Abstract
We report experimental results on the minority of three-game, where three players choose one of two alternatives and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non-strict and payoff-asymmetric and a unique symmetric mixed strategy equilibrium in which each player’s behavior is based on the toss of a fair coin. This straightforward behavior is predicted by equilibrium selection, impulse-balance equilibrium, and payoff-sampling equilibrium. Experimental participants rely on various decision rules, and only a quarter of them perfectly randomize.
Highlights
Many games have multiple equilibria so that the equilibrium concept alone does not answer or explain how the game will be played
We present experimental evidence on the minority of three-game, which in one important aspect differs from previously studied market entry games: all its asymmetric equilibria in pure strategies are non-strict and imply earning discrepancies
Market entry games are prototypical of coordination problems arising from a newly emergent profit opportunity that can be exploited only by a limited number of individuals
Summary
Many games have multiple (perfect) equilibria so that the equilibrium concept alone does not answer or explain how the game will be played. In view of the complete symmetry of the (ε-uniformly perturbed) minority of three-game as well as of the tracing procedure, this means selecting the completely mixed equilibrium according to which all three players use both choices with equal probability. In the asymmetric (trembles) case, the two “pure strategy equilibria” qualify as primitive formations since both equilibria are strict Since neither of these two solution candidates can (payoff or) risk dominate the other, the theory of Harsanyi and Selten [4] suggests to neglect them, which essentially means to apply the tracing procedure to the full minority of three-games with asymmetric trembles. We establish that the completely mixed equilibrium is predicted by alternative solution concepts which, arguably, rely on less stringent assumptions regarding the knowledge and understanding of players
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