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Haley Cope

Continuous Wright-Fisher Model

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The male peacock hasa long tail.

This makes him visibleto predators and morelikely to be killed.

Thus, it would make

sense for naturalselection to selectagainst this trait.

Proposed ideas:

Group selection

Costly signaling

Motivation

8/12/2019 Continuous Wright-Fisher Model

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SenderA player sending

HighA desirable send

LowAn undesirable se

ReceiverA player making

based on the sign

Specific to this mod

GameModel of interacting decision-

makers

Players

Decision makers

Strategy Rules players use to make

decisions

Payoff

Represent the motivations ofplayers (profit, etc)

Game Theory

Definitions

8/12/2019 Continuous Wright-Fisher Model

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Senders (high & low), receivers

Senders pay some cost to send a signal

Receivers choose to accept or reject based on the sig

Nash Equilibrium:

Pooling EquilibriumOstentatious Separating

Efficient Separating

Costly Signaling

Which equilibrium will the system tend toward?

8/12/2019 Continuous Wright-Fisher Model

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Randomly initialize a population with strategies {0, 1, 2, 3} for senders, any combination for receivers

Assign each player payoffs, and fitness +5 for senders accepted & receivers accepting a high type

-5 for receivers accepting a low type

Players have offspring proportional to their finessesOffspring take strategy of parent, small probability try new stra

Old generation dies, and keep average of the strateg

Start the process over for some number of generation

Wright Fisher Model

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Graph showing thpossible equilibria

Results

Efficient Separa

Pooling

Ostentatious Separating

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Strategies on a range

Cost defined by a cont

Can partially accept Payoffs are in a range

acceptance)

Continuous

Discrete possible strategies

Discrete cost

Discrete acceptanceDiscrete payoff

Discrete

Wright Fisher Model

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Costs must be increasing as the strategy increases

High types must pay a lower cost than low types

Receivers must be able to have fractional acceptancDifficulty arises here

If we want the strategies to be truly continuous, we need them

able to choose any strategy in the space.

Requirements

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Results

My implementation of continuous costlysignaling

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Find a way to allow all possible functions Requires a great deal of mathematical background

Revise the way receivers choose strategiesAllow for drift as opposed to hopping between functions

Continuous types

Instead of high-low, allow for degrees of quality

Further Research