Strong Stackelberg reasoning in symmetric games: An experimental replication and extension

Abstract

In common interest games in which players are motivated to coordinate their strategies to achieve a jointly optimal outcome, orthodox game theory provides no general reason or justification for choosing the required strategies. In the simplest cases, where the optimal strategies are intuitively obvious, human decision makers generally coordinate without difficulty, but how they achieve this is poorly understood. Most theories seeking to explain strategic coordination have limited applicability, or require changes to the game specification, or introduce implausible assumptions or radical departures from fundamental game-theoretic assumptions. The theory of strong Stackelberg reasoning, according to which players choose strategies that would maximize their own payoffs if their co-players could invariably anticipate any strategy and respond with a best reply to it, avoids these problems and explains strategic coordination in all dyadic common interest games. Previous experimental evidence has provided evidence for strong Stackelberg reasoning in asymmetric games. Here we report evidence from two experiments consistent with players being influenced by strong Stackelberg reasoning in a wide variety of symmetric 3 × 3 games but tending to revert to other choice criteria when strong Stackelberg reasoning generates small payoffs.

Team Reasoning and the Rational Choice of Payoff-Dominant Outcomes in Games

“…Even completely self-sacrificing players cannot solve their problem in the Prisoner's Dilemma. If λ = 1, we have what Parfit (1984) calls "the altruists dilemma": the players each want to play D in order to benefit the other (and this remains the dominant strategy) but they could have each helped the other more if they had both agreed to play C.…”

“…First, even in game theory, the real locus of decision-making is the timeslice, it is just that in most games the individual players' preferences are stable over the time frame of the interaction, so we can model them as one single individual preference ordering. Second, once we think of individuals like this, the case for privileging the evaluative stance of the locus of decision making looks less appealing (although Parfit 1984 does take that position). That would involve privileging the timeslice in the intra-personal case, whereas most people's intuition is that it is the individual over time that is privileged, not the timeslice.…”

“…Even if such a theory can be constructed, it will not be a theory of instrumental rationality. For instance, Parfit (1984) argues that rationality resides with the timeslice, but that the timeslice may be required to do what is best for the individual or the group as a part of a consequentialist morality. In contrast, Korsgaard (1989) argues that the rationality of pursuing intertemporal projects implies that it is rational to prioritise the individual rather than the timeslice.…”

Team reasoning: Solving the puzzle of coordination

“…Strong Stackelberg reasoning (Colman & Bacharach, 1997;Colman et al, 2014;Colman & Stirk, 1998;Pulford et al, 2014;Pulford et al, 2017) entails an assumption that players choose strategies as though their co-players could anticipate their choices. Thus, a Stackelberg reasoner chooses as though expecting a choice of H to be anticipated by the coplayer, who would therefore choose H because it is the best reply, and an L choice to be met with an L choice by the coplayer for the same reason.…”

Team reasoning cannot be viewed as a payoff transformation

“…Having shown that team reasoning cannot be viewed as a payoff transformation, I conclude by commenting that team reasoning is not the only modification of standard game-theoretic reasoning that can explain strategic coordination in games with payoff-dominant Nash equilibria. Three other notable suggestions are cognitive hierarchy theory (Camerer et al 2004), Berge equilibrium (Colman et al 2011; Salukvadze and Zhukovskiy 2020) and strong Stackelberg reasoning (Colman and Bacharach 1997; Colman et al 2014; Pulford et al 2014). Cognitive hierarchy theory abandons the standard common knowledge of rationality assumption in favour of an assumption that players choose best responses to their co-players’ expected strategies given an assumption that their co-players choose their own strategies using a shallower depth of strategic reasoning than they use themselves.…”