Leader Election (LE) is crucial in distributed systems and blockchain technology, ensuring one participant acts as the leader. Traditional LE methods often depend on distributed random number generation (RNG), facing issues like vulnerability to manipulation, lack of fairness, and the need for complex procedures such as verifiable delay functions (VDFs) and publicly-verifiable secret sharing (PVSS). This Bachelor's thesis presents a novel approach to randomized LE, leveraging a game-theoretic assumption that participants, aiming to be chosen as leaders, will naturally avoid actions that diminish their chances. This perspective simplifies LE by eliminating the need for decentralized RNG. Introducing PureLottery, inspired by single-elimination sports tournaments, this method offers a fair, bias-resistant, and efficient LE solution for blockchain environments. It operates on the principle of two participants competing in each match, rendering collusion efforts useless. PureLottery stands out for its low computational and communication complexity, suitable for smart contract implementation. It provides strong game-theoretic incentives for honesty and is robust against adversaries, ensuring no increase in election chances through dishonesty. The protocol guarantees that each honest player has at least a 1/n chance of winning, irrespective of adversary manipulation among the other n-1 participants. PureLottery can also address related problems like participant ranking, electing multiple leaders, and leader aversion, showcasing its versatility across various applications, including lotteries and blockchain protocols. An open-source implementation is made available for public use.