In the 1960s Shapley provided an example of a two-player fictitious game with periodic behaviour. In this game, player A aims to copy B's behaviour and player B aims to play one ahead of player A. In this paper we generalise Shapley's example by introducing an external parameter. We show that...

"We study a dynamic-contracting problem involving risk sharing between two parties - the Proposer and the Responder - who invest in a risky asset until an exogenous but random termination time. In any time period they must invest all their wealth in the risky asset, but they can share the...