Nash equilibria in shared effort games

Shared effort games model people’s contribution to projects and sharing the obtained profits. Those games generalize both public projects like writing for Wikipedia, where everybody shares the resulting benefits, and all-pay auctions such as contests and political campaigns, where only the winner obtains a profit. In θ-equal sharing (effort) games, a threshold for effort defines which contributors win and then receive their (equal) share. (For public projects θ = 0 and for all-pay auctions θ = 1.) Thresholds between 0 and 1 can model games such as paper co-authorship and shared homework assignments. We study existence and efficiency of such games, to know what will happen in a given situation and where an intervention may be needed to improve the social welfare. First, we fully characterize the conditions for the existence of a pure-strategy Nash equilibrium for two-player shared effort games with close budgets and project value functions that are linear on the received contribution and prove some efficiency results. Second, since the theory does not work for more players, fictitious play simulations are used to show when such an equilibrium exists and what its efficiency is. The results about existence and efficiency of these equilibria provide the likely strategy profiles and the socially preferred strategies to use in real life situations of contribution to public projects.