Socially smart software agents entice people to use higher-order theory of mind in the Mod game

In social settings, people often need to reason about unob-servable mental content of other people, such as their beliefs, goals, orintentions. This ability helps them to understand, to predict, and evento influence the behavior of others. People can take this ability furtherby applying it recursively. For example, they use second-order theory ofmind to reason about the way others use theory of mind, as in ‘Alicebelieves that Bob does not know about the surprise party’. However,empirical evidence so far suggests that people do not spontaneously usehigher-order theory of mind in strategic games. Previous agent-basedmodeling simulations also suggest that the ability to recursively applytheory of mind may be especially effective in competitive settings. Inthis paper, we use a combination of computational agents and Bayesianmodel selection to determine to what extent people make use of higher-order theory of mind reasoning in a particular competitive game, theMod game, which can be seen as a much larger variant of the well-knownrock-paper-scissors game.We let participants play the competitive Mod game against computa-tional theory of mind agents. We find that people adapt their level oftheory of mind to that of their software opponent. Surprisingly, know-ingly playing against second- and third-order theory of mind agents en-tices human participants to apply up to fourth-order theory of mindthemselves, thereby improving their results in the Mod game. This phe-nomenon contrasts with earlier experiments about other strategic one-shot and sequential games, in which human players only displayed lowerorders of theory of mind