Strategic risk-taking in dynamic contests

Abstract

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 explain the rest of behavioral findings obtained from the data and compare the relative importance of these components.