Experimental Economics Seminar - Paul Pezanis-Christou (The University of Adelaide)

Title: On the symmetry assumption of n-person binary-choice games: a specification test

Extended Abstract: We propose a specification test for the consistency of player behaviour with the restrictions imposed by the symmetric assumption of n-person binary-choice models of participation games such as market-entry games, volunteer’s games and step-level public good games. The test checks the ability of a model specification to fit the vector of entry probabilities when players with similar entry probabilities are clustered in groups. We consider two behavioural models, ‘Exploration vs Exploration’ (EvE), which is equivalent to logit-Quantal Response Equilibrium (McKelvey and Palfrey, 1995), and Impulse Balance Equilibrium (IBE, Selten and Chmura, 2008), and we assess our test using data of market-entry experiments that manipulate payoff levels (i.e., High or Low) and payoff structures (i.e., saliency of network effects in entry decisions). Overall, the models fit the data equally well, with IBE performing marginally better, and our analysis reveals important differences regarding i) the conclusions drawn from session or pooled data and ii) the models’ sensitivity to the restrictions imposed by symmetry. In terms of entry-probabilities, the pooled data indicates a significant under-entry in all High payoff structures that is best supported by session data when network effects are salient. In Low payoff treatments, the session data is mostly in line with the symmetric Nash equilibrium predictions no matter the payoff structure considered whereas the pooled data is not. When the estimated models impose symmetry and assume only one cluster of (homogenous) players, as is usually done in the literature, IBE yields far more consistent estimates than EvE no matter the payoff treatment or the type of data considered. We reject the null of consistency with the restrictions imposed by EvE (IBE) on symmetric players with homogenous traits in 16 (24) sessions (out of 24). By allowing for up to four clusters of players to capture their heterogeneity, the number of rejections reduces to 4 (10) for EvE (IBE), but 30% of EvE’s estimates then indicate ‘maximal exploration’ and refer to 18% of participants, whereas 18% of IBE’s estimates are not significantly different from 0 and refer to only 5% of participants. Our study thus indicates that although EvE is more likely to pass the specification test than IBE, especially when allowing for heterogeneous traits, its estimated parameters are more volatile, sometimes inconsistent and often support a purely random behaviour.