Examining Monotonicity and Saliency Using Level-<i>k</i> Reasoning in a Voting Game

This paper presents an experiment that evaluates the effect of financial incentives and complexity in political science voting experiments. To evaluate the effect of complexity we adopt a level-<i>k</i> reasoning model concept. This model by Nagel [1] postulates that players might be of different types, each corresponding to the level of reasoning in which they engage. Furthermore, to postulate the effect of financial incentives on subjects’ choice, we used the Quantal Response Equilibrium (QRE) concept. In a QRE, players’ decisions are noisy, with the probability of playing a given strategy increasing in its expected payoff. Hence, the choice probability is a function of the magnitude of the financial incentives. Our results show that low complexity promotes the highest degree of level-<i>k</i> strategic reasoning in every payment treatment. Standard financial incentives are enough to induce equilibrium behavior, and the marginal effect of extra incentives on equilibrium behavior seems to be negligible. High complexity, instead, decreases the rate of convergence to equilibrium play. With a sufficiently high complexity, increasing payoff amounts does promote more strategic behavior in a significant manner. Our results show with complex voting games, higher financial incentives are required for the subjects to exert the effort needed to complete the task.