ADAPTATION: An aspect of the phenotype, whether behavioral or morphological that is heritable and that confers a reproductive advantage on its possessor(s) as compared to some alternative trait(s). Thus, the amplification of the genes partially responsible for these traits is due to Darwinian evolution. Traits that are relatively disadvantageous are termed non-adaptive or maladaptive.
Note that the term non-adaptive also often is used for traits that have no significant advantage or disadvantage with respect to each other as occurs in Wrightian evolution (genetic drift). Perhaps a better adjective for these traits is neutrally adaptive.
ASYMMETRY: Where there are differences in the competitiveness of the players. Thus, the outcome of a contest is not simply a matter of chance. Asymmetries can be due to many factors, for instance different ability, experience, motivation, present ownership, and/or condition.
BOUNDARY: In the mathematical sense used in a number of models at this site, a boundary is a frequency above or below which selection forces change from favoring some trait to favoring an alternative.
CONTEST: the game theory term for the competitive interaction that occurs when two or more individuals attempt to obtain the same resource item.
COOPERATIVE COMMUNICATION: where action by the receiver of a signal increases the fitness of both the signaler and receiver. Also see honest communication.
CURRENCY: units that either directly or indirectly measure fitness, examples are grandchildren, offspring, eggs, energy, time, chance of death, etc. In both games and optimality models, benefits and costs must be stated in a common currency and that currency must be used throughout the model. Attempting to find the correct currency is one of the most important aspects of modeling.
"DISHONEST" COMMUNICATION: where action by the receiver of a signal decreases the receivers fitness but increases the sender's fitness. Please note that dishonest is used as a shorthand; no ethical or moral dimensions are necessarily part of this definition. (synonyms --deceit, non-cooperative).
DISPLAY: a behavior that has been modified to serve as a form of communication. These conventional behavior patterns that have no chance of leading to injury. By contrast, fighting behavior is referred to as escalation and has some finite chance of injury. (thanks to Sue Riechert on this one!)
EQUILIBRIUM: In evolution, constancy, stasis. A population is in equilibrium when there is no change in the frequency of occurrence of competing phenotypes (e.g., behavioral strategies) or alleles in a population, measured over generational time.
ESCALATED CONFLICT: when a conflict moves to increasingly direct confrontation and perhaps fights. An often cited example of an escalated conflict occurs in red deer -- two well-matched males initially display acoustically by roaring, this may be followed by visual displays typified by parallel walks and may finally escalate into fights with antlers.
EVOLUTIONARILY STABLE STRATEGY (ESS): A strategy that cannot be displaced by any other known strategy. 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. It is a static condition. ESS's can come in two general types -- pure and mixed.
FITNESS (W): the sum of direct and indirect fitness. For our purposes, it is largely direct fitness which is usually defined as the number of grandchildren. However, many other definitions or stand-ins for fitness are often used -- for example, fecundity, number of mates, number of eggs, territory size, territory quality, etc. For more detailed information about fitness and especially about calculating relative fitness, press here.
"FIXED": a population genetics term -- a strategy and the "gene" that causes it are said to be fixed when their frequencies are 1.0 (i.e., no alternatives exist in the population).
FREQUENCY-DEPENDENCE: when the relative fitness of some phenotypic trait such as a behavioral strategy depends on how commonly certain events or interactions occur. In the context of games, these events would be certain types of contests. Imagine that an animal with a particular behavioral strategy (focal animal) can experience two particular type of interactions. Further, imagine that one of these interactions is beneficial to the focal animal while the other is detrimental. Clearly the fitness of the focal individual will depend on the relative frequencies of each type of interaction -- this is frequency dependence. (To see a detailed discussion of frequency-dependence that is tangential to game theory, press here.)
GAME: a series of contests between all strategies in proportion to their frequency. The summed outcome of these contests determines the outcome of a game; a game could be viewed as the interactions that occur over one generation although other definitions are certainly possible.
"HONEST" COMMUNICATION: a shorthand for cooperative communication, please note that intent and morality are not implied.
MIXED ESS: an ESS where individuals either (a) play different strategies a fixed portion of the time (e.g., Hawk 60% and Dove 40% -- termed a mixed strategy) such that no other mix would be any more successful or where (b) certain portions of individuals play one strategy all the time (e.g., always Hawk or Dove) such that the fitness of practitioners of each strategy is equal. (also see pure ESS and pure Strategy).
MIXED STRATEGY: when an individual plays two or more behavioral strategies, usually as a matter of probability (see Bishop and Cannings, 1978). Thus, selecting a random amount of time to display is an example of a mixed strategy. By contrast, a pure strategy involves selecting a particular strategy, for example, always "display for time t".
