Effort Decisions in Correlated Competitions

Individuals and organizations often face competitions requiring various skills which can be acquired or improved through efforts such as investments in time and resources. Consider homogeneous competitors engaging in two competitions, each with some attributes and a reward to the winner or winners in case of a tie. Competitors can make an effort at some costs to improve their competitiveness in some or all attributes to maximize their expected net gain (rewards minus effort costs). Since competitions can be correlated as they may share some attributes while having their specific attributes, improvement in one attribute will have different impacts on the winning chances in different competitions. Thus, deciding the amount of efforts to the attributes is a challenging problem. We show that competitors will adopt a mixed strategy unless the competitions are highly random and the structure of their equilibrium strategy depends on the correlation. We extend some analytical results to and propose simple heuristic strategies for multiple competitions and shed light on the impact of competition correlation on heterogeneous competitors.