-coordination games, in which it is mutually beneficial for the players to play different strategies. In this way, it can be thought of as the opposite of a coordination game, where playing the same strategy Pareto dominates playing different strategies. The underlying concept is that players use a shared resource. In coordination games, sharing the resource creates a benefit for all: the resource is non-rivalrous, and the shared usage creates positive externalities. In anti-coordination games the resource is rivalrous but non-excludable and sharing comes at a cost (or negative externality).
Because the loss of swerving is so trivial compared to the crash that occurs if nobody swerves, the reasonable strategy would seem to be to swerve before a crash is likely. Yet, knowing this, if one believes one's opponent to be reasonable, one may well decide not to swerve at all, in the belief that he will be reasonable and decide to swerve, leaving the other player the winner. This unstable situation can be formalized by saying there is more than one Nash equilibrium, which is a pair of strategies for which neither player gains by changing his own strategy while the other stays the same. (In this case, the pure strategy equilibria are the two situations wherein one player swerves while the other does not.)

[edit]Hawk-Dove

HawkDove
Hawk(V−C)/2, (V−C)/2V, 0
Dove0, VV/2, V/2
Fig. 3: Hawk-Dove game
HawkDove
HawkX, XW, L
DoveL, WT, T
Fig. 4: General Hawk-Dove game
In the biological literature, this game is referred to as Hawk-Dove. The earliest presentation of a form of the Hawk-Dove game was by John Maynard Smith and George Price in their 1973 Nature paper, "The logic of animal conflict".[6] The traditional [4][7]payoff matrix for the Hawk-Dove game is given in Figure 3, where V is the value of the contested resource, and C is the cost of an escalated fight. It is (almost always) assumed that the value of the resource is less than the cost of a fight, i.e., C > V > 0. If C ≤ V, the resulting game is not a game of Chicken but is instead a Prisoner's Dilemma.
The exact value of the Dove vs. Dove playoff varies between model formulations. Sometimes the players are assumed to split the payoff equally (V/2 each), other times the payoff is assumed to be zero (since this is the expected payoff to a war of attrition game, which is the presumed models for a contest decided by display duration).
While the Hawk-Dove game is typically taught and discussed with the payoffs in terms of V and C, the solutions hold true for any matrix with the payoffs in Figure 4, where W > T > L > X.[7]

[edit]Hawk-Dove variants

Biologists have explored modified versions of classic Hawk-Dove game to investigate a number of biologically relevant factors. These include adding variation in resource holding potential, and differences in the value of winning to the different players,[8]allowing the players to threaten each other before choosing moves in the game,[9] and extending the interaction to two plays of the game.[10]

[edit]Pre-commitment

One tactic in the game is for one party to signal their intentions convincingly before the game begins. For example, if one party were to ostentatiously disable their steering wheel just before the match, the other party would be compelled to swerve.[11]This shows that, in some circumstances, reducing one's own options can be a good strategy. One real-world example is a protester who handcuffs himself to an object, so that no threat can be made which would compel him to move (since he cannot move). Another example, taken from fiction, is found in Stanley Kubrick's Dr. Strangelove. In that film, the Russians sought to deter American attack by building a "doomsday machine," a device that would trigger world annihilation if Russia was hit by nuclear weapons or if any attempt were made to disarm it. However, the Russians failed to signal—they deployed their doomsday machine covertly.
Players may also make non-binding threats to not swerve. This has been modeled explicitly in the Hawk-Dove game. Such threats work, but must be wastefully costly if the threat is one of two possible signals ("I will not swerve"/"I will swerve"), or they will be costless if there are three or more signals (in which case the signals will function as a game of "Rock, Paper, Scissors").[9]

[edit]Best response mapping and Nash equilibria

Fig.5 - Reaction correspondences for both players in a discoordination game. Compare with replicator dynamic vector fields below
All anti-coordination games have three Nash equilibria. Two of these are pure contingent strategy profiles, in which each player plays one of the pair of strategies, and the other player chooses the opposite strategy. The third one is a mixed equilibrium, in which each player probabilisticallychooses between the two pure strategies. Either the pure, or mixed, Nash equilibria will be evolutionarily stable strategies depending upon whether uncorrelated asymmetries exist.
The best response mapping for all 2x2 anti-coordination games is shown in Figure 5. The variables x and y in Figure 5 are the probabilities of playing the escalated strategy ("Hawk" or "Don't swerve") for players X and Y respectively. The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of x. The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of y (the axes have not been rotated, so the dependent variable is plotted on the abscissa, and theindependent variable is plotted on the ordinate). The Nash equilibria are where the players' correspondences agree, i.e., cross. These are shown with points in the right hand graph. The best response mappings agree (i.e., cross) at three points. The first two Nash equilibria are in the top left and bottom right corners, where one player chooses one strategy, the other player chooses the opposite strategy. The third Nash equilibrium is a mixed strategy which lies along the diagonal from the bottom left to top right corners. If the players do not know which one of them is which, then the mixed Nash is an evolutionarily stable strategy (ESS), as play is confined to the bottom left to top right diagonal line. Otherwise an uncorrelated asymmetry is said to exist, and the corner Nash equilibria are ESSes.

[edit]Strategy polymorphism vs strategy mixing

The ESS for the Hawk-Dove game is a mixed strategy. Formal game theory is indifferent to whether this mixture is due to all players in a population choosing randomly between the two pure strategies (a range of possible instinctive reactions for a single situation) or whether the population is a polymorphic mixture of players dedicated to choosing a particular pure strategy(a single reaction differing from individual to individual). Biologically, these two options are strikingly different ideas. The Hawk-Dove game has been used as a basis for evolutionary simulations to explore which of these two modes of mixing ought to predominate in reality.[12]

[edit]Symmetry breaking

In both "Chicken" and "Hawk-Dove", the only symmetric Nash equilibrium is the mixed strategy Nash equilibrium, where both individuals randomly chose between playing Hawk/Straight or Dove/Swerve. This mixed strategy equilibrium is often sub-optimal—both players would do better if they could coordinate their actions in some way. This observation has been made independently in two different contexts, with almost identical results.[13]

[edit]Correlated equilibrium and Chicken

DareChicken
Dare0,07,2
Chicken2,76,6
Fig. 6: A version of Chicken
Consider the version of "Chicken" pictured in Figure 6. Like all forms of the game, there are three Nash equilibria. The two pure strategy Nash equilibria are (DC) and (CD). There is also a mixed strategy equilibrium where each player Dares with probability 1/3. It results in expected payoffs of 14/3 = 4.667 for each player.
Now consider a third party (or some natural event) that draws one of three cards labeled: (CC), (DC), and (CD). This exogenous draw event is assumed to be uniformly at random over the 3 outcomes. After drawing the card the third party informs the players of the strategy assigned to them on the card (but not the strategy assigned to their opponent). Suppose a player is assigned D, he would not want to deviate supposing the other player played their assigned strategy since he will get 7 (the highest payoff possible). Suppose a player is assigned C. Then the other player has been assigned C with probability 1/2 and D with probability 1/2 (due to the nature of the exogenous draw). The expected utility of Daring is 0(1/2) + 7(1/2) = 3.5 and the expected utility of chickening out is 2(1/2) + 6(1/2) = 4. So, the player would prefer to chicken out.
Since neither player has an incentive to deviate from the drawn assignments, this probability distribution over the strategies is known as a correlated equilibrium of the game. Notably, the expected payoff for this equilibrium is 7(1/3) + 2(1/3) + 6(1/3) = 5 which is higher than the expected payoff of the mixed strategy Nash equilibrium.

