Persistence or decay of strategic asymmetric dominance in repeated dyadic games?

Abstract

In a dyadic game, strategic asymmetric dominance occurs when a player’s preference for one strategy A relative to another B is systematically increased by the addition of a third strategy Z, strictly dominated by A but not by B. There are theoretical and empirical grounds for believing that this effect should decline over repetitions, and other grounds for believing, on the contrary, that it should persist. To investigate this question experimentally, 30 participant pairs played 50 rounds of one symmetric and two asymmetric 3 × 3 games each having one strategy strictly dominated by one other, and a control group played 2 × 2 versions of the same games with dominated strategies removed. The strategic asymmetric dominance effect was observed in the repeated-choice data: dominant strategies in the 3 × 3 versions were chosen more frequently than the corresponding strategies in the 2 × 2 versions. Time series analysis revealed a significant decline in the effect over repetitions in the symmetric game only. Supplementary verbal protocol analysis helped to clarify the players’ reasoning and to explain the results.