Ordinal imitative dynamics

George Loginov ()

International Journal of Game Theory, 2022, vol. 51, issue 2, No 6, 412 pages

Abstract: Abstract This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, an agent in a population game imitates the strategy of a randomly chosen opponent whenever the opponent’s realized payoff is higher than his or her own. Such behavior generates a mean dynamics which depends on the order of payoffs, but not their magnitudes, and is polynomial in strategy utilization frequencies. We demonstrate that while the dynamics does not possess Nash stationarity or payoff monotonicity, under it pure strategies iteratively strictly dominated by pure strategies are eliminated and strict equilibria are locally stable. We investigate the relationship between the dynamics based on the IBR rule and the replicator dynamics. In trivial cases, the two dynamics are topologically equivalent. In Rock-Paper-Scissors games we conjecture that both dynamics exhibit the same types of behavior, but the partitions of the game set do not coincide. In other cases, the IBR dynamics exhibits behaviors that are impossible under the replicator dynamics.

Date: 2022
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Working Paper: Ordinal Imitative Dynamics (2019)
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DOI: 10.1007/s00182-021-00797-7

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