Strategic behavior in risky competitive settings

In the first chapter of this dissertation, I propose a novel and tractable structural model for ascending auctions with both common and private value components in which heterogeneous bidders exhibit loss aversion. Importantly, I find that loss averse bidders bid noticeably lower than risk neutral ones. I also consider a more general framework in which bidders incorporate into their strategies the information of those bidders who are present but decide not to participate after observing the item put up for auction. This results in bidders reducing the aggressiveness of their bids even further. To empirically assess my model, I use data from storage locker auctions in the popular cable TV show Storage Wars, finding that the behavior of most of its bidders is consistent with loss aversion. Thus, I document for the first time the presence of loss aversion in actual ascending auctions. In Chapter 2, I report the results of a (quasi) field experiment in the training grounds of a professional soccer team to check if individuals, when repeatedly facing the same opponents, satisfy the main mixed strategy equilibrium predictions in soccer penalty kicks, a real-life example of strategic play. This is the first time that the implications of mixed strategy equilibria are tested in the field using repeated observations on specific heterogeneous pairs of players, a situation that rarely repeats in real life. In this respect, I also study the effects of the usual practice of treating heterogeneous rivals as if they all came from the same pair because of the lack of repeated observations for specific pairs. In particular, I show that false rejections may arise when heterogeneous pairs are treated as homogeneous and suggest valid aggregate tests that combine statistics from different opponents. My empirical results suggests that the behavior of most soccer players, when repeatedly facing the same opponents, is consistent with equal scoring probabilities across strategies except for the least professional kickers, as well as with serial independence of player's actions. However, I find dependence between the kicker's and goalkeeper's actions. I also find that the least professional goalkeepers tend to replicate each other's actions. In contrast, players do not seem to follow a reinforcement learning model. In the third chapter, I prove the numerical equivalence for general categorical variables between many seemingly unrelated independent tests. Specifically, I prove that the Pearson's independence test in a contingency table is numerically equivalent to the Lagrange Multiplier test in several popular linear and non-linear regression models: the multivariate linear probability model, the conditional and unconditional multinomial model, the multinomial logit and probit models; as well as the overidentifying restrictions test in GMM. Therefore, different researchers using different econometric procedures will reach exactly the same conclusions if they use any of those tests. Additionally, I show that the asymptotically equivalent Likelihood Ratio tests in the non-linear regression models are numerically identical, and that the heteroskedasticity-robust Wald tests in the multivariate linear probability model and GMM coincide with the Wald test in the conditional multinomial model. All these equivalences also apply to tests of serial independence in a discrete Markov chain, which can be regarded as a time series analogue of the multinomial model. Finally, I use these tests to analyze if professional soccer players follow optimal mixed strategies in penalty kicks. For some players, my empirical results are not consistent with equal scoring probabilities across strategies. In contrast, I find that player's actions are serially independent.