Glossary: Difference between revisions
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A player's traits include their inherent [[#Draw vs Selection for Fitness|fitness]]. If they [[#Reproduction|reproduce]], their offspring inherits a copy of their traits. If they imitate another player, they adopt the other player's traits. If [[#Mutation|mutation]] happens, their traits may be modified. If as usual an interaction [[#Game|game]] is being played, their traits determine their [[#Game|strategy]] which will impact their behavior, which will impact how much the game [[#Payoff|pays off]] for them, which will increase their [[#Draw vs Selection for Fitness|fitness]]. | A player's traits include their inherent [[#Draw vs Selection for Fitness|fitness]]. If they [[#Reproduction|reproduce]], their offspring inherits a copy of their traits. If they imitate another player, they adopt the other player's traits. If [[#Mutation|mutation]] happens, their traits may be modified. If as usual an interaction [[#Game|game]] is being played, their traits determine their [[#Game|strategy]] which will impact their behavior, which will impact how much the game [[#Payoff|pays off]] for them, which will increase their [[#Draw vs Selection for Fitness|fitness]]. | ||
Sometimes when the situation is | Sometimes when the situation is simple, like traits = [[#Game|strategy]] = behavior (for instance every players is either a Defector or a Cooperator and that's their sole trait and their [[#Game|strategy]] and their behavior) then the word "strategy" is often used for trait or behavior too. | ||
==Graph== | ==Graph== | ||
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===Interaction=== | ===Interaction=== | ||
In the interaction relation your neighbors are the players with whom you could choose to play a game. | In the interaction relation your neighbors are the players with whom you could choose to play a [[#Game|game]]. | ||
===Replacement=== | ===Replacement=== | ||
In the replacement relation your neighbors are the players who might die to be replaced by your [[#Reproduction|offspring]], or who might [[#Imitation|imitate]] you. | In the replacement relation your neighbors are the players who might die to be replaced by your [[#Reproduction|offspring]], or who might [[#Imitation|imitate]] you. In both cases they take on your [[#Player|traits]]. | ||
If the replacement graph is undirected, one could think of the graph vertices as territories in a territorial species, under the assumption that each territory is occupied by exactly one player. The replacement graph would then model which territories adjoin, under the assumption that territories are static and deaths are replaced by births from adjacent territories. | If the replacement graph is undirected, one could think of the graph vertices as territories in a territorial species, under the assumption that each territory is occupied by exactly one player. The replacement graph would then model which territories adjoin, under the assumption that territories are static and deaths are replaced by births from adjacent territories. | ||
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A player who acts may [[#Imitation|imitate]] a neighbor, they may [[#Reproduction|reproduce]] (prompting a neighbor to die to make room for the offspring), they may [[Parameters/Population#Moran process (death-birth)|die]] (prompting a neighboring player to reproduce to replace them), all of which may change someone's game [[#Game|strategy]] and [[#Game|payoffs]]. Which of these actions occur, and in what order, is governed primarily by the [[Parameters/Population#Population update|population update settings]]. | A player who acts may [[#Imitation|imitate]] a neighbor, they may [[#Reproduction|reproduce]] (prompting a neighbor to die to make room for the offspring), they may [[Parameters/Population#Moran process (death-birth)|die]] (prompting a neighboring player to reproduce to replace them), all of which may change someone's game [[#Game|strategy]] and [[#Game|payoffs]]. Which of these actions occur, and in what order, is governed primarily by the [[Parameters/Population#Population update|population update settings]]. | ||
If you wish to model that interactions occur only a few times per MC time step, then use parameter nInteractions to indicate the | If you wish to model that interactions occur only a few times per player per MC time step, then use parameter nInteractions to indicate the number of interactions. For instance, if each player has four interaction neighbors, and nInteractions was 3 (or 7), then an action would play games with a randomly chosen 3 (or 7) of the four neighbors, with replacement, and the scores accumulated or averaged. Note that the chosen neighbors' scores will change too, since their scores reflect the additional games played. | ||
If you wish to model per-player interactions as very frequent vis à vis the MC time step, you can set the parameters so that whenever a vertex's traits change (via mutation, imitation, or death and replacement by someone else's offspring), the new player plays games with all their neighbors to arrive at the limiting case, as if nInteractions was infinite with averaged scores. Neighbors scores are also adjusted to reflect their score accounting for the change in their neighborhood. | |||
====synchronous time==== | ====synchronous time==== | ||
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====asynchronous time==== | ====asynchronous time==== | ||
Under favorable climatic conditions animals may breed and reproduce throughout the year. To model this, during each MC step a sequence of <math>N</math> players are chosen at random (with replacement) to act in turn. This implies that in a given time step, some players may not be chosen to act at all, and others may be chosen multiple times. | Under favorable climatic conditions animals may breed and reproduce throughout the year. To model this, during each MC step a sequence of <math>N</math> players are chosen at random (with replacement) to act in turn. This implies that in a given time step, some players may not be chosen to act at all, and others may be chosen multiple times. | ||
==Reproduction and Imitation== | ==Reproduction and Imitation== | ||
===Draw vs Selection for Fitness=== | ===Draw vs Selection for Fitness=== | ||
In this documentation we attach special meaning to the terms draw and select. To ''draw'' a player is to chose a player at random with no regard for fitness. Whereas to ''select'' a player is to chose a player weighted by their fitness, i.e. fitter players have a greater chance of being chosen. Players are always selected to reproduce, and drawn to die. | In this documentation we attach special meaning to the terms draw and select. To ''draw'' a player is to chose a player at random with no regard for fitness. Whereas to ''select'' a player is to chose a player weighted by their fitness, i.e. fitter players have a greater chance of being chosen. Players are always selected to [[#Reproduction|reproduce]], and drawn to die; selected to be [[#Imitation:imitated]], drawn to imitate; in other words selected to be the source of [[#Player||traits]], and drawn to take on those traits. | ||
===birth and death=== | ===birth and death=== | ||
To give birth is to be selected to reproduce. Your offspring replaces | To give birth is to be selected to reproduce. Your offspring replaces one of your [[#Replacement|replacement]] neighbors. To die is to be drawn to be replaced by some neighbor's offspring, a neighbor that has you in their [[#Replacement|replacement]] neighborhood. Which happens first is important, see [[Parameters/Population#Population update|birth-death and death-birth]]. | ||
===imitation=== | ===imitation=== | ||
