Smart contracts are pieces of software stored on the blockchain that control the transfer of assets between parties under certain conditions. In this paper we analyze the bahaviour of smart contracts and the interaction with external actors in order to maximize objective functions. We define a core language of programs with a minimal set of smart contract primitives and we describe the whole system as a parallel composition of smart contracts and users. We therefore express the system behaviour as a first logic formula in Presburger arithmetics and study the maximum profit for each actor by solving arithmetic constraints.