"N - PERSON GAME" (or "PLAYING THE FIELD"): terms to describe situations where an individual is not engaged at a certain moment in a contest with just one other individual (who employs a certain strategy) as in pairwise contests, but instead with many individuals. An explanation based on a plant simultaneously competing for water with many neighbors is developed in Riechert and Hammerstein (1983); the interested reader is urged to use this as a starting point as the explanation is quite clear. The rules for discovering whether or not there is a pure ESS for an example of this type of contest are somewhat different than for pairwise contests. This site does not consider n-person games.
OPTIMALITY: An optimal behavior is one that maximizes the difference between benefit and cost in some common currency -- for instance fitness, energy, time, rate, etc. Optimality theory is used to predict the best way to perform a behavior for a given set of environmental and physiological conditions. It makes predictions that are independent of the behaviors being used by other individuals.
PAIRWISE CONTESTS: Maynard Smith (1982) wrote about pairwise contests as games where two individuals face off against each other over some resource. The outcomes of these contests, if an individual engages in more than one, have additive effects on the individual's fitness. The games considered at this website involving sequential interactions of Hawk, Dove and Bourgeois are pairwise contests. The rules for determining whether or not an ESS exists in pairwise contests are somewhat different than those of a another model of interaction "playing the field".
PAYOFF: the net benefit (B-C) to a focal animal due to a single type of contest or interaction. In the honest vs. dishonest communication, the payoffs to the receiver were either B or C, while in the Hawk vs. Dove each strategy (Dove or Hawk) had two possible payoffs (one when playing against the same strategy, e.g. D vs. D, and the other against the opposite strategy, e.g. D vs. H. Multi-strategy games have even more payoffs, their number depending on the number of strategies being played.
PLAYER: in game theory, an individual engaged in a contest. Sometimes used broadly as a synonym for a strategy in a contest.
PURE ESS: an ESS where one strategy is fixed and all known alternatives are unable to invade since they have lower fitnesses (see mixed ESS).
PURE STRATEGY: A pure strategy is a set of behaviors that an individual will employ in a given set of circumstances. They are usually defined by some consistent element such as "display exactly time t" or "always be willing to fight for a resource". It contrasts with a mixed strategy where an individual plays two or more strategies at some probability. Note that a pure strategy does not need to be a single behavior -- it could be relatively complex,such as the behaviors exhibited by "Dove" ("display for a resource but retreat if attacked").
RESOURCE: any environmental feature (biotic or abiotic) of importance to an organism's fitness. Examples include food, nesting sites, shelter, mates, symbionts, or specific places in the environment that are favorable physiologically or for behavioral reasons. Contests are waged over resources.
SATELLITE: Usually used in discussions of sexual selection in regards to advertisement behaviors (generally by males). The classical example is from acoustic signaling where satellites are individuals who remain silent but take up a positions (usually hidden) near an actively advertising individual. They attempt to intercept females that approach the caller. Thus, they do not pay as large a cost as do the advertisers. 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.
STASIS: equilibrium, no generational change in allele (or the phenotype determined by the alleles) frequency.
STRATEGY: a behavior or set of behaviors used by an individual to deal with an important life-history problem (for example finding a mate, rearing young, obtaining food, etc.). 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. The use of the word "strategy" is simply a shorthand that expresses the appearance of the result of some behaviors. It is generally assumed that in most species strategies are largely innate, are produced by the usual genetic and developmental mechanisms, and are acted on by natural selection. However, strategies can also be learned, even in relatively simple animals.
SUPPORTING STRATEGY: in reference to a mixed strategy -- a supporting strategy part of the mixed strategy. Supporting strategies are particular behaviors (for example, displays of a certain length of time) that are played at a probability more than zero (in other words they will be performed at least sometime).
SYMMETRY: equality with respect to competitive ability as defined in a particular type of contest. An unlikely situation. In most of the models we consider, we assume symmetry as a simplification. If contestants are truly of equal ability, we assume that each has a 50% chance of winning the conflict with no resort to further escalation. In real situations, the closer the competitive abilities of two contestants, the more likely that a highly escalated conflict will occur. Symmetry can also refer to information availability or to a contestant's knowledge of the environment (including its opponent). So, for instance, when neither contestant in a pairwise contest knows before the contest starts the strategy the opponent will play or when both assess a resource at the same value, the contest is symmetrical with respect to these pieces of information. Clearly the presence or lack of informational symmetry could be an important factor in deciding a contest!
WINDOWS 32: This one has nothing to do with game theory. The term Windows 32 refers to thirty two bit implementations of Microsoft's Windows Operating System. This would include all recent versions of Windows95, Windows98 and Windows NT. To run the simulations on a windows/Intel machine you must use one of these operating systems.
Note:Windows 3.x and MS-DOS will not work properly, to the best of my knowledge.
ZERO-SUM GAME: when there is a finite resource that different strategies compete for; the resource is divided between all competitors according to their competitive ability. While there certainly are many examples of what are essentially zero sum situations, there are also cases where one alternative behavior allows its possessors to exploit a resource not previously available (i.e., not available to alternative strategies) in which case it is a non-zero sum game.
Copyright © 1998 by Kenneth N. Prestwich
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