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Consider example T > R > P > S

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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Consider example T > R > P > S

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  1. 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 Fortune cookie Enriching in D reduces fitness of both cell types (because T > P and R > S) t 0

  2. Connections: Mechanistic model and quantitative reasoning Fitness of C Fitness of D Other cell $ $ $ +R +T +R +S You +S +P +T +P

  3. Population dynamics with table of progeny numbers Fitness of C Fitness of D Other cell +R +S You

  4. Population dynamics with table of progeny numbers Fitness of C Fitness of D Other cell +R +S You

  5. Population dynamics with table of progeny numbers Fitness of C Fitness of D Other cell +R +S You

  6. 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”)

  7. Population dynamics with table of progeny numbers Fitness of C Fitness of D Other cell +R +R +S You +S

  8. Population dynamics with table of progeny numbers Fitness of C Fitness of D Other cell +R +T +R +S You +S +P +T +P

  9. 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

  10. Quantitative reasoning What propositions might we model? How might conclusions depend on our propositions? Population dynamics Business payoff analysis 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

  11. Quantitative reasoning What propositions might we model? How might conclusions depend on our propositions? Population dynamics Business payoff analysis 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

  12. Quantitative reasoning What propositions might we model? How might conclusions depend on our propositions? Population dynamics Business payoff analysis 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.

  13. Quantitative reasoning What propositions might we model? How might conclusions depend on our propositions? Population dynamics Business payoff analysis 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.

  14. Connections: Mechanistic model and quantitative reasoning Fitness of C Fitness of D Other cell $ $ $ +R +T +R +S You +S +P +T +P

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