# Ordinal Imitative Dynamics

## TL;DR

This paper introduces a new evolutionary dynamic based on imitation of better-performing strategies, which eliminates dominated strategies and stabilizes strict equilibria, differing from traditional replicator dynamics in complex games.

## Contribution

It proposes an ordinal mean dynamics derived from IBR, demonstrating unique stability properties and behavioral differences from replicator dynamics in various game settings.

## Key findings

- Eliminates strictly dominated strategies
- Locally stabilizes strict equilibria
- Exhibits behaviors different from replicator dynamics in complex games

## Abstract

This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, agents in a population game imitate the strategy of a randomly chosen opponent whenever the opponent`s realized payoff is higher than their own. Such behavior generates an ordinal mean dynamics which 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.