The attraction of uncertainty: Interactions between skill and levels of uncertainty in market-entry games

Abstract

The experimental market entry paradigm has been used to illuminate the role of self-assessed skill in risk taking. Specifically, success only accompanies entry if a participant is one of the better ranked entrants on the skill criterion. We investigate what happens when participants face an additional source of uncertainty that perturbs relative skill rankings. Interestingly, this has asymmetric effects. On average, chances of success are increased for those with low rankings but decreased for those with high rankings. Thus, we predicted that the additional uncertainty would lead to more entry by the former but less by the latter. Our data supported the first prediction but, for those with high skill rankings, the existence of additional uncertainty made little difference. Finally, although we observed “excess entry” (i.e., too many participants entered markets), this could not be attributed to overconfidence. We conclude by contrasting our results with others in the literature.

Appendix

1.1 Equilibrium entry predictions

Assuming risk neutrality and no private information about the probability of success on entry, there are multiple pure-strategy Nash equilibria with seven players (47%) entering a market that has a capacity of five. At equilibrium, participants do not expect to receive a larger payoff by changing their strategy, i.e., by entering if the decision was to stay out and staying out if the decision was to enter. In our game, when there are fewer than seven entrants, a participant who stayed out could have received a positive payoff by entering, and with more than seven entrants, a participant who entered could have avoided an expected loss by staying out. In particular, the expected payoff of each of seven entrants is . If there are eight entrants, the individual expected payoff is . Expected payoffs for all numbers of entrants are detailed in Table 5 (lower panel, first column).

Table 5 Equilibrium analysis

Provided that players cannot coordinate, there is a mixed-strategy equilibrium in which each risk-neutral player (without private information about the probability of success on entry) enters with a probability p. The value of p is found by equating the expected payoff of entry and the payoff of staying out (see also Rapoport et al. 1998): . In this game, each player enters with probability p of 53%. That is, 7.9 players (out of 15) will enter on average each round (Table 5, lower panel, first column).

If all players know their relative performance on the test, then clearly only the top five players (33% of all potential entrants) will enter. However, if players have imperfect information about their test performance, it is instructive to speculate how they might take account of competitors when assessing relative performance. Considerable evidence suggests that people tend focus on themselves and neglect others, thereby adopting a so-called “inside view” (Kahneman and Lovallo 1993; Camerer and Lovallo 1999; Kruger 1999; Moore et al. 2007). Thus, imperfect information about test performance could imply biased subjective estimates of probabilities of success. For example, assume that this bias is captured by a parameter α (-1 > α > 1) that adjusts the probability of success on entry. Then, a player’s (biased) expected payoff of entry when there are E entrants (E > 5) is . Table 5 provides equilibrium results for α ≠ 0. For example, if α = 0.2, pure-strategy Nash equilibria occur when nine players (60%) enter the market, and if α = -0.2 six players (40%) enter. In terms of mixed strategies, if α = 0.2 the equilibrium probability of entry is 62% (9.3 entrants), and if α = -0.2 it is 46% (6.9 entrants).

Table 6 Logit models of entry, by gender