Consider example T > R > P > S

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Tantalizing connections in game theory. Evolutionary dynamics providing insight into a related game theory model. Game theory. +R. +T. +R. +S. +S. +P. p D. +T. +P. 1. Prisoner’s dilemma. Consider example T > R > P > S. Consider example T > R > P > S.

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Presentation Transcript

Tantalizing connections in game theory

Evolutionary dynamics providing insight into a related game theory model

Game theory

+R

+T

+R

+S

+S

+P

pD

+T

+P

1

Prisoner’s dilemma

Consider exampleT > R> P > S

Consider exampleT > R> P > S

T, R, P, and S are cell-replication coefficients associated with pairwise collisions

Agents try to maximize payoff

Rationality

Replicators with fitness

Solution := no agent can increase payoff through unilateral change of strategy. E.g., D-vs.-D (T> R and P > S).

Stable homogeneous steady state, i.e. pD → 1 because T > R and P > S.

ESS

Nash equilibrium

Each agent obtains less-than-maximum payoff (P < T) owing to other agent’s adoption of strategy D

Enriching in D reduces fitness of both cell types (because T > P and R > S)

t

0

Connections: Mechanistic model and quantitative reasoning

Fitness of C

Fitness of D

Other cell

\$

\$

\$

+R

+T

+R

+S

You

+S

+P

+T

+P

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+S

You

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+S

You

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+S

You

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+R

+S

You

+S

(Purple “stuff” need not be same as blue “stuff”)

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+R

+S

You

+S

Population dynamics with table of progeny numbers

Fitness of C

Fitness of D

Other cell

+R

+T

+R

+S

You

+S

+P

+T

+P

Evolution resulting from repeated games

Fitness of C

Fitness of D

Evolutionarygame theory

Partner 2

Other cell

Game theory

\$

\$

\$

+R

+T

+R

+T

+R

+S

+R

+S

Partner 1

You

+S

+P

+S

+P

+T

+P

+T

+P

Quantitative reasoning

What propositions might we model? How might conclusions depend on our propositions?

Population dynamics

Yes

Proposition 1:Consequences depend on social context

Yes

?

No

Proposition 2: Strategy decisions based on social context

Yes

Sloppy guess: Similarities not expected in conclusions for Pr. 1 vs. Pr. 1 and Pr. 2

\$

\$

\$

Recall prisoner’s dilemma examples (T > R > P > S): Denim is eventually prevalent.

Cell population eventually denimrich

Bothagents choose denim strategy

+R

+R

+T

+T

?

+R

+R

+S

+S

+S

+S

+P

+P

+T

+T

+P

+P

Quantitative reasoning

What propositions might we model? How might conclusions depend on our propositions?

Population dynamics

Yes

Proposition 1:Consequences depend on social context

Yes

?

No

Proposition 2: Strategy decisions based on social context

Yes

Sloppy guess: Similarities not expected in conclusions for Pr. 1 vs. Pr. 1 and Pr. 2

\$

\$

\$

Recall prisoner’s dilemma examples (T > R > P > S): Denim is eventually prevalent.

Cell population eventually denimrich

Bothagents choose denim strategy

+R

+R

+T

+T

?

+R

+R

+S

+S

+S

+S

+P

+P

+T

+T

+P

+P

Quantitative reasoning

What propositions might we model? How might conclusions depend on our propositions?

Population dynamics

Yes

Proposition 1:Consequences depend on social context

Yes

?

No

Proposition 2: Strategy decisions based on social context

Yes

Sloppy guess: Similarities not expected in conclusions for Pr. 1 vs. Pr. 1 and Pr. 2

\$

\$

\$

Recall prisoner’s dilemma examples (T > R > P > S): Denim is eventually prevalent.

Cell population eventually denimrich

Bothagents choose denim strategy

+R

+R

+T

+T

?

+R

+R

+S

+S

+S

+S

+P

+P

+T

+T

+P

+P

Repetition of Pr. 1 can yield conclusions that seem to have “similarity” with applying Pr. 1 and Pr. 2 once. Beware that timecan compensate for lack of thinking.

Quantitative reasoning

What propositions might we model? How might conclusions depend on our propositions?

Population dynamics

Yes

Proposition 1:Consequences depend on social context

Yes

?

No

Proposition 2: Strategy decisions based on social context

Yes

Sloppy guess: Similarities not expected in conclusions for Pr. 1 vs. Pr. 1 and Pr. 2

\$

\$

\$

Recall prisoner’s dilemma examples (T > R > P > S): Denim is eventually prevalent.

Cell population eventually denimrich

Bothagents choose denim strategy

+R

+R

+T

+T

?

+R

+R

+S

+S

+S

+S

+P

+P

+T

+T

+P

+P

Repetition of Pr. 1 can yield conclusions that seem to have “similarity” with applying Pr. 1 and Pr. 2 once. Beware that timecan compensate for lack of thinking.

Connections: Mechanistic model and quantitative reasoning

Fitness of C

Fitness of D

Other cell

\$

\$

\$

+R

+T

+R

+S

You

+S

+P

+T

+P