Algorand is a recent, open-source public or permissionless blockchain system that employs a novel proof-of-stake Byzantine consensus protocol to efficiently scale the distributed transaction agreement problem to billions of users. Despite its promise, one relatively understudied aspect of this protocol has been the incentive compatibility of its reward sharing approach, without which cooperation among rational network users cannot be guaranteed, resulting in protocol failure. This paper is the first attempt to address this problem. By carefully modeling the participation costs and rewards received within a strategic interaction scenario in Algorand, we first show that even a small number of non-participating users (due to insufficiency of the expected incentives) can result in the network failing to append new transaction blocks. We further show that this effect, which was observed in simulations, can be formalized by means of a game-theoretic model that realistically captures the strategic interactions between users in Algorand. Specifically, we formally prove that mutual cooperation under the currently proposed reward sharing approach in Algorand is not a Nash equilibrium. To remedy this, we propose a novel reward sharing approach for Algorand and formally show that it is incentive-compatible, i.e., it can guarantee cooperation within a group of selfish users. Extensive numerical and Algorand simulation results further confirm our analytical findings. Moreover, these results show that for a given distribution of stakes in the network, our reward sharing approach can guarantee cooperation with a significantly smaller reward per round.