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Microeconomics Seminar: Rules, Mutation and Selection: Evolving Efficiency and Egalitarianism

  Add to Calendar 2020-02-18 13:30 2020-02-18 15:00 Europe/Paris Microeconomics Seminar: Rules, Mutation and Selection: Evolving Efficiency and Egalitarianism

In this paper, for any arbitrary game, we provide an argument for why in the long-run only outcomes that are both efficient and egalitarian (symmetric) in the Rawlsian sense are mostly observed. We do this by constructing an adaptive dynamic framework with four attractive features. First, at any stage agents select rules (amongst many) to implement their actions. Second, rule selection satisfies some minimal payoff monotonicity condition - rules that have done best are chosen with a positive probability. Third, in choosing their rules agents are subject to "small" perpetual random mutation. Fourth, mutation is payoff-dependent in the sense that agents are more likely to mutate when they have done badly than when they have done well. Our main result is the following: if the set of allowable rules is sufficiently rich then outcomes that survive in the long-run (those that are stochastically stable) maximise the payoff of the player that does least well, i.e. they are both efficient and egalitarian in the Rawlsian sense. The tendency towards efficiency and egalitarianism also holds if we put some restriction on the set of feasible rules. For example, we show that if the set of feasible rules is restricted to those that do best replies on uniform histories then outcomes that survive in the long-run are efficient and egalitarian amongst the set of minimum weak CURB sets. Finally, we also consider the long-run outcome of the model assuming that mutation rate is independent of the history of the agents. In contrast to our strong selection result above, with history independent mutation we show a strong indeterminacy result: any outcome can survive in the long-run if the set of feasible rules is sufficiently rich.

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In this paper, for any arbitrary game, we provide an argument for why in the long-run only outcomes that are both efficient and egalitarian (symmetric) in the Rawlsian sense are mostly observed. We do this by constructing an adaptive dynamic framework with four attractive features. First, at any stage agents select rules (amongst many) to implement their actions. Second, rule selection satisfies some minimal payoff monotonicity condition - rules that have done best are chosen with a positive probability. Third, in choosing their rules agents are subject to "small" perpetual random mutation. Fourth, mutation is payoff-dependent in the sense that agents are more likely to mutate when they have done badly than when they have done well. Our main result is the following: if the set of allowable rules is sufficiently rich then outcomes that survive in the long-run (those that are stochastically stable) maximise the payoff of the player that does least well, i.e. they are both efficient and egalitarian in the Rawlsian sense. The tendency towards efficiency and egalitarianism also holds if we put some restriction on the set of feasible rules. For example, we show that if the set of feasible rules is restricted to those that do best replies on uniform histories then outcomes that survive in the long-run are efficient and egalitarian amongst the set of minimum weak CURB sets. Finally, we also consider the long-run outcome of the model assuming that mutation rate is independent of the history of the agents. In contrast to our strong selection result above, with history independent mutation we show a strong indeterminacy result: any outcome can survive in the long-run if the set of feasible rules is sufficiently rich.


Location:
-

Affiliation:
Department of Economics

Type:
Seminar series

Organiser:
Prof. Hamid Sabourian (University of Cambridge)

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