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Glossary: Difference between revisions
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==THE BIG PICTURE (population is to player as graph is to vertex)== | ==THE BIG PICTURE (population is to player as graph is to vertex)== | ||
A player is an individual member of the population being modeled. If the population is structured, that is, modeled with | A player is an individual member of the population being modeled. If the population is structured, that is, modeled with a [[#Graph|graph]], each player occupies a vertex (a position, a node) in the [[#Graph|graph]], and each vertex is occupied by a player. This being so, we sometimes say "player" to refer to their "vertex" and vice versa. | ||
===Player=== | ===Player=== | ||
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Sometimes when the situation is simplified, 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. | Sometimes when the situation is simplified, 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== | ||
A graph models a relation between players. It is a list, for each player p, of the players that p considers to be its neighbors in the relation modeled by the graph. | A graph models a relation between players. It is a list, for each player p, of the players that p considers to be its neighbors in the relation modeled by the graph. Usually the graph is ''undirected'' (bidirected), i.e. whenever p is among v's neighbors, v is among p's neighbors. If the graph contains even one exception to that rule, it is called a ''directed'' graph. Unrequited neighborliness. | ||
There are two logically distinct relations that are represented by a graph in ''Evoludo'', called [[#Interaction|interaction]] and [[#Replacement|replacement]]. For the moment both concepts have the same graph, so that for every player, its interaction neighbors and its replacement neighbors are the same neighbors. | |||
===Interaction=== | |||
In the interaction relation your neighbors are the players with whom you could choose to play a 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. | ||
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. | |||
==Time== | ==Time== | ||
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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 average number of interactions. For instance, if in the graph you are using, each player has four neighbors, then nInteractions could be 2 (indicating that each action would play games with a randomly chosen 2 of the four neighbors) or 6 (the random choice is with replacement), and so on. | |||
If | If you wish to model interaction as very frequent vis à vis reproduction, use parameter X 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. | ||
=====lingering asynchronous time===== | =====lingering asynchronous time===== | ||
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=====memoryless asynchronous time===== | =====memoryless asynchronous time===== | ||
The payoffs of the players who play with the changed player are recalculated from scratch, modeling biology where earlier interactions have no residual effect on [[#Draw vs Selection for Fitness|fitness]]. | The payoffs of the players who play with the changed player are recalculated from scratch, modeling biology where earlier interactions have no residual effect on [[#Draw vs Selection for Fitness|fitness]]. | ||
====synchronous time==== | |||
All <math>N</math> players act simultaneously, in parallel, each MC step. This models situations where external influences such as diurnal rhythms or seasonal changes lead to a synchronization of the breeding season or where competitive interactions are synchronized under harsh environmental conditions such as occur in the arctic or in a desert. | |||
====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. | |||
If a player is changed, that player's game [[#Game|payoffs]] are calculated by playing a round of [[#Game|games]] with their [[#Interaction|interaction]] neighbors. | |||
==Reproduction and Imitation== | ==Reproduction and Imitation== | ||
