Question

3 models of aggression (Collectively called Game Theory Models): 1) The Hawk-Dove Game, 2) The War of Attrition Model and 3) The Sequential Assessment Model

The Hawk-Dove Game

Developed by Maynard Smith and Prince

•In simplest form, heuristic model

•Imagine that individuals can adopt one of two behavioral strategies

1.Hawk – player escalates and continues to escalate until either it is injured or its opponent cedes the resource

2.Dove – in which a player displays as it if will escalate but retreats and cedes the resource if its opponents escalate.

The War of Attrition Model

•Some agnostic encounters are settled by animals displaying aggressively to one another but not actually fighting, and the victor is the individual that displays the longest

•War of attrition model – 3 underlying assumptions

1.Individuals can chose to display aggressively for any duration of time

2.Display behavior is costly – the longer the display the more of a cost

3.There are no clear cues such as size, territory possession and so forth that contestants can use to settle a contest.

The Sequential Assessment Model

•Developed by Magnus Enquist

•Designed to analyze fights in which individuals continuously assess one another in a series of “bouts”

•In this model, individuals assess their opponent’s fighting abilities

•Analogous to a process of statistical sampling

•A single sample, a single assessment of fighting ability, introduces significant sampling error

•The more sampling one does, the lower the error rate, hence more confidence one can be in whatever is being estimated (in this case, opponent’s fighting ability)

Briefly describe the premise of the model, what are the underlying assumptions and how are cost / benefits measured? Provide an example. Briefly describe one potential limitation of the model.

Answer 1

Fights between Hawks are brutal affairs with the loser being the one who first sustains injury. The winner takes sole possession of the resource.
Although Hawks that lose a contest are injured, the mathematics of the game requires that they not die and in fact are fully mended before their next expected contest.

Assumption-

1. All Hawks are equal in fighting ability, that is, each Hawk has a 50% chance of winning a Hawk, that is Hawk versus Hawk contests are symmetrical.
2. All Doves are equally good at displaying and and they adapt a strategy of waiting for a random time period therefore when two Doves face off , each has a 50% chance of winning.

3. The attacking animal (the one that either starts first to physically attack or to
display) has no knowledge of the strategy that its opponent will play.
4. These interactions increase or decrease the animal's fitness from some baseline fitness. In other words, these interactions simply modify an animal's tness up or down- winning a contest does create tness. This assumption is associated with our convention that injuries and display costs will be assigned negative scores- losing animals do not have negative fitnesses.