[edit]Uncorrelated asymmetries and solutions to the Hawk-Dove game

Although there are three Nash equilibria in the Hawk-Dove game, the one which emerges as the evolutionarily stable strategy (ESS) depends upon the existence of any uncorrelated asymmetry in the game (in the sense of anti-coordination games). In order for row players to choose one strategy and column players the other, the players must be able to distinguish which role (column or row player) they have. If no such uncorrelated asymmetry exists then both players must choose the same strategy, and the ESS will be the mixing Nash equilibrium. If there is an uncorrelated asymmetry, then the mixing Nash is not an ESS, but the two pure, role contingent, Nash equilibria are.
The standard biological interpretation of this uncorrelated asymmetry is that one player is the territory owner, while the other is an intruder on the territory. In most cases, the territory owner plays Hawk while the intruder plays Dove. In this sense, the evolution of strategies in Hawk-Dove can be seen as the evolution of a sort of prototypical version of ownership. Game-theoretically, however, there is nothing special about this solution. The opposite solution—where the owner plays dove and the intruder plays Hawk—is equally stable. In fact, this solution is present in a certain species of spider; when an invader appears the occupying spider leaves. In order to explain the prevalence of property rights over "anti-property rights" one must discover a way to break this additional symmetry.[13]

[edit]Replicator dynamics

Fig 7a: Vector field for two population replicator dynamics and Hawk-Dove
Replicator dynamics is a simple model of strategy change commonly used in evolutionary game theory. In this model, a strategy which does better than the average increases in frequency at the expense of strategies that do worse than the average. There are two versions of the replicator dynamics. In one version, there is a single population which plays against itself. In another, there are two population models where each population only plays against the other population (and not against itself).
In the one population model, the only stable state is the mixed strategy Nash equilibrium. Every initial population proportion (except all Hawk and all Dove) converge to the mixed strategy Nash Equilibrium where part of the population plays Hawk and part of the population plays Dove. (This occurs because the only ESS is the mixed strategy equilibrium.) In the two population model, this mixed point becomes unstable. In fact, the only stable states in the two population model correspond to the pure strategy equilibria, where one population is composed of all Hawks and the other of all Doves. In this model one population becomes the aggressive population while the other becomes passive. This model is illustrated by the vector field pictured in Figure 7a. The one dimensional vector field of the single population model (Figure 7b) corresponds to the bottom left to top right diagonal of the two population model.
Fig. 7b: Vector field for single population replicator dynamics
The single population model presents a situation where no uncorrelated asymmetries exist, and so the best players can do is randomize their strategies. The two population models provide such an asymmetry and the members of each population will then use that to correlate their strategies. In the two population model, one population gains at the expense of another. Hawk-Dove and Chicken thus illustrate an interesting case where the qualitative results for the two different version of the replicator dynamics differ wildly.[14]

[edit]Related games

[edit]Brinkmanship

"Chicken" and "Brinkmanship" are often used synonymously in the context of conflict, but in the strict game-theoretic sense, "brinkmanship" refers to a strategic move designed to avert the possibility of the opponent switching to aggressive behavior. The move involves a credible threat of the risk of irrational behavior in the face of aggression. If player 1 unilaterally moves to A, a rational player 2 cannot retaliate since (A, C) is preferable to (A, A). Only if player 1 has grounds to believe that there is sufficient risk that player 2 responds irrationally (usually by giving up control over the response, so that there is sufficient risk that player 2 responds with A) player 1 will retract and agree on the compromise.

[edit]War of attrition

Like "Chicken", the "War of attrition" game models escalation of conflict, but they differ in the form in which the conflict can escalate. Chicken models a situation in which the catastrophic outcome differs in kind from the agreeable outcome, e.g., if the conflict is over life and death. War of attrition models a situation in which the outcomes differ only in degrees, such as a boxing match in which the contestants have to decide whether the ultimate prize of victory is worth the ongoing cost of deteriorating health and stamina.

[edit]Schedule Chicken & Project Management

The term "Schedule Chicken"[15] is used in project management and software development circles. The condition occurs when two or more areas of a product team claim they can deliver features at an unrealistically early date because each assumes the other teams are stretching the predictions even more than they are. This pretense continually moves forward past one project checkpoint to the next until feature integration begins or just before the functionality is actually due.
The practice of "Schedule Chicken"[16] often results in contagious schedules slips due to the inter-team dependencies and is difficult to identify and resolve, as it is in the best interest of each team not to be the first bearer of bad news. The psychological drivers underlining the "Schedule Chicken" behavior in many ways mimic the Hawk-Dove or Snowdrift model of conflict.[17]

[edit]See also

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