Strategic investment decisions in multi-stage contests with heterogeneous players

When heterogeneous players make strategic investment decisions in multi-stage contests, they might conserve resources in a current contest to spend more in a subsequent contest, if the degree of heterogeneity in the current (subsequent) contest is sufficiently large (small). We confirm these predictions using data from German professional soccer, in which players are subject to a one-match ban if they accumulate five yellow cards. Players with four yellow cards facing the risk of being suspended for the next match are (i) less likely to be fielded when the heterogeneity in the current match increases and (ii) more likely to receive a fifth yellow card in the current match when heterogeneity in the next match increases or heterogeneity in the next match but one (when they return from their ban) decreases.

Fatter or Fitter? On rewarding and training in a contest

Competition between heterogeneous participants often leads to low effort provision in contests. We consider a principal who can divide her fixed budget between skill-enhancing training and the contest prize. Training can reduce heterogeneity, which increases effort. But it also reduces the contest prize, which makes effort fall. We set up an incomplete-information contest with heterogeneous players and show how this trade-off is related to the size of the budget when the principal maximizes expected effort. A selection problem can also arise in this framework in which there is a cost associated with a contest win by the inferior player. This gives the principal a larger incentive to train the expected laggard, reducing the size of the prize on offer.

Analysing group contract design using a threshold public goods experiment

This paper presents the results of a threshold public goods game experiment with heterogeneous players. The experiment is designed in close collaboration with the Dutch association of agri-environmental farmer collectives. Subjects are recruited at a university (study 1) and a farm management training centre (study 2), the subjects of the second study most resembling the subjects in the field. The experiment consists of several treatments and each treatment has two different distribution rules, which are varied in a within-subjects manner. After subjects have experienced both, they can vote for one of the two rules: either a differentiated bonus that results in equal payoff for all, or an undifferentiated, equal share of the group bonus. In a between-subjects manner, subjects can vote for a (minimum or average) threshold or are faced with an exogenous threshold. The results indicate that exogenous thresholds perform better, possibly because the focal point they provide facilitates coordination. With regard to the two distribution rules, the results are mixed: in study 1, average contributions and payoffs are higher under the ‘equal-payoff’ rule, but there is no significant difference between the two in study 2. Overall, our results suggest that environmental payment schemes should consider cost heterogeneity in the design of group contracts, and pay explicit attention to coordination problems too.

Investigations of Nonlinear Triopoly Models with Different Mechanisms

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism (LMA) while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable.