Conflict Resolution

• Threat-display contests– Hawk-dove-bully– Hawk-dove-assessor

• Variable length contests– War-of-attrition– Sequential assessment

• Variable sequence contests

Dove-Bully GameOpponent: Bully Dove

Actor: BullyDove

V/2 V 0 V/2

Opponent: Bully Dove

Actor: Bully 1 2Dove 0 1

If V = 2 then

Bully is a pure ESS

Hawk-Bully GameOpponent: Bully Hawk

Actor: BullyHawk

Opponent: Bully Hawk

Actor: Bully 1 0Hawk 2 -1

If V = 2, C = 4 then

Yes, Hawks can invade Bullies, but Bullies invade HawksTherefore, this is a mixed ESS

V/2 0 V (V-C)/2

Correlated asymmetry• Opponents differ in RHP• Example: hawk - dove - assessor

– Assessor strategy: if larger play hawk, if smaller play dove

– If owner and intruder are equally frequent and get equal payoffs:

Opponent: Hawk Dove Assessor

Actor: HawkDoveAssessor

(V-C)/2 V (V-C)/2 0 V/2 V/4 V/2 3V/4 V/2

When there is a cost to fighting, Assessor is pure ESSassuming that assessment is costless and accurate

Calling in toads

War of attrition - the waiting game• Assumptions

– Resource cannot be shared– Cost of display increases with length of contest– No information is received during contest and

opponents are symmetrical– Winner is the contestant willing to accept the

higher cost– The cost to both contestants equals the cost

acceptable to the loser– The range of actions of each contestant is

continuous

War of attrition - Payoff matrixxi = amount of time individual i displaysk = rate at which costs are expendedV = value of resource

Payoff to: Player A Player B

Actor : xA > xB

Opponent: xA < xB

V - kxB - kxB

- kxA V - kxA

No pure ESS is possible, since an opponent that displayed a littlebit longer would have higher fitnessSolution is a mixed ESS where the probability of leaving at anytime is a constant. The times an individual stays should bedistributed as a negative exponential.

Asymmetric war-of-attrition

• If animals experience different costs of display or the resource differs in value to them, the game is asymmetric

• Which player has the largest V/k will win, but this may not be known

• This may lead to two different giving up time strategies

War-of-attrition solutions

Fight duration and resource value in newts

Males fight longer overlarger females. Largerfemales carry more eggs and are, therefore, morevaluable.

Sequential assessment

• Assumptions– Animals display in order to acquire information about

each other’s fighting ability and resource value

– Fights only occur when animals are closely matched

• Predictions– Fight duration increases as the asymmetry in fighting

ability decreases and/or as resource value increases

– The cost of a fight increases as the asymmetry in fighting ability decreases

– Probability of winning increases with asymmetry

Sequential assessment ESS

War of attrition in spiders

Resource value equal

Ownership effects in spider fights

War of attrition in spiders

Assessment in red deer

Jumping spider contest stages

Sequential assessment in phases

Sequential assessment in cichlids

Why give multiple signals?

• Each display serves a different function

• Signal erosion: threat displays lose effectiveness as the frequency of bluff increases

• Displays transmit graded information about display intentions– Multiple signals may lower potential risk

associated with escalation

Cricket display costs

Little blue penguin fights

Cave dwellers use more displays, but have lower escalated fights

Little blue penguin display repertoire