Selten's Horse an Experiment on Sequential Rationality∗

In a seminal paper, Selten (Selten, 1975) developed the game Selten’s Horse to illustrate some aspects of rationality. In our experimental study of Selten’s Horse we find that behaviour is not according to conventional sequential rationality based refinements. Some behaviour is better explained by Ideal Reactive Equilibrium (Sadanand, 2019), an extension of Manipulated Nash Equilibrium (Amershi, Sadanand, and Sadanand, 1985a,b,c). We provide a simple model of Level–k thinking incorporating the idea of virtual observability, where the players behave as if their subsequent opponents could in effect observe their actions. We find that participants’ behaviour is somewhat explained by virtual observability, but this is limited to immediate successors and is more prevalent in the more complex version of the game. Moreover, at times we see first movers na¨ıvely move towards their most-preferred equilibrium and follower players anticipate and exploit it by systematically reaching off-equilibrium outcomes that are favourable to them