Risk-Taking in Dynamic Contests

We investigate a process of decision-making in a multi-period winner-take-all contest, in which competing players simultaneously choose among actions with different levels of risk every period. Strategic risk-taking is analyzed in isolation from effort choices, and, according to expected utility theory, risk preferences are irrelevant. We derive a closed-form solution of the dynamic game for any number of periods. In the equilibrium, a leading player chooses the lowest level of risk, a trailing player chooses the highest level of risk, and all elements of the action space with intermediate levels of risk are irrelevant. We design a laboratory experiment to test various comparative statics of the model and explore behavioral deviations. Our findings are consistent with theoretical predictions - subjects tend to choose riskier lotteries when they are behind and safer lotteries when they are ahead, while the magnitude of the advantage does not seem to affect the risk-taking levels. We also observe some behavioral deviations such as a decline in risk-taking in the absence of the safe option, which only occurs while being behind. We find the quantal response equilibrium of our dynamic game and explain some of behavioral deviations; incorporating learning, subject types, and the probability weighting function into the behavioral model allows us to achieve a 40% improvement in fit and explain the rest of behavioral findings obtained from